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This book provides state-of-the-art coverage for making measurements on RF and Microwave Components, both active and passive. A perfect reference for R&D and Test Engineers, with topics ranging from the best practices for basic measurements, to an in-depth analysis of errors, correction methods, and uncertainty analysis, this book provides everything you need to understand microwave measurements.
IET ELECTRICAL MEASUREMENT SERIES 12
Microwave Measurements 3rd Edition
Other volumes in this series: Volume 4 Volume 5 Volume 7 Volume 8 Volume 9 Volume 11
The current comparator W.J.M. Moore and P.N. Miljanic Principles of microwave measurements G.H. Bryant Radio frequency and microwave power measurement A.E. Fantom A handbook for EMC testing and measurement D. Morgan Microwave circuit theory and foundations of microwave metrology G. Engen Digital and analogue instrumentation: testing and measurement N. Kularatna
Microwave Measurements 3rd Edition Edited by R.J. Collier and A.D. Skinner
The Institution of Engineering and Technology
Published by The Institution of Engineering and Technology, London, United Kingdom © 1985, 1989 Peter Peregrinus Ltd © 2007 The Institution of Engineering and Technology First published 1985 (0 86341 048 0) Second edition 1989 (0 86341 184 3) Third edition 2007 (978 0 86341 735 1) This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted, in any form or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Inquiries concerning reproduction outside those terms should be sent to the publishers at the undermentioned address: The Institution of Engineering and Technology Michael Faraday House Six Hills Way, Stevenage Herts, SG1 2AY, United Kingdom www.theiet.org While the authors and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgement when making use of them. Neither the authors nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral rights of the author to be identified as author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
British Library Cataloguing in Publication Data Microwave measurements. – 3rd ed. 1. Microwave measurements I. Collier, Richard II. Skinner, Douglas III. Institution of Engineering and Technology 621.3’813 ISBN 978-0-86341-735-1
Typeset in India by Newgen Imaging Systems (P) Ltd, Chennai Printed in the UK by Athenaeum Press Ltd, Gateshead, Tyne & Wear
Contents
List of contributors Preface 1
Transmission lines – basic principles R. J. Collier
1
1.1 1.2
1
1.3
1.4
2
xvii xix
Introduction Lossless two-conductor transmission lines – equivalent circuit and velocity of propagation 1.2.1 Characteristic impedance 1.2.2 Reflection coefficient 1.2.3 Phase velocity and phase constant for sinusoidal waves 1.2.4 Power flow for sinusoidal waves 1.2.5 Standing waves resulting from sinusoidal waves Two-conductor transmission lines with losses – equivalent circuit and low-loss approximation 1.3.1 Pulses on transmission lines with losses 1.3.2 Sinusoidal waves on transmission lines with losses Lossless waveguides 1.4.1 Plane (or transverse) electromagnetic waves 1.4.2 Rectangular metallic waveguides 1.4.3 The cut-off condition 1.4.4 The phase velocity 1.4.5 The wave impedance 1.4.6 The group velocity 1.4.7 General solution Further reading
1 4 5 5 6 7 8 9 10 10 10 12 14 15 15 16 16 17
Scattering parameters and circuit analysis P. R. Young
19
2.1 2.2
19 19
Introduction One-port devices
vi
Contents 2.3 2.4 2.5 2.6 2.7 2.8
2.9
3
4
Generalised scattering parameters Impedance and admittance parameters 2.4.1 Examples of S-parameter matrices Cascade parameters Renormalisation of S-parameters De-embedding of S-parameters Characteristic impedance 2.8.1 Characteristic impedance in real transmission lines 2.8.2 Characteristic impedance in non-TEM waveguides 2.8.3 Measurement of Z0 Signal flow graphs Appendices 2.A Reciprocity 2.B Losslessness 2.C Two-port transforms References Further reading
22 24 27 27 28 29 30 30 33 35 36 37 37 39 40 41 41
Uncertainty and confidence in measurements John Hurll
43
3.1 3.2
43 52 52 54 54 54
Introduction Sources of uncertainty in RF and microwave measurements 3.2.1 RF mismatch errors and uncertainty 3.2.2 Directivity 3.2.3 Test port match 3.2.4 RF connector repeatability 3.2.5 Example – calibration of a coaxial power sensor at a frequency of 18 GHz References
54 56
Using coaxial connectors in measurement Doug Skinner
59
4.1
59 60 61 61 61 62 62 62 63 64 64 65
4.2
4.3 4.4 4.5
4.6
Introduction 4.1.1 Coaxial line sizes Connector repeatability 4.2.1 Handling of airlines 4.2.2 Assessment of connector repeatability Coaxial connector specifications Interface dimensions and gauging 4.4.1 Gauging connectors Connector cleaning 4.5.1 Cleaning procedure 4.5.2 Cleaning connectors on static sensitive devices Connector life
Contents 4.7 4.8 4.9 4.A 4.B 4.C 4.D 4.E
5
Adaptors Connector recession Conclusions Appendix A Appendix B Appendix C Appendix D Appendix E Further reading
65 65 66 66 66 85 86 87 88
Attenuation measurement Alan Coster
91
5.1 5.2 5.3
5.4
5.5
6
vii
Introduction Basic principles Measurement systems 5.3.1 Power ratio method 5.3.2 Voltage ratio method 5.3.3 The inductive voltage divider 5.3.4 AF substitution method 5.3.5 IF substitution method 5.3.6 RF substitution method 5.3.7 The automatic network analyser Important considerations when making attenuation measurements 5.4.1 Mismatch uncertainty 5.4.2 RF leakage 5.4.3 Detector linearity 5.4.4 Detector linearity measurement uncertainty budget 5.4.5 System resolution 5.4.6 System noise 5.4.7 Stability and drift 5.4.8 Repeatability 5.4.9 Calibration standard A worked example of a 30 dB attenuation measurement 5.5.1 Contributions to measurement uncertainty References Further reading
91 91 93 94 97 98 104 105 107 108 110 110 112 112 114 115 115 115 115 116 116 117 119 120
RF voltage measurement Paul C. A. Roberts
121
6.1 6.2
121 122 122 124
Introduction RF voltage measuring instruments 6.2.1 Wideband AC voltmeters 6.2.2 Fast sampling and digitising DMMs
viii
Contents
6.3 6.4
7
8
6.2.3 RF millivoltmeters 6.2.4 Sampling RF voltmeters 6.2.5 Oscilloscopes 6.2.6 Switched input impedance oscilloscopes 6.2.7 Instrument input impedance effects 6.2.8 Source loading and bandwidth AC and RF/microwave traceability 6.3.1 Thermal converters and micropotentiometers Impedance matching and mismatch errors 6.4.1 Uncertainty analysis considerations 6.4.2 Example: Oscilloscope bandwidth test 6.4.3 Harmonic content errors 6.4.4 Example: Oscilloscope calibrator calibration 6.4.5 RF millivoltmeter calibration Further reading
125 126 127 129 130 132 133 133 135 136 137 137 138 140 143
Structures and properties of transmission lines R. J. Collier
147
7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9
147 148 150 150 151 152 153 154 154 155 156
Introduction Coaxial lines Rectangular waveguides Ridged waveguide Microstrip Slot guide Coplanar waveguide Finline Dielectric waveguide References Further reading
Noise measurements David Adamson
157
8.1 8.2
157 158 158 159 159 160 162 162 163 163 163
8.3 8.4
Introduction Types of noise 8.2.1 Thermal noise 8.2.2 Shot noise 8.2.3 Flicker noise Definitions Types of noise source 8.4.1 Thermal noise sources 8.4.2 The temperature-limited diode 8.4.3 Gas discharge tubes 8.4.4 Avalanche diode noise sources
Contents 8.5
8.6
8.7 8.8
8.9
9
164 164 166 166 169 169 171 172 174 175 175 176 176 176
Connectors, air lines and RF impedance N. M. Ridler
179
9.1 9.2
179 180 180 181 181 182 182 185 187 188 189 190 192 193 194 198 200 201 203
9.3
9.4
9.5
9.6
10
Measuring noise 8.5.1 The total power radiometer 8.5.2 Radiometer sensitivity Measurement accuracy 8.6.1 Cascaded receivers 8.6.2 Noise from passive two-ports Mismatch effects 8.7.1 Measurement of receivers and amplifiers Automated noise measurements 8.8.1 Noise figure meters or analysers 8.8.2 On-wafer measurements Conclusion Acknowledgements References
ix
Introduction Historical perspective 9.2.1 Coaxial connectors 9.2.2 Coaxial air lines 9.2.3 RF impedance Connectors 9.3.1 Types of coaxial connector 9.3.2 Mechanical characteristics 9.3.3 Electrical characteristics Air lines 9.4.1 Types of precision air line 9.4.2 Air line standards 9.4.3 Conductor imperfections RF impedance 9.5.1 Air lines 9.5.2 Terminations Future developments Appendix: 7/16 connectors References
Microwave network analysers Roger D. Pollard
207
10.1 10.2
207 208 208 214 216
10.3
Introduction Reference plane 10.2.1 Elements of a microwave network analyser Network analyser block diagram Further reading
x 11
Contents RFIC and MMIC measurement techniques Stepan Lucyszyn
217
11.1 11.2
217 218 220 229 230 230 231 236 240 240 241 243 243 246 246 247 249 249 250 251 254 255
11.3
11.4
11.5
11.6
12
Introduction Test fixture measurements 11.2.1 Two-tier calibration 11.2.2 One-tier calibration 11.2.3 Test fixture design considerations Probe station measurements 11.3.1 Passive microwave probe design 11.3.2 Probe calibration 11.3.3 Measurement errors 11.3.4 DC biasing 11.3.5 MMIC layout considerations 11.3.6 Low-cost multiple DC biasing technique 11.3.7 Upper-millimetre-wave measurements Thermal and cryogenic measurements 11.4.1 Thermal measurements 11.4.2 Cryogenic measurements Experimental field probing techniques 11.5.1 Electromagnetic-field probing 11.5.2 Magnetic-field probing 11.5.3 Electric-field probing Summary References
Calibration of automatic network analysers Ian Instone
263
12.1 12.2 12.3 12.4 12.5
263 263 263 266 267 267 267
12.6 12.7 12.8
Introduction Definition of calibration Scalar network analysers Vector network analyser Calibration of a scalar network analyser 12.5.1 Transmission measurements 12.5.2 Reflection measurements Problems associated with scalar network analyser measurements Calibration of a vector network analyser Accuracy enhancement 12.8.1 What causes measurement errors? 12.8.2 Directivity 12.8.3 Source match 12.8.4 Load match 12.8.5 Isolation (crosstalk) 12.8.6 Frequency response (tracking)
269 269 270 270 270 271 272 273 273
Contents 12.9 12.10 12.11 12.12
12.13
13
273 273 276 279 284 284 286 287 289 289
Verification of automatic network analysers Ian Instone
291
13.1 13.2 13.3
291 291 292 292 292 293 293 293 296 299 299 299 300 301 301 302 304
13.4 13.5
13.6
14
Characterising microwave systematic errors 12.9.1 One-port error model One-port device measurement Two-port error model TRL calibration 12.12.1 TRL terminology 12.12.2 True TRL/LRL 12.12.3 The TRL calibration procedure) but to use a less precise name (i.e. 14 mm).
Table 9.3
Electrical discontinuities caused by joining mechanically compatible connectors
Connector pair
Centre conductor pin diameter for both connectors (mm)
Equivalent discontinuity capacitance (fF)
Maximum linear reflection coefficient magnitude
3.5 mm and K connector 2.4 mm and V connector
0.927 0.511
8 10
0.04 (at 33 GHz) 0.08 (at 50 GHz)
line and can be represented electrically as a single shunt capacitance at the reference plane of the connector pair [32]. This discontinuity capacitance produces a reflection at the connector interface that varies with frequency. This effect has been investigated in [33], and typical maximum values for this reflection are given in Table 9.3. In addition to the mechanical compatibility of the above precision connectors, the 3.5 mm and K connectors are also mechanically compatible with the SMA connector. In this case, the presence of a solid dielectric (e.g. Teflon) at the reference plane of the SMA connector causes an additional discontinuity capacitance (this time due to the dielectric) leading to even larger electrical reflections than those produced from a 3.5 mm to K-connection. However, as mentioned previously, the WSMA precision 3.5 mm connector was designed specifically to produce high-performance mating with SMA connectors [31]. This is achieved by deliberately setting back the position
Connectors, air lines and RF impedance 187 of the centre conductor pin by a prescribed amount, and hence introducing an amount of inductance to compensate for the additional capacitance caused by the SMA’s dielectric [34].
9.3.3 Electrical characteristics Two very important electrical characteristics of a coaxial connector are the nominal characteristic impedance and the maximum recommended operating frequency to ensure a stable, and repeatable, measurement. The characteristic impedance of coaxial air lines is discussed in detail in Section 9.4 of this chapter. This discussion is also applicable to the precision coaxial connectors used with these air lines. The maximum recommended operating frequency for a coaxial line is usually chosen so that only a single electromagnetic mode of propagation is likely to be present in the coaxial line at a given frequency. This is the dominant transverse electromagnetic (or TEM) mode and operates exclusively from DC to the maximum recommended operating frequency. Above this frequency, other higher-order modes7 can also propagate to some extent. The maximum recommended operating frequency is often called the ‘cut-off frequency’ as it corresponds to the lower frequency cut-off for these higher-order waveguide modes. The first higher-order mode in 50 0001 coaxial line is the TE11 mode (also known as the H11 mode in some references). The cut-off frequency is given by [35] c fc = √ (9.1) λ c µ r εr It has been shown in [36] that the approximate cut-off wavelength for the TE11 mode is given by λc ≈ π(a + b)
(9.2)
which corresponds to the average circumference of the line’s conductors. More precise expressions for the cut-off wavelength can be obtained from [37] and these produce the theoretical upper frequency limits (i.e. the cut-off frequencies) for each line size shown in Table 9.4. Table 9.4 also gives recommended usable upper frequency limits for each line size. These are lower than the theoretical upper frequency limits and this is due to potential higher-order mode resonances (again, the TE11 mode being the most likely) caused by solid material dielectric (e.g. Teflon) being present between the two conductors of the coaxial line. These resonances are most problematic when they occur in the vicinity of the transitions from air to solid dielectric, such as when a dielectric bead is 7 These modes are often called ‘waveguide modes’ since they are similar to the modes found in hollow waveguide. These modes are either transverse electric (TE) or transverse magnetic (TM) and have a longitudinal component to their propagation. It should be noted that the TEM mode can continue to propagate at frequencies where TE and TM modes are also possible, since the TEM mode does not actually have an upper frequency limit.
188 Microwave measurements Table 9.4
Theoretical and recommended upper frequency limits for coaxial connectors
Connector name
Theoretical upper frequency limit (GHz)
Recommended usable upper frequency limit (GHz)
14 mm (e.g. GR900) 7 mm (e.g. APC-7) Type N 3.5 mm 2.92 mm (K connector) 2.4 mm 1.85 mm (V connector) 1 mm
9.5 19.4 19.4 38.8 46.5 56.5 73.3 135.7
8.5 18.0 18.0 33.0 40.0 50.0 65.0 110.0
used to support the centre conductor of the coaxial line (as in GPCs). Such resonances can occur in single connector beads as well as in a mated connector pair containing two dielectric beads. These higher-order mode resonances can cause significant electromagnetic changes in both the reflection and transmission properties of the coaxial line. (In general, these changes cause the reflection coefficient of the line to increase whereas the transmission coefficient decreases.) These resonances are highly unpredictable and can be initiated by subtle asymmetries, eccentricities or other irregularities that may be present in the line – as can be the case at connector interfaces. For example, if dielectric beads form part of the connector interface (as in GPCs), these electromagnetic changes can vary according to the orientation of the connectors each time a connection is made. Under these conditions, even pristine precision connectors can exhibit very poor repeatability of connection. The presence of bead resonances in precision coaxial connectors has been investigated in [38], while [39] presents some methods proposed to reduce the likelihood of excitation of these modes (e.g. through connector bead design). In any case, care should be taken when performing measurements near the upper frequency limits of coaxial connectors – even the recommended usable upper frequency limits, given in Table 9.4. Acute changes in the reflection and transmission coefficients (or a lack of repeatability of these coefficients) may indicate the presence of a higher-order mode resonance.
9.4
Air lines
Precision air-dielectric coaxial transmission lines (or, air lines, for short) can be used as reference devices, or standards, for impedance measurements at RF and microwave frequencies. (The term impedance is used here to imply a wide range of
Connectors, air lines and RF impedance 189 electrical quantities, such as S-parameters, impedance and admittance parameters, VSWR, and return loss.) This includes the use of air lines as calibration and verification standards for measuring instruments such as vector network analysers (VNAs) [40]. For example, VNA calibration schemes, such as Thru-Reflect-Line (TRL) [41] and Line-Reflect-Line (LRL) [42], use air lines as standards to achieve very high accuracy impedance measurement capabilities. This is the method currently used to realise the UK primary national standard for impedance quantities [43] at RF and microwave frequencies (typically, from 45 MHz and above). Similarly, verification schemes determining the residual systematic errors in a calibrated VNA [44] use air lines as the reference devices, and these methods are currently endorsed by organisations involved in the accreditation of measurement, such as the European co-operation for Accreditation (EA) [45]. This section describes the different types of air line that are available and reviews their use as standards of characteristic impedance and/or phase change. Consideration is also given for the effects caused by imperfections in the conductors used to realise these air lines.
9.4.1 Types of precision air line There are basically three types of air line depending on the number of dielectric beads used to support the centre conductor of the line. These beads are usually to aid in the connection of the line during measurement. 9.4.1.1 Unsupported air lines These lines do not contain any support beads and therefore the connector interfaces conform to the LPC category. The ends of the centre conductor are usually fitted with spring-loaded contacting tips to facilitate connecting the line to other connectors. The line’s centre conductor is held in place by the test ports of a measuring instrument (or whatever else is being connected to the line). The centre and outer conductors of these lines come in two separate parts and are assembled during connection. These lines (which are of a calculable geometry) are used where the very highest levels of accuracy are required. Therefore, such lines are often found in VNA calibration kits used to realise TRL and LRL calibration schemes. 9.4.1.2 Partially supported air lines These lines contain a support bead at only one end of the line. This design is often used for relatively long lengths of line that may be difficult to connect if they were not supported in some way. The unsupported end of the line is usually connected first – this being the more difficult of the two connections – followed by the supported end (which connects like a conventional connector). Such a line therefore has connections that are LPC at one end and GPC at the other. The centre and outer conductors of these lines often come as two separate components, although fully assembled versions also exist where the centre conductor is held in place by the bead in the air line’s GPC. Semi-supported lines are often found in VNA verification kits where a calculable geometry is not required (although a high-electrical performance is still necessary).
190 Microwave measurements These lines can also be used in applications where minor reflections from one end of the line do not cause problems (e.g. some applications of the ‘ripple’ technique [44]). 9.4.1.3 Fully supported air lines These lines contain support beads at both ends of the line. This is equivalent to GPCs being present at both ends of the line thus making it relatively easy to connect. These lines come fully assembled with the centre conductor being held in place by both beads in the air line’s GPCs. Such lines find application where only relatively modest levels of accuracy are required or where only a part of the length of a line needs to be of a known, or calculable, impedance (e.g. when calibrating time-domain reflectometers). In such applications, the minor reflections and discontinuities caused by the presence of the beads will be inconsequential.
9.4.2 Air line standards In the above applications, the air lines are used as references of either characteristic impedance or phase change, or both. These two applications are discussed in the following subsections. 9.4.2.1 Characteristic impedance In general, the characteristic impedance of a particular electromagnetic mode supported by a coaxial line is a complex function of the dimensions and alignment of the conductors, the physical properties of the materials of the line, and the presence of discontinuities such as connectors. However, for a uniform line with lossless conductors and air between the centre and outer conductors, the characteristic impedance of the TEM mode can be approximated by 1 Z0 = 2π
0001
µ loge ε
0002 0003 0002 0003 b b ≈ 59.93904 × loge a a
(9.3)
From the above expression, it is clear that the characteristic impedance of a line can be found from measurements of the diameters of the line’s conductors. Such measurements are often made using air gauging techniques [46] that enable measurements to be made continuously along the entire lengths, and at all possible orientations, of both conductors. This is a very useful technique since the determination of an air line’s characteristic impedance can be made with direct traceability to the SI base unit of length (i.e. the metre). Similarly, it is also clear that, from the above expression, values of characteristic impedance can be established by using different diameters for a line’s conductors. This is evident from the diameter values presented in Table 9.2 that show a range of diameter values for coaxial air lines each with a nominal characteristic impedance of 50 0001. Similarly, Table 9.5 gives diameter values that achieve a nominal characteristic impedance of 75 0001 for the 14 and 7 mm line sizes, mentioned previously. These
Connectors, air lines and RF impedance 191 Table 9.5
Line diameters for 75 0001 line sizes
Connector name
Line size, i.e. the internal diameter of the outer conductor (mm)
Centre conductor diameter (mm)
GR900 Type N
14.2875 7.000
4.088 2.003
diameters are used to realise 75 0001 versions of the GR900 and Type N connectors, respectively8 . Having established that a wide range of characteristic impedance values can be achieved simply by choosing different diameters for the centre and outer conductors, this raises the question ‘Why is 50 0001 a preferred value for the characteristic impedance of coaxial lines?’ The answer appears to be that it was chosen as a compromise in performance between the theoretical characteristic impedance needed to obtain minimum attenuation in a line (which occurs at nominally 77.5 00019 ) and the theoretical characteristic impedance needed to obtain the maximum power transfer along a line (which occurs nominally at 30 0001). The average of these two values is 53.75 0001, which rounds to 50 0001 (to one significant figure). Hence, 50 0001 is a good compromise value for the characteristic impedance of lines used in many and diverse applications. 9.4.2.2 Phase change Air lines can also be used as standards of phase change since a lossless line will only introduce a phase change to a signal, which relates directly to the line’s length. The phase change is given by √ εr ϕ = 2π f l (radians) c or √ εr ϕ = 360 f l (degrees) c Air lines have been used successfully as phase change standards to calibrate reflectometers and VNAs at the very highest levels of accuracy (e.g. see [47,48]). These techniques use the lines in conjunction with high reflecting terminations (such as short-circuits and open-circuits) to produce a known phase change at the instrument 8 Caution! Great care should be taken when performing measurements where both 75 and 50 0001 versions of the same connector type are available. For the Type N connector, damage will occur to a 75 0001 female connector if an attempt is made to mate it with a 50 0001 male connector. This is due to the substantial difference in diameters of the male pin and the female socket. (Note that the same situation occurs with 50 and 75 0001 versions of BNC connectors!). 9 This may also explain why 75 0001 is also often used in some applications (such as in certain areas of the communications industry).
192 Microwave measurements test port. In recent years, the use of such techniques is beginning to re-emerge in applications where it is not practical to use unsupported air lines primarily as standards of characteristic impedance (e.g. in calibration schemes such as TRL and LRL). For example, a kit currently available for VNA calibrations in the 1 mm coaxial line size [10] uses short-circuits offset by different lengths of line to achieve calibrations from around 50 to 110 GHz. An important consideration when using air lines in conjunction with high reflecting terminations (e.g. as offset short-circuits) is that the effective electrical length of the offset line is actually double the mechanical length. This is because the electrical signal has to make a ‘there-and-back’ journey along the length of the line having been reflected back from the termination at the end of the line.
9.4.3 Conductor imperfections In the above discussion concerning using air lines as standards of characteristic impedance and phase change, it has been assumed that the line’s conductors are made up of lossless material (i.e. the conductors are perfectly conducting or, in other words, possess infinite conductivity). However, in practice, conductors are not perfectly conducting and therefore possess finite conductivity (or loss). This causes problems for the electrical properties of lines especially at low frequencies when the conductivity at the surface of the conductors becomes important. Manufacturers attempt to minimise these problems by producing lines made up of high-conductivity materials (such as alloys of copper) or by applying a plated layer of high-conductivity material (such as silver) to the surface of the conductors in the coaxial line. Even so, as frequency decreases, the finite conductivity of a line causes the propagating wave to penetrate the walls of the conductors to some extent. The attenuation constant associated with the wave propagating into the walls of the conductors10 is considerably higher than for the wave propagating in the dielectric between the conductors, and therefore the wave attenuates rapidly as it penetrates the walls of the conductors. The reciprocal of this attenuation constant is called the skin depth and is defined as the distance travelled into the walls of the conductors by the wave before being attenuated by one neper (≈8.686 dB). The skin depth is given by 0004 1 (9.4) δs = πf σ µ This indicates that skin depth increases as the frequency decreases. The skin depth will also be larger for a line with a lower value of conductivity. To illustrate this, values for skin depth are given in Table 9.6, for conductors made up of silver, brass and beryllium copper (BeCu), with assumed conductivities of 62, 16 and 13 MS m−1 , respectively, as these are materials often used to fabricate precision air lines. Further detailed discussions on skin depth effects can be found in [49]. 10 The wave decays exponentially as it penetrates the walls of the conductors.
Connectors, air lines and RF impedance 193 Table 9.6
Skin depth values as a function of frequency
Frequency (MHz)
1 10 100 1000
Skin depth (µm) Silver (σ = 62 MS m−1 )
Brass (σ = 16 MS m−1 )
BeCu (σ = 13 MS m−1 )
64 20 6 2
126 40 13 4
140 44 14 4
It is generally only necessary to accurately determine the conductivity of a line’s conductors at RF (typically, between 1 MHz and 1 GHz) in order to determine the line’s characteristics. This is because lines are rarely used as impedance standards below these frequencies and skin depth becomes less of a problem at higher frequencies. This requirement, however, is not trivial. If the line’s constitution is known then a value may be obtained from tables of physical data (e.g. from sources such as [50]). However values specified in tables usually refer to bulk material samples. These values are often different from actual values for the same material after it has been subject to manufacturing processes, as is the case for air lines (e.g. see [51,52]). An additional problem in determining a value for the conductivity of a line is caused by plating layers that may be applied by manufacturers either to increase conductivity (e.g. silver plating) or increase longevity (e.g. gold ‘flashing’). Several studies have been carried out evaluating effects of plating on the effective conductivity of conductors [53–55] but these assume prior knowledge of the material of each layer and ignore additional complications caused by impurities which will doubtlessly be present. A recent validation of theoretical predictions based on assumed conductivity values has been performed by comparison with precision attenuation measurements [56]. Finally, another consideration concerning the characteristics of a line relates to the non-uniformity of the conductor’s surfaces caused either by changes in the longitudinal dimensions of the line [57,58] or surface roughness [59]. In both cases, these effects will cause the properties of the line to depart significantly from ideal values.
9.5
RF impedance
The measurement of impedance, and impedance-related quantities, requires special consideration when the measurement frequency is in the RF region (i.e. from 1 MHz to 1 GHz). This is generally due to techniques used at the higher frequencies becoming inappropriate at these longer wavelengths. Similarly, low-frequency techniques, used
194 Microwave measurements
R
L
G
Figure 9.3
C
Distributed circuit model for a section of coaxial line
below 1 MHz, are also unsuitable – for example, because the connector configurations are often different (e.g. four-terminal pair connections). Information concerning use of air lines and terminations (i.e. one-port devices) as impedance standards at RF is given below – for example, to calibrate a VNA. More detailed information can be found in [60].
9.5.1 Air lines Air lines can be used in conjunction with terminations as calibration items for reflectometers (or VNA one-port calibrations). In this configuration, one end of the air line is connected to the instrument test port while the other end is connected to the termination. Lines can also be used for VNA two-port calibrations (such as TRL and LRL, where they act as the Line standard) and are connected between the two test ports during calibration. In either application, the accuracy achieved using modern VNAs requires that the electrical characteristics of the air lines are defined very precisely, as shown in Figure 9.3. A coaxial line can be characterised using the distributed circuit model given in Figure 9.3, where R, L, G and C are the series resistance and inductance, and the shunt conductance and capacitance, respectively, per unit length of line. Expressions for the four line elements R, L, G and C can be used to obtain further expressions for two fundamental line parameters – the characteristic impedance and the propagation constant – which are defined as follows: 0004 (R + jωL) (9.5) Z= (G + jωC) 0005 γ = α + jβ = (R + jωL)(G + jωC) (9.6) 9.5.1.1 Lossless lines For a lossless line (i.e. with conductors of infinite conductivity) both the series resistance and the shunt conductance are zero. The series inductance and the shunt
Connectors, air lines and RF impedance 195 capacitance have fixed values independent of frequency and are given by 0006 µ loge (b a) L0 = 2π 2πε 0006 C0 = loge (b a)
(9.7) (9.8)
The characteristic impedance of the lossless line is therefore (as before) 0004 Z0 =
L0 1 = C0 2π
0001
µ loge ε
0002 0003 b a
(9.9)
This shows that the line’s characteristic impedance is a purely real quantity (i.e. containing no imaginary component), is independent of frequency and determined by the ratio (b/a). For example, to achieve a characteristic impedance of 50 0001 this ratio is approximately 2.3. The propagation constant of the lossless line is 0005 ω 2π √ (rad m−1 ) γ0 = jβ = jω L0 C0 = jω µε = j = j v λ
(9.10)
This shows that the line’s propagation constant is purely imaginary (i.e. containing no real component) and is determined only by the wavelength (or equivalent) of the propagating wave. The attenuation constant is zero which is consistent with a line having no loss. The phase constant is a linear function of frequency, indicating a non-dispersive line. 9.5.1.2 Lossy lines As mentioned previously, metallic air-filled coaxial lines are not lossless. An important part of line characterisation at RF is a determination of the effects due to line loss. An attempt at dealing with this problem for RF impedance standardisation has been given in [61]. Further work has since been presented in [62], giving expressions for all four line elements – R, L, C and G – containing frequency-dependent terms for each element. Additional work has also solved this problem for frequencies below the RF region, obtaining exact field equations for lossy coaxial lines [63]. The expressions derived in [62] for the four line elements at RF are as follows: 0002
0003 k 2 a2 F 0 R = 2ωL0 d0 1 − 2 0007 0002 0003 k 2 a 2 F0 L = L0 1 + 2d0 1 − 2 G = ωC0 d0 k 2 a2 F0 2 2
C = C0 (1 + d0 k a F0 )
(9.11) (9.12) (9.13) (9.14)
196 Microwave measurements
Z change from 50 Ω(mΩ)
3000 2500 2000 1500 1000 500 0 1
10
100
1000
Frequency (MHz)
Figure 9.4
Change in characteristic impedance magnitude for a 7 mm BeCu line 0
Z phase (mDegrees)
−500 −1000 −1500 −2000
−2500
1
10
100
1000
Frequency (MHz)
Figure 9.5 where
Characteristic impedance phase angle for a 7 mm BeCu line
F0 =
0007 (b2 /a2 ) − 1 (b/a) loge (b/a) 1 b − − +1 2 loge (b/a) (b/a) + 1 2 a
(9.15)
d0 =
δs (1 + (b/a)) 4b loge (b/a)
(9.16)
These expressions can be used to calculate the characteristic impedance, which, for a line with finite conductivity, is clearly a complex quantity, material dependent and a function of frequency. Figures 9.4 and 9.5 illustrate the effect on the characteristic impedance of a nominal 50 0001 7 mm air line made up of BeCu with an assumed conductivity of 13 MS m−1 . The deviation in the characteristic impedance causes a problem for impedance measurements (such as S-parameters) since they are usually specified with respect to the lossless line value (e.g. 50 0001). Measurements made on instruments calibrated with lines of different material will vary systematically since the impedance parameters will be measured with respect to different characteristic impedances. This problem is
Connectors, air lines and RF impedance 197
Attenuation constant (dB/m)
0.25 0.20 0.15 0.10 0.05 0.00 1
10
100
1000
Frequency (MHz)
Figure 9.6
Attenuation constant for a 7 mm BeCu line
Phase constant change(Deg/m)
1.6
1.2
0.8
0.4
0.0 1
10
100
1000
Frequency (MHz)
Figure 9.7
Change in phase constant for a 7 mm BeCu line
overcome by transforming from the actual line characteristic impedance to the defined lossless value (e.g. 50 0001 for the 50 0001 line size). Further information on impedance transformations of this type is given in [64]. The above expressions can also be used to calculate the propagation constant, which, for a line with finite conductivity has both real and imaginary parts and is non-linear with frequency. Figures 9.6 and 9.7 illustrate the effect on the propagation constant for a nominal 50 0001 7 mm air line made up of BeCu. The attenuation constant is non-zero (Figure 9.6), which is consistent with a line containing loss. The increase in the phase constant from its lossless value indicates that the line’s electrical length is longer than its physical length – this discrepancy varying as a function of frequency. The line is therefore dispersive and imparts group delay to broadband signals. A comparison of parameters characterising lossless and lossy lines reveals that only one extra term is included to allow for the loss effects, that is, the conductor’s conductivity. If the conductivity is assumed to be infinite, the skin depth becomes zero and the term d0 in the expressions for the four lossy line elements vanishes. This
198 Microwave measurements causes R and G to become zero and L and C to revert to their lossless values (i.e. L0 and C0 ). The finite conductivity (and hence non-zero skin depth) of the conductors is therefore solely responsible for departures from the lossless line conditions. The √ expression given earlier for skin depth also contains a 1/ f term indicating that skin depth increases as frequency decreases, causing a subsequent increase in the values for all four line elements.
9.5.2 Terminations It is often very convenient to use terminations (i.e. one-port devices) as calibration standards for reflectometers and VNAs. These terminations can be used in both one-port and two-port VNA calibration schemes. The terminations can be connected directly to the instrument test port or separated by a length of air line called an ‘offset’. The air line section can be an integral part of the item or connected separately. The three most common terminations used for this purpose are shortcircuits, open-circuits and near-matched terminations (including so-called sliding loads). Mismatched terminations (and capacitors) can also be used, particularly at lower frequencies. 9.5.2.1 Short-circuits A coaxial line short-circuit is simply a flat metallic disc connected normally to the line’s centre and outer conductors. Its radius must exceed the internal radius of the outer conductor and be of sufficient thickness to form an effective shield for the electromagnetic wave propagating in the line. The disc is usually made up of a similar material as the line’s conductors. Short-circuits can be connected directly to an instrument test port or via a length of line producing an offset short-circuit. Short-circuits provide a good approximation to the lossless condition at RF (i.e. with both series resistance and inductive reactance being close to zero). This produces a reflection coefficient with real and imaginary parts of −1 and 0, respectively. Loss due to skin depth and surface finish of the disc can be considered for high-precision metrology applications. Such losses have been considered in [65] by analysing the effects of a TEM wave incident normally to a conducting plane. 9.5.2.2 Open-circuits In principle, a coaxial open-circuit is produced by having nothing connected to the instrument test port. However, this produces a poorly defined standard for two reasons: (1) it will radiate energy producing a reflected signal dependent on obstacles in the vicinity of the test port and (2) the test port connector’s mating mechanism affects the established measurement reference plane which limits accurate characterisation as a standard. The first of these problems can be overcome by extending the line’s outer conductor sufficiently beyond the position of the open-circuited centre conductor so that the evanescent radiating field decays to zero within the outer conductor shield – the extended outer conductor acting as an effectively infinite length of circular waveguide below cut-off.
Connectors, air lines and RF impedance 199 The second problem can be overcome either by depressing the mating mechanism using a dielectric plug or attaching a length of line to the centre conductor, terminated in an abrupt truncation. The dielectric plug technique is used as a standard with numerous VNA calibration kits. The abruptly truncated line technique has been used to realise primary national impedance standards [47,66]. In both cases, the opencircuit behaves as a frequency-dependent ‘fringing’ capacitance. Calculations for the capacitance of an abruptly truncated coaxial line can be found in the literature (i.e. [67–69]). These values have been verified for RF impedance applications using a computer-intensive equivalent circuit technique [70]. Coaxial open-circuits have a reflection coefficient of nominally unity magnitude and a phase angle dependent on the fringing capacitance and the length of any line used to fabricate the device. They can therefore be very useful as standards for calibrating reflectometers and VNAs. 9.5.2.3 Near-matched terminations A low-reflection (or near-matched) termination can be produced by mounting a cylindrical thin-film resistive load in the centre conductor of a line with a tractorially shaped outer conductor. A parabolic transition between the conventional coaxial line and the tractorial section transforms incident plane wave fronts to spherical wave fronts required to propagate in the tractorial section of the termination. This produces near-uniform power dissipation along the length of the resistive load element with minimal frequency dependence. This design of low reflecting termination has been discussed in [71]. Low-reflection terminations are usually assumed to have zero reflection during a reflectometer, or VNA, calibration (and are therefore often called ‘matched’ loads). Alternatively, low reflecting load elements can be used to ‘synthesise’ the performance of a matched termination, using sliding load techniques. This is achieved by measuring the response of a load element at several positions along a variable length of precision air line. The characteristics of a ‘perfectly’ matched termination can then be computed by fitting a circle to the measured reflection values (the centre of the fitted circle being the point in the complex reflection coefficient plane corresponding to a perfect match, i.e. zero reflection). However, problems due to imperfections in the air line section and inadequate phase differences produced by realisable lengths of air line make this technique of limited use at RF. 9.5.2.4 Mismatched terminations In principle, mismatched terminations (and capacitors) can be very useful devices for providing values of reflection that are significantly different from those achieved using short-circuit, open-circuit and near-matched terminations. Such reflection values could be used in certain calibration applications (e.g. as alternatives to the shortopen-load values used during conventional VNA calibration schemes). However, devices used for calibration (i.e. standards) are usually assumed to have ‘known’
200 Microwave measurements values based on either a calculated and/or measured performance11 . In general, it is not possible to calculate, to any degree of accuracy, the performance of a mismatched termination. Indeed, the same can be said of near-matched terminations where an assumed value (i.e. zero) is often used for calibration purposes. There have been several attempts recently at characterising near-matched terminations using measurement data at DC and RF. Some work in the 1990s [72] used equivalent circuit models for characterising these devices at lower RF (300 kHz to 30 MHz) based on measurement data at higher RF. More recent work [73,74] has concentrated on implementing interpolation schemes for characterising these devices. The interpolation schemes have the advantage that very few assumptions need to be made concerning the characteristics of the device. In principle, such schemes can be extended to characterise ‘any’ device (e.g. mismatch terminations) without requiring detailed knowledge concerning the physical (i.e. calculable) properties of the device. This is leading to the development of generalised techniques for VNA calibrations [75] that do not need to rely on the classical assumptions implicit in the short-open-load calibration schemes. Such techniques are expected to greatly enhance our knowledge of calibration devices and instruments used traditionally to perform RF impedance measurements.
9.6
Future developments
Coaxial connectors and coaxial transmission lines continue to play a crucial role in the realisation of the majority of measurements made at radio and microwave frequencies. This chapter has presented some of the important issues relating to the various types of coaxial connector currently available for making high-precision measurements. Even so, the connector itself can still be the limiting factor for the accuracy achieved by today’s measurement systems. Similarly, coaxial air lines provide very useful standard reference artefacts for realising impedance quantities for these connector types and the associated transmission lines. These devices are simple structures with well-defined electromagnetic properties. But once again, the precision at which today’s instruments can operate means that these standards will need to be defined to an even greater level of precision. This is particularly true at lower RF (and, indeed, at extremely high frequencies) where the line’s characteristics depart substantially from their idealised values. It is unlikely that future requirements for these technologies will be less demanding than they are at present. Indeed, it can be expected that most measurement applications will require broader bandwidths, improved electrical capabilities (including repeatability, insertion loss and lower passive inter-modulation) and higher levels of accuracy. These demands are likely to continue to drive developments in precision coaxial connectors, air lines and other impedance standards for the foreseeable future. 11 For example, the characteristics of unsupported air lines can be calculated based on the measured values of the diameters of the line’s conductors.
Connectors, air lines and RF impedance 201
Appendix: 7/16 connectors The 7/16 connector was developed during the 1960s primarily for high-performance military applications. In recent years, it has become a popular choice for certain applications in the mobile communications industry, such as in base stations and antenna feed lines. This is due to its suitability for uses involving high power levels, low receiver noise levels and where there are requirements for low passive intermodulation (PIM). The 7/16 connector is a sexed connector with a nominal characteristic impedance of 50 0001. It is available in both GPC and LPC versions – LPCs are found on 7/16 unsupported air lines used in VNA calibration kits to realise calibration schemes such as TRL and LRL. Terminations are also available which can be used for Short-OpenLoad calibration schemes. The nominal diameters of the centre and outer conductors are 7 and 16 mm, respectively, and this yields a recommended usable upper frequency limit of approximately 7.5 GHz. Primary national standards of impedance for 7/16 connectors have recently been introduced at the UK’s National Physical Laboratory.
Symbols a α b β γ
= = = = =
γ0 = C = C0 c δs φ e ε εr
= = = = = = =
ε0 = f = fc =
Radius of coaxial line centre conductor (m). Attenuation constant (Np m−1 ). Radius of coaxial line outer conductor (m). Phase constant (rad m−1 ). Propagation constant for coaxial line containing conductor loss. This is generally a complex-valued quantity (m−1 ). Propagation constant of lossless coaxial line. This is an imaginary-valued quantity (m−1 ). Shunt capacitance, per unit length, of coaxial line including conductor loss (F m−1 ). Shunt capacitance, per unit length, of lossless coaxial line (F m−1 ). Speed of light in vacuum (defined exactly as 299,792,458 m s−1 ). Skin depth of air line conductors (m). Phase change (in degrees or radians) introduced by a length of line, l. 2.718281828…(base of Naperian logarithms). Permittivity, ε = ε0 εr (F m−1 ). Relative permittivity of an air line’s dielectric (e.g. εr = 1.000649 for ‘standard’ air at 23 ◦ C, 50 per cent relative humidity and 1013.25 hPa atmospheric pressure). Permittivity of free space (defined exactly as (c2 µ0 )−1 = 8.854187817 . . . × 10−12 F m−1 ). Frequency (Hz). Cut-off frequency for the TEM mode (Hz).
202 Microwave measurements G = Shunt conductance, per unit length, for a coaxial line including conductor −1 √loss (S m ). j = − 1. k = Angular wave number, k = 2π/λ (rad m−1 ). l = Length of air line (m). L = Series inductance, per unit length, for a coaxial line including conductor loss (H m−1 ). L0 = Series inductance, per unit length, for a lossless coaxial line (H m−1 ). λ = Wavelength = v/f (m). λc = Cut-off wavelength for the TEM mode (m). µ = Permeability, µ = µ0 µr (H m−1 ). µr = Relative permeability of an air line’s dielectric (e.g. µr = 1 for ‘standard’ air, to six decimal places). µ0 = Permeability of free space (defined exactly as 4π × 10−7 H m−1 ). π = 3.141592653. . . R = Series resistance, per unit length, for a coaxial line including conductor loss (0001 m−1 ). σ = Conductivity of an air line’s conductors (S m−1 ). √ v = Speed of the electromagnetic wave in the air line [v = c/ εr (m s−1 )]. ω = Angular frequency, ω = 2π f (rad s−1 ). Z = Characteristic impedance of a coaxial line containing conductor loss. This is generally a complex-valued quantity (0001). Z0 = Characteristic impedance of a coaxial line with lossless conductors. This is a real-valued quantity (0001).
References 1 Hertz, H.: Electric waves, being researches on the propagation of electric action with finite velocity through space, Trans. Jones, D. E. (Dover Publications Inc, New York, 1962), Chapter 10 2 Maxwell, J. C.: A treatise of electricity and magnetism, 3rd edn, vol. 2 (Oxford University Press, London, 1892) 3 Bryant, J. H.: ‘Coaxial transmission lines, related two-conductor transmission lines, connectors, and components: A US historical perspective’, IEEE Transactions on Microwave Theory and Techniques, 1984;32 (9):970–83 4 G-IM Subcommittee on Precision Coaxial Connectors: ‘IEEE standard for precision coaxial connectors’, IEEE Transactions on Instrumentation and Measurement, 1968;17 (3):204–18 5 Adam, S. F., Kirkpatrick, G. R., Sladek, N. J., and Bruno, S. T.: ‘A high performance 3.5 mm connector to 34 GHz’, Microwave Journal, 1976;19 (7):50–4 6 Maury, M. A., and Wambach, W. A.: ‘A new 40 GHz coaxial connector’, Millimeter Waves Techniques Conference Digest (NELC, San Diego, CA, 1974) 7 Browne, J.: ‘Precision coaxial cables and connectors reach 45 GHz’, Microwaves & RF, Sep 1983;131–6
Connectors, air lines and RF impedance 203 8 Kachigan, K., Botka, J., and Watson, P.: ‘The 2.4 mm connector vital to the future of 50 GHz coax’, Microwave Systems News, 1986;16 (2):90–4 9 Manz, B.: ‘Coaxial technology vies for emerging V-band applications’, Microwaves & RF, Jul 1989;35–41 10 Howell, K., and Wong, K.: ‘DC to 110 GHz measurements in coax using the 1 mm connector’, Microwave Journal, 1999;42 (7):22–34 11 Weinschel, B. O.: ‘Air-filled coaxial lines as absolute impedance standards’, Microwave Journal, Apr 1964;47–50 12 Harris, I. A., and Spinney, R. E.: ‘The realization of high-frequency impedance standards using air spaced coaxial lines’, IEEE Transactions on Instrumentation and Measurement, 1964;13:265–72 13 Rayleigh, L.: ‘On the self-inductance and resistance of straight conductors’, Philosophical Magazine S5, 1886;21 (132):381–94 14 Russell, A.: ‘The effective resistance and inductance of a concentric main, and methods of computing the Ber and Bei and allied functions’, Philosophical Magazine, 1909;17:524–52 15 Wheeler, H. A.: ‘Formulas for the skin effect’, Proceedings of the Institute of Radio Engineers, 1942;30:412–24 16 Stratton, J. A.: Electromagnetic theory (McGraw-Hill Book Company Inc, New York and London, 1941), Chapter 9 17 Harris, I. A.: ‘The theory and design of coaxial resistor mounts for the frequency band 0-4000 Mc/s’, Proc. Inst. Electr. Eng., 1956;103 Part C(3):1–10 18 MacKenzie, T. E., and Sanderson, A. E.: ‘Some fundamental design principles for the development of precision coaxial standards and components’, IEEE Transactions on Microwave Theory and Techniques, 1966;14 (1):29–39 19 Ridler, N. M., and Medley, J. C.: ‘Improvements to traceability for impedance measurements at RF in the UK’, IEE Engineering, Science and Education Journal, 1997;6 (1):17–24 20 Ridler, N. M., and Medley, J. C.: ‘Improving the traceability of coaxial impedance measurements at lower RF in the UK’, IEE Proceedings Science Measurement and Technology, 1996;143 (4):241–45 21 Skinner, A. D.: ANAMET connector guide, ANAMET Report 032, 2001 (Available at: www.npl.co.uk/anamet) 22 ‘Coaxial Systems. Principles of microwave connector care (for higher reliability and better measurements)’, Hewlett Packard Application Note 326, July 1986 23 ‘Coaxial connectors in radio frequency and microwave measurements’, NAMAS Information Sheet 4303, edn 1, December 1991 24 Maury, M. A.: ‘Microwave coaxial connector technology: a continuing evolution’, Microwave Journal (State of the Art Preference Supplement), Sep 1990; 39–59 25 Weinschel, B. O.: ‘Coaxial connectors: a look to the past and future’, Microwave Systems News, 1990;20 (2):24–31 26 Anderson, T. N.: ‘Evolution of precision coaxial connectors’, Microwave Journal, Jan 1968;18–28
204 Microwave measurements 27 Huber, F. R., and Neubauer, H.: ‘The Dezifix connector – a sexless precision connector for microwave techniques’, Microwave Journal, Jun 1963;79–85 28 Weinschel, B. O.: ‘Standardization of precision coaxial connectors’, Proceedings of the IEEE, 1967;55 (6):923–32 29 Sladek, N. J., and Jesch, R. L.: ‘Standardization of coaxial connectors in the IEC’, Proceedings of the IEEE, 1986;74 (1):14–18 30 Botka, J.: ‘Major improvement in measurement accuracy using precision slotless connectors’, Microwave Journal, 1988;31 (3):221–26 31 ‘Connector relieves nagging SMA measurement problems’, Microwaves, Jan 1979;97–9 32 Whinnery, J. R., Jamieson, H. W., and Robbins, T. E.: ‘Coaxial line discontinuities’, Proceedings of the Institute of Radio Engineers, 1944;32:695–709 33 Ide, J. P.: ‘Estimating the electrical compatibility of mechanically compatible connectors’, Microwave Engineering Europe, 1994;43:39–40 34 Oldfield, W. W.: ‘Comparing miniature coaxial connectors’, Microwaves and RF, 1985;24 (9):171–74 35 Dimitrios, J.: ‘Exact cutoff frequencies of precision coax’, Microwaves, Jun 1965; 28–31 36 Ramo, S., and Whinnery, J.: Fields and waves in modern radio (John Wiley & Sons, New York, 1959) 37 Marcuvitz, N.: Waveguide handbook, MIT Radiation Laboratory Series 10 (McGraw-Hill Book Company, New York, 1951), pp. 72–80 38 Gilmore, J. F.: ‘TE11 -mode resonances in precision coaxial connectors’, GR Experimenter, 1966;40 (8):10–13 39 Neubauer, H., and Huber, R. F.: ‘Higher modes in coaxial RF lines’, Microwave Journal, 1969;12 (6):57–66 40 Wong, K. H.: ‘Using precision coaxial air dielectric transmission lines as calibration and verification standards’, Microwave Journal, Dec 1998; 83–92 41 Engen, G. F., and Hoer, C. A.: ‘Thru-Reflect-Line: an improved technique for calibrating the dual six-port automatic network analyzer’, IEEE Transactions on Microwave Theory Techniques, 1979;MTT-27 (12):987–93 42 Hoer, C. A., and Engen, G. F.: ‘On-line accuracy assessment for the dual six-port ANA: extension to nonmating connectors’, IEEE Transactions on Instrumentation and Measurement, 1987;IM-36 (2):524–29 43 Ridler, N. M.: A review of existing national measurement standards for RF and microwave impedance parameters in the UK, IEE Colloquium Digest No 99/008, 1999, pp. 6/1–6/6 44 Baxter, W., and Dunwoodie, D.: An easy-to-use method for measuring small SWRs to better than computer-aided accuracy levels, Wiltron Technical Review, No 8, 1978 45 EA: Guidelines on the evaluation of Vector Network Analysers (VNA), EA-10/12, 2000 (Available at www.european-accreditation.org) 46 Ide, J. P.: ‘Traceability for radio frequency coaxial line standards’, NPL Report DES 114, 1992
Connectors, air lines and RF impedance 205 47 Ridler, N. M., and Medley, J. C.: An uncertainty budget for VHF and UHF reflectometers, NPL Report DES 120, 1992 48 Ridler, N. M.: ‘Improved RF calibration techniques for network analyzers and reflectometers’, Microwave Engineering Europe, Oct 1993;35–39 49 Zorzy, J.: ‘Skin-effect corrections in immittance and scattering coefficient standards employing precision air-dielectric coaxial lines’, IEEE Transactions on Instrumentation and Measurement, 1966;IM-15 (4):358–64 50 Kaye, G. W. C., and Laby, T. H.: Tables of physical and chemical constants, 15th edn (Longman, London and New York, 1986), pp. 117–20 51 Gray, D. A.: Handbook of coaxial microwave measurements (General Radio Company, Massachusetts, USA, 1968), Chapter 1 52 Weinschel, B. O.: ‘Errors in coaxial air line standards due to skin effect’, Microwave Journal, 1990;33 (11):131–43 53 Faraday Proctor, R.: ‘High-frequency resistance of plated conductors’, Wireless Engineer, 1943;20:56–65 54 von Baeyer, H. C.: ‘The effect of silver plating on attenuation at microwave frequencies’, Microwave Journal, 1960;3 (4):47–50 55 Somlo, P. I.: The computation of the surface impedance of multi-layer cylindrical conductors, CSIRO National Standards Laboratory (Australia), Report No APR 12, 1966 56 Kilby, G. J., and Ridler, N. M.: ‘Comparison of theoretical and measured values for attenuation of precision coaxial lines’, IEE Electronics Letters, 1992;28 (21):1992–94 57 Hill, D. A.: ‘Reflection coefficient of a waveguide with slightly uneven walls’, IEEE Transactions on Microwave Theory Techniques, 1989;MTT-37 (1):244–52 58 Holt, D. R.: ‘Scattering parameters representing imperfections in precision coaxial air lines’, Journal of Research of NIST (USA), 1989;94 (2):117–33 59 Sanderson, A. E.: ‘Effect of surface roughness on propagation of the TEM mode’, in Young, L. (ed.), Advances in Microwaves, vol. 7 (Academic Press Inc, New York, 1971), pp. 1–57 60 Ridler, N. M.: VHF impedance – a review, NPL Report DES 127, 1993 61 Nelson, R. E., and Coryell, M. R.: ‘Electrical parameters of precision, coaxial, airdielectric transmission lines’, NBS Monograph 96, National Bureau of Standards (USA), 1966 62 Daywitt, W. C.: ‘First-order symmetric modes for a slightly lossy coaxial transmission line’, IEEE Transactions on Microwave Theory Techniques, 1990;MTT-38 (11):1644–51 63 Daywitt, W. C.: ‘Exact principal mode field for a lossy coaxial line’, IEEE Transactions on Microwave Theory Techniques, 1991;MTT-39 (8):1313–22 64 Woods, D.: ‘Relevance of complex normalisation in precision reflectometry’, IEE Electronics Letters, 1983;19 (15):596–98 65 Collin, R. E.: Foundations for microwave engineering, (McGraw-Hill Book Company, New York, 1966) 66 Ridler, N. M., and Medley, J. C.: ‘Calibration technique using new calculable standard for RF reflectometers fitted with GPC-7 connectors’, Conference on
206 Microwave measurements
67 68 69 70 71 72 73
74
75
Precision Electromagnetic Measurements (CPEM) Digest, Boulder, CO, 1994, pp. 117–18 Somlo, P. I.: ‘The computation of coaxial line step capacitances’, IEEE Transactions on Microwave Theory Techniques, 1967;MTT-15 (1):48–53 Razaz, M., and Davies, J. B.: ‘Capacitance of the abrupt transition from coaxialto-circular waveguide’, IEEE Transactions on Microwave Theory Techniques, 1979;MTT-27 (6):564–69 Bianco, B., Corana, A., Gogioso, L., and Ridella, S.: ‘Open-circuited coaxial lines as standards for microwave measurements’, IEE Electronics Letters, 1980;16 (10):373–74 Ridler, N. M., Medley, J. C., Baden Fuller, A. J., and Runham, M.: ‘Computer generated equivalent circuit models for coaxial-line offset open circuits’, IEE Proceedings A, Science, Measurement and Technology, 1992;139 (5): 229–31 Fantom, A. E.: Radio frequency and microwave power measurement (Peter Perigrinus Ltd, London, 1990), Appendix A Ridler, N. M., and Medley, J. C.: Traceable reflection coefficient measurements in coaxial line at MF and HF, IEE Colloquium Digest No 1994/042, 1994, pp. 8/1–8/4 Cox, M. G., Dainton, M. P., and Ridler, N. M.: ‘An interpolation scheme for precision reflection coefficient measurements at intermediate frequencies. Part 1: theoretical development’, IMTC’2001 Proceedings of the 18th IEEE Instrumentation and Measurement Technology Conference, Budapest, Hungary, 21–23 May 2001, pp. 1720–25 Ridler, N. M., Salter, M. J., and Young, P. R.: ‘An interpolation scheme for precision reflection coefficient measurements at intermediate frequencies. Part 2: practical implementation’, IMTC’2001 Proceedings of the 18th IEEE Instrumentation and Measurement Technology Conference, Budapest, Hungary, 21–23 May 2001, pp. 1731–35 Morgan, A. G., Ridler, N. M., and Salter, M. J.: ‘Generalised calibration schemes for RF vector network analysers’, IMTC’2002 Proceedings of the 18th IEEE Instrumentation and Measurement Technology Conference, Anchorage, AL, 21–23 May 2002
Chapter 10
Microwave network analysers Roger D. Pollard
10.1
Introduction
This chapter is intended to cover the basic principles of measuring microwave networks by using a network analyser. The objectives are to discuss the kind of measurements which can be made and the major components in a network analyser covering the basic block diagram, the elements and the advantages and disadvantages of different hardware approaches. Material on error correction is the subject of another chapter. The fundamental concept of microwave network analysis involves incident, reflected and transmitted waves travelling along a transmission line. It must be appreciated, at the outset, that measurement in terms of impedance, which is the ratio of voltage to current, implies knowledge of the characteristic impedance Z0 which describes the mode of propagation in the transmission line. Microwave network analysis is concerned with measuring accurately the incident, reflected and transmitted signals associated with a linear component in a transmission line environment. It is important to appreciate that the same quantities may be defined as different values, for example, return loss, reflection coefficient, VSWR, S11 , impedance and admittance are all ways of describing reflection coefficient, and, similarly, gain, insertion loss, transmission, group delay and insertion phase are all ways of describing transmission coefficient. It is also necessary to understand the fundamental difference between a network analyser and a spectrum analyser. Network analysers are used to measure components, devices and circuits, but a network analyser is always looking at a known signal in terms of frequency and is described as a stimulus–response system. With a network analyser, for example, it is very hard to get an accurate trace on the display, for reasons which will be explained later, but very easy to interpret the results using vector error correction. A network analyser can provide much higher accuracy than a spectrum analyser. Spectrum analysers on the other hand are used to measure signal
208 Microwave measurements characteristics on unknown signals. They are usually a single channel receiver without a source and have a much wider range of IF bandwidths than a network analyser. With a spectrum analyser it is easy to get a trace on the display, but interpreting the results can often be much more difficult than with a network analyser.
10.2
Reference plane
The measurements under consideration are those which characterise travelling waves on a uniform transmission line and the (usually voltage) ratios which are detected are functions of position on the lines. Furthermore, any change in the cross section of the transmission line will give rise to a reflection and the launch of evanescent modes. It is therefore necessary to be able to specify a reference plane which is appropriately located in a sufficient length of uniform transmission line. The reference plane often, but not necessarily, is the plane of contact of the outer conductors of a mating pair of coaxial connectors or a pair of waveguide flanges.
10.2.1 Elements of a microwave network analyser Figure 10.1 shows the general block diagram of a network analyser showing the major signal processing parts.
DUT
Reflected
Source
Signal separation
Incident (R)
Reflected (A)
Transmitted (B)
Receiver/detector
Processor/display
Figure 10.1
General block diagram of a network analyser
Microwave network analysers 209 50 Ω
6 dB Main signal
50 Ω
6 dB Coupled signal
Figure 10.2
Separation of reference signal using power splitter or directional coupler
Four elements are present: (1) source to provide a stimulus, (2) signal separation devices, (3) a receiver for detecting the signals, and (4) a processor and display for calculating and showing the results. 10.2.1.1 Source The signal source supplies the stimulus for the test system and can either sweep the frequency of the source or its power level. Traditionally, most network analysers had a separate source but nowadays the source is often a built-in part of the instrument. The source may be either a voltage-controlled oscillator or a synthesised sweeper. 10.2.1.2 Signal separation This is normally described as the test set, which can be a separate box or integrated into a network analyser. The signal separation hardware must provide two functions. The first is to separate a portion of the incident signal to provide the reference signalling for ratioing. This can be done with a power splitter or a directional coupler (Figure 10.2). Power splitters are usually resistive, non-directional devices and can be very broadband; the trade-off is that they have some loss (usually 6 dB or more) in each port. Directional couplers can be built to have very low loss through the main arm and offer good isolation and directivity, but it is difficult to make them operate at very low frequencies. The second function is to separate the incident and reflected travelling waves at the input to the device under test (DUT). Directional couplers are ideal because they have the necessary directional properties, low loss in the main arm and good reverse isolation. However, owing to the difficulty of making very broadband couplers, directional bridges are often used. Bridges can operate over a very wide range of frequency but exhibit more loss to the transmitted signal resulting in less power delivered to the DUT. A directional coupler is a device that separates a component of the signal travelling in one direction only. In the diagrams in Figure 10.3, the signal flowing through the main arm is shown as a solid line, the coupled signal as a dotted line. Note that the fourth port of the coupler is terminated with a matched load. The signal appearing at the coupled port is a fraction of the input signal; this fraction is the coupling factor. In the example in Figure 10.3, the coupling factor is 20 dB and therefore when 1 mW (0 dBm) is supplied to the input port, 0.01 mW (−20 dBm) will appear at the coupled
210 Microwave measurements Coupling, forward − 20 dBm 0.01 mW Source Z0 0 dBm 1 mW Coupling reverse − 50 dBm 0.00001 mW
−0.046 dBm 0.99 mW This is an error signal during measurements
Source Z0 0 dBm 1 mW
Figure 10.3
−0.046 dBm 0.99 mW
Directional coupler: coupling and directivity
port. Note that as a result there is a small loss through the main arm. The coupling factor is rarely constant with frequency and the frequency response can become a significant measurement error term. In an ideal coupler, there will be no component of a signal travelling in the reverse direction at the coupled port, but in practice a coupler has finite isolation and some energy will leak in the reverse direction. In the example in Figure 10.3, the coupler is reversed and the isolation measured at −50 dB. The most important single parameter for a directional coupler is its directivity, which is a measure of a coupler’s ability to separate signals flowing in opposite directions. It can be thought of as the dynamic range for reflection measurements. By definition, directivity is the ratio between the reverse coupling factor (isolation) and the forward coupling factor. In the example of Figure 10.3, the coupler has a directivity of 30 dB. During a reflection measurement the error signal can be, at best, the directivity below the desired signal. The better the match of the DUT the greater measurement error the directivity error will cause. Directivity error is the main reason that will be seen as a large ripple pattern in many measurements of return loss. At the peak of the ripple, directivity is added in phase with the signal reflected from the device. In other cases the directivity will cancel the DUT reflection, resulting in a sharp dip in the response (Figure 10.4). The directional bridge is similar in operation to the Wheatstone bridge. If all four arms have equal resistance and 50 0001 is connected to the test port then a voltage null will be measured at the detector and the bridge is balanced. If the load at the test port is not 50 0001 then the voltage across the detector is proportional to the mismatch presented by the DUT. If both magnitude and phase are measured at the detector, the complex impedance of the test port can be calculated. A bridge also has an
Microwave network analysers 211 0 Data Max Directivity
Device
Return loss
DUT RL = 40 dB
30
Add in phase
60
Figure 10.4
Device
Directivity
Device
Frequency Data Min
Data = Vector sum
Directivity
Cancel ∴ Data ≈ 0
Return loss ripple caused by coupler directivity
50 Ω
50 Ω standard
50
Ω
50
50 Ω
Ω 50 Ω source
50 Ω detector
Detector
50
Ω
50 Ω
Figure 10.5
Test port Γ
Directional bridge: theoretical and actual circuit
equivalent directivity that is the ratio between the best balance measuring a perfect load and the worst balance measuring an open circuit or a short circuit. The effect of bridge directivity on measurement accuracy is exactly the same as for a directional coupler. The basic arrangement of a directional bridge is shown in Figure 10.5. Notice that in a microwave system there is generally a requirement that one terminal of each component is connectable to ground; the key therefore to designing a successful broadband directional bridge to operate at microwave frequencies is the provision of a suitable balun as shown in Figure 10.5. 10.2.1.3 Detectors and receivers There are two basic ways of providing detection in network analysers – diode detectors, which simply convert the RF to a proportional DC level, or tuned receivers. Diode
212 Microwave measurements
RF R A B
Detector
Bridge
Termination
DUT
Reflection
RF R A B
Detector Detector Transmission
Figure 10.6
DUT
Scalar network analyser measurements using diode detectors
detection is inherently scalar and loses phase information. The main advantages of diode detection are low cost and broadband frequency range which is a significant benefit when measuring frequency translating devices (Figure 10.6). Offset against this is the limited sensitivity and dynamic range and susceptibility to source harmonics and spurious signals. Drift in a diode detector, a major source of measurement error, can be eliminated by the use of AC detection that also reduces noise and susceptibility to unwanted signals. However, the necessary modulation of the RF signal can affect the measurements of some devices (e.g. amplifiers with AGC). The tuned receiver uses a local oscillator (LO) to mix the RF down to an intermediate frequency (IF). The LO is locked either to the RF or to the IF so that the receiver in the network analyser is always correctly tuned to the RF present at the input (Figure 10.7). The IF signal is filtered, which narrows the receiver bandwidth, allows large amounts of gain and greatly improves the sensitivity and the dynamic range. A modern network analyser uses an analogue-to-digital converter (ADC) and digital signal processing to extract the magnitude and phase information from the IF signal. Tuned receivers not only provide the best sensitivity and dynamic range but also provide harmonic and spurious signal rejection. The narrow band IF filter produces a considerably lower noise floor resulting in significant improvement in sensitivity and dynamic range. For example, a microwave network analyser might have a 3 KHz IF bandwidth and an achievable dynamic range, better than 100 dB. The dynamic range can be improved by increasing the input power by decreasing the IF bandwidth
Microwave network analysers 213 IF = FLO ± FRF
RF
ADC / DSP
IF filter
LO
Figure 10.7
Downconverting tuned receiver
or by averaging. This provides a trade-off between noise floor and measurement speed. Averaging reduces the noise floor of the network analyser because complex data are being averaged. Without phase information, as in, for example, a spectrum analyser, averaging only reduces the noise amplitude and does not improve sensitivity. Also because the RF signal is downconverted and filtered before it is measured, any harmonics associated with the source appear at frequencies outside the IF bandwidth and are removed. This eliminates response to harmonics and spurious signals and results in increased dynamic range. A tuned receiver can be implemented with a mixer or a sampler based front-end. It is often cheaper and easier to make wide band front-ends using samplers instead of mixers. The sampler uses diodes to sample very short time slices of the incoming RF signal. Conceptually the sampler can be thought of as a mixer with an internal pulse generator. The pulse generator creates a broadband frequency spectrum (often known as a ‘comb’) composed of harmonics of a local oscillator. The RF signal mixes with one of the spectral lines (or ‘comb-tooth’) to produce the desired IF. Figure 10.8 shows the block diagram of a sampler system. The local oscillator is tuneable and drives a harmonic generator. The output from the harmonic generator drives a diode that can be thought of simply as a switch. In terms of frequency behaviour the output from the harmonic generator provides a comb of harmonics of the local oscillator and by tuning the local oscillator to the right frequency, the difference between the incoming RF and one of the comb-teeth will be exactly the IF frequency which can pass through the IF filter. A phase lock loop will ensure that the local oscillator is always correctly tuned as the source frequency changes. In most modern designs the local oscillator is pre-tuned to ensure that the same comb-tooth of the local oscillator is used every time that the same frequency is input. Compared to a mixer-based network analyser the LO in a sampler-based front-end covers a much smaller frequency range and a broadband mixer is no longer needed. The trade-off is that the phase lock algorithms for locking the various comb-teeth are much more complex. Sampler based front-ends also have a somewhat lower dynamic range than those based on mixers and fundamental local oscillators because the additional noise is converted into the IF from all of the comb-teeth. Nonetheless, network analysers
214 Microwave measurements
IF output
IF filter
Source
Reference oscillator
LO Harmonic generator
IF filter IF = nfLO −fRF LO harmonics
Frequency
Figure 10.8
Principle of operation of a sampling receiver in a network analyser
with narrow band detection based on samplers still have far greater dynamic range than analysers based on diode detection. Dynamic range is usually defined as the maximum power the receiver can measure accurately minus the receiver noise floor. There are many applications requiring large dynamic range, the most common being filter applications. Also the presence of harmonics from the source may create a false response which will be removed by a tuned receiver.
10.3
Network analyser block diagram
Figure 10.9 shows the general schematic of an S-parameter measurement system whilst Figure 10.10 is the block diagram of a modern microwave vector network analyser. The schematic diagram shown in Figure 10.10 is a RF system which has an integrated source and a tuned receiver based on samplers (labelled S). The system can be configured with a three-channel or four-channel receiver and consequently the test set can be either a transmission/reflection type or capable of full S-parameters. There are two basic types of test set that are used with network analysers for transmission/reflection (TR) test sets. The RF power always comes out of test port 1 and test port 2 is always connected to a receiver. To measure reverse transmission
Microwave network analysers 215 RF source
a0
a3 IF
IF
LO source IF
IF b0
b3
Port - 1
Port - 2 a1
Cable
b2
Cable
DUT b1
IF
a2
Figure 10.9
Proc display
A/D
BPF
Schematic of an S-parameter measurement system Synthesiser 15 MHz to 60 MHz
996 kHz
MUX Reference
RF
detector
Test set
300 kHz to 3 GHz Phase lock
DUT
Source
Figure 10.10
Test set
A
S
B
S
R
S
4 kHz
4 kHz
4 kHz
ADC
CPU Digital control
Receiver
Block diagram of an RF network analyser
Display
216 Microwave measurements or output reflection the device must be disconnected, turned around and reconnected again. TR-based network analysers offer only response and one-port calibration so measurement accuracy is not as good as the one that can be achieved using S-parameter test sets. An S-parameter test set allows both forward and reverse measurements without reconnection and allows characterisation of all four S-parameters. RF power can come out of either test port 1 or test port 2 and either test port can be connected to a receiver. The internals rearrangement is carried out by switches inside the test set. These are usually solid-state switches which are fast and do not wear out. Although it is possible to configure an S-parameter test set with only three samplers or mixers the architecture provides fewer choices for calibration as does a four receiver architecture. The display and processor section allows in current systems is usually an in-built, full-featured PC that not only the reflection and transmission data to be formatted in many ways to allow for easy display, comparison and interpretation but also supports algorithms for calibration, data storage and various other features.
Further reading Warner, F. L.: ‘Microwave vector network analysers’ in Bailey, A. E. (ed.), Microwave Measurements, 2nd edn (Peter Peregrinus Ltd, London, 1989), Chapter 11
Chapter 11
RFIC and MMIC measurement techniques Stepan Lucyszyn
11.1
Introduction
All electronic sub-systems are made up of devices and networks. In order to simulate the overall performance of a sub-system under development, all the components that make up the sub-system must be accurately characterised. To this end, precision measurement techniques must be employed at component level. Not only do precision measurements enable a manufacturer to check whether devices are within their target specifications, and to monitor variations in parameter tolerances due to process variations, they also allow more accurate empirical models to be extracted from the measurements and help new modelling techniques to be validated. Also, the operation and performance of some experimental devices can often only be understood from accurate measurements and subsequent modelling. Conversely, poor measurements could result in the needless, and therefore expensive, redesign of high-performance components or sub-systems. Devices and networks are traditionally characterised using Z, Y or h-parameters. To measure these parameters directly, ideal open and short circuit terminations are required. These impedances can be easily realised at low frequencies. However, at microwave frequencies such impedances can only be achieved over narrow bandwidths (when tuned circuits are employed) and can also result in circuits that are conditionally stable (when embedded within a ‘matched load’ reference impedance environment) becoming unstable. Fortunately, scattering- (or S)- parameters can be determined at any frequency. To perform such measurements, the device under test (DUT) is terminated with matched loads. This enables extremely wideband measurements to be made and also greatly reduces the risk of instability; however, only when the DUT is terminated with near ideal matched loads (this is irrespective of whether the measurement system is calibrated or not). S-parameter measurements
218 Microwave measurements also offer the following advantages: (1) Any movement in a measurement reference plane along an ideal transmission line will vary the phase angle only. (2) For a linear device or network, voltage or current and measured power are related through the measurement reference impedance (normally 75 or 50 0001 for coaxial lines and 1 0001 for rectangular waveguides). (3) With some passive and reciprocal structures, ideal S-parameters can be deduced from spatial considerations, enabling the measurements of the structure to be checked intuitively. By applying a known incident wave to the DUT and then measuring the reflected and transmitted wave amplitudes, S-parameters can be calculated from the resulting wave amplitude ratios. The equipment most commonly used to perform this measurement is called a vector network analyser (VNA) [1]. The DUT can now be characterised using complete S-parameter measurements (along with DC measurements). The element values associated with the small-signal equivalent circuit model of the DUT can be determined using direct calculations, iterative optimisation and intuitive tuning. This process is referred to as parameter extraction. With a radio frequency integrated circuit (RFIC), also known as a monolithic microwave integrated circuit (MMIC), either a test fixture or probe station is employed to secure the MMIC in place and to provide a stable means of electrically connecting the MMIC to the measurement system [2]. In this chapter, the use of test fixtures and probe stations at ambient room temperature is reviewed and their role at thermal and cryogenic temperatures is discussed. Finally, with the increasing need for performing non-invasive (or non-contacting) measurements, experimental field probing technologies are introduced.
11.2
Test fixture measurements
Although probe stations result in much more accurate and reproducible measurements, test fixtures are still widely used. The principal reasons are that they are very much cheaper than probe stations and they offer a greater degree of flexibility, such as facilitating larger numbers of RF ports and enabling DC bias circuitry and any offchip resonators to be located next to the chip. Also, the heat dissipation required when testing monolithic power amplifiers can be easily provided with test fixtures. In addition, test fixtures are ideally suited when RF measurements are required during temperature-cycling and when cryogenic device characterisation is required [3–5]. An illustration of a basic two-port test fixture is shown in Figure 11.1. Most test fixtures are, in principle, based on this generic design, typically consisting of four different components: (1) a detachable metal chip carrier with high-permittivity substrate, (2) a rigid metal housing, (3) connector/launchers and (4) bond wires. The MMIC is permanently attached to the chip carrier with either conductive epoxy glue or solder. The metal housing is employed to hold the chip carrier and the connector/launchers in place. The launcher is basically an extension of the coaxial
RFIC and MMIC measurement techniques 219 50 Ω microstrip transmission line Microstrip launcher
Bond wires
Housing Ridge-mounted MMIC under test
50 Ω coaxial cable/connector to the VNA Coaxial calibration VNA reference plane
50 Ω flange-mounted coaxial connector Chip carrier High permittivity ground plane chip carrier substrate
Figure 11.1
Chip carrier
Generic design of a two-port test fixture
connector’s centre conductor, which passes through the housing wall to make electrical contact with the associated chip carrier’s microstrip transmission line. Bond wires or straps are used to connect the other end of the microstrip line to the MMIC under test. The parasitic element values associated with a test fixture are typically an order of magnitude greater than those of the MMIC under test. Before any accurate measurements can be performed, measurement systems must first be calibrated, in order to correct for the systematic errors resulting from the numerous reflection and transmission losses within the measurement system. A calibration kit is required to perform this calibration procedure. This ‘cal. kit’ has a number of electrical reference standards and software that must be downloaded into the VNA’s non-volatile memory or associated PC/workstation controller. For a two-port measurement system, the calibration standards must: (1) define the primary reference planes; (2) remove any phase ambiguity using open circuit and/or short circuit reflection standard(s); and (3) define the reference impedance using delay line, matched load or attenuator impedance standard(s). Some of the various combinations of different standards that can be employed in a two-port calibration procedure are listed in Table 11.1. The software should contain accurate models for the associated standards and the algorithms required to implement the chosen calibration method. The accuracy of subsequent measurements ultimately depends on how well all the standards remain characterised. Any deviation in the electrical parameters of the standards will degrade the magnitudes of the effective directivity and source match for the measurement system. As a result, great care must be taken to look after these calibration standards. The non-idealities of a measurement system are characterised using mathematical error correction models, represented by flow diagrams (also known as error adapters or boxes). The function of the calibration procedure is to solve for the error coefficients in these models by applying the raw, uncorrected, S-parameter measurements of the
220 Microwave measurements Table 11.1
Common calibration methods
Method
Calibration standard Through L=0
TRL LRL TRM LRM TRA LRA TSD
• • • •
Reflect
L 0002= 0
• • •
Reference impedance
ρ1 = ρ2
Line
• • • • • • ρ = −1
• •
•
Match
• •
Atten.
• •
standards to a set of independent linear equations. The basic two-port calibration procedures have an eight-term error model (four terms associated with each port) and require only three standards. These error terms should correspond directly to the raw hardware performance, including the directivity, source match and frequency tracking. A more accurate 12-term error model, as used in two-port coaxial calibration, takes crosstalk and the effects of impedance mismatches at the RF switches within the VNA’s test-set into account. Once the calibration procedure has been performed, it can be verified by measuring separate verification standards.
11.2.1 Two-tier calibration One method of calibrating the measurement system is to split the process into two tiers [6]. Initially, a coaxial calibration is performed, where the VNA reference planes are located at the end of its cable connectors. Historically, the VNA was calibrated using short-open-load-through (SOLT) standards. These lumped-element standards can give high-quality coaxial calibrations across an ultra-broad bandwidth (e.g. DC to 50 GHz), so long as all the standards remain accurately characterised across the entire bandwidth. Since test fixtures are far from ideal, a second process is required to shift the initial VNA reference planes to the MMIC under test, in order to eliminate the effect of the test fixture. This second process is known as de-embedding or deconvolution [7]. To perform de-embedding it is necessary to accurately characterise the test fixture [8]. Another reason why you may need to characterise a test fixture is when multiple RF port MMICs are to be measured using a two-port VNA [9]. Here, power reflected from impedance-mismatched loads on the auxiliary ports of the MMIC can result in significant measurement errors. These errors will increase as the mismatch losses increase and/or the number of RF ports increases. As a result, MMICs that have more RF ports than the VNA require all the loads to be individually characterised, and a further process of matrix renormalisation [9–13] in order to remove the effects of
RFIC and MMIC measurement techniques 221 the mismatched loads on the auxiliary ports. Three methods that can, in principle, be employed to characterise a test fixture are (1) time-domain (T-D) gating, (2) in-fixture calibration and (3) equivalent circuit modelling. 11.2.1.1 Time-domain gating Some VNAs can be upgraded with a synthetic-pulse T-D reflectometry (TDR) option [14–20]. Here, the discrete form of the inverse Fourier transform (IFT) is applied to a real sequence of harmonically related frequency-domain (F-D) measurements; in our case, of the MMIC embedded within its test fixture. This is directly equivalent to mathematically generating synthetic unity-amplitude impulses (or unity-amplitude steps), which are then ‘applied’ to the embedded MMIC. The resulting T-D reflection and transmission responses can then be analysed to provide information about the MMIC and test fixture discontinuities. In reflection measurements, it is possible to remove the effects of unwanted impedance mismatches or else isolate and view the response of an individual feature. With a multiple port test fixture, transmission measurements can give the propagation delay and insertion loss of signals travelling through a particular path by removing the responses from the unwanted paths. With an MMIC fed with transmission lines that only support a pure TEM mode of propagation, time and actual physical distance are simply related: 0001 c0003tζ /2 with reflection measurements Physical distance = c0003tζ with transmission measurements where c is the speed of light in free space; 0003t is the time difference, relative to a √ reference (e.g. t = 0); and ζ = 1/ εr is the velocity factor. Also, F-D nulls in |S11 | are at frequency harmonics of 1/0003t, where 0003t is the time difference between two reflected impulses. If the feed lines are non-TEM, and therefore dispersive, impulse spreading will occur, which could significantly distort the impulse shape (in time and amplitude). If the dispersive nature is known, the frequency sweep can be pre-warped [20]. With either a banded VNA (which may cover just one of the main waveguide bands), or a broadband VNA, the band-pass T-D mode can be selected, where only synthetic impulses are generated. This is useful for band-limited guided-wave structures (e.g. rectangular waveguides). In general, in this mode, only the magnitudes of the individual reflection and transmission coefficients are available. As a result, the exact nature of any discontinuity (e.g. resistive, inductive and capacitive) cannot be identified. However, it is still possible to extract some information about the nature of a defect in band-pass mode with a phasor impulse. With a broadband VNA, a low-pass T-D mode is also available where both synthetic impulses and synthetic steps can be generated. The low-pass mode is used to emulate a real-pulse TDR measurement system. This allows the user to identify the nature of any discontinuity. F-D measurements are taken from the start frequency, f1 , to the stop frequency, f2 . When compared with band-pass, for the same bandwidth (i.e. frequency-span) B = f2 − f1 , the low-pass mode offers twice the response resolution in the T-D. However, with the low-pass mode, the F-D measurements must be
222 Microwave measurements harmonically related, from DC to f2 , such that f2 = nfd f1 , where nfd is the number of points in the F-D (e.g. 51, 101, 201, 401 and 801). The DC data point is extrapolated from the f1 measurement. However, if the measurement at f1 is noisy, the T-D trace will be unstable and difficult to interpret. In TDR, the width of a band-limited unit impulse (or window function) is defined as the interval between its two half-amplitude (i.e. −6 dB power) points. The corresponding response resolution is defined as the interval between two impulses that are just distinguishable from each other as separate peaks. With equal amplitude impulses, the response resolution is equal to the 6 dB impulse width. With no window function applied to the F-D measurements: 1.2 for band-pass B 6 dB Impulse width = 0.6 for low-pass B 2 for band-pass B Main Lobe’s null-to-null width = 1 for low-pass B The time range is the length of time that measurements can be made without encountering a repetition of the same response. The range must be set longer than the furthest discontinuity, otherwise aliasing will occur, where out-of-range discontinuities will fold-over and appear in-range at (two range – target position) Range =
1 0003f
where 0003f = B/(nfd − 1). If a feature lies exactly midway between two T-D points then the energy associated with the discontinuity will be distributed between the two points, resulting in the displayed amplitude being reduced by almost 4 dB [20]. Therefore, care must be taken to ensure there is sufficient range resolution (or point spacing) in the T-D. Range resolution =
Range ntd
where ntd is the number of points in the T-D. The point spacing can be reduced to any desired level, at the expense of processing time, by using a chirp-Z fast Fourier transform algorithm. This allows range to be replaced by an arbitrary display time-span in the above range resolution equation. It is worth noting that with range and range resolution, either the one-way time or round-trip time may be quoted, depending on the manufacturer. De-embedding using synthetic-pulse TDR is not de-embedding in the true sense. It is specifically T-D gating, which can isolate a time feature and emphasise its frequency response. With time-gating, a mathematical window (called a gate or time filter) is used to isolate the embedded MMIC,so that only the MMIC’s frequency
RFIC and MMIC measurement techniques 223 response can be emphasised. When the gate is switched on, all reflections outside the gate are set to zero. This is equivalent to terminating the MMIC with the complex conjugate of its respective port impedance(s). The synthetic-pulse TDR option can be a very useful tool, although it can suffer from a number of sources of errors [15,19,20]; some of these are listed as follows: (1) Noise errors [15]. (a) Sweep mode: The VNA’s synthesised source can be operated in either the ramp-sweep or step-sweep mode. With the former, small non-linearities and phase discontinuities generate low-level noise sidebands on the T-D impulse and step stimuli. However, with the step-sweep mode, the improved source stability eliminates these noise sidebands and improves the T-D’s dynamic range by as much as 30 dB. Moreover, to reduce the noise floor of the T-D measurements further, the step-sweep mode enables more averaging of the F-D measurements, compared with the ramp-sweep mode, without greatly increasing the sweep time. (b) Bandwidth: The noise floor in the T-D response is directly related to noise in the F-D data. Therefore, the number of F-D data points taken at, or below, the system’s noise floor can be minimised by reducing the frequency-span to the bandwidth of the MMIC. (c) Test-set: If the test-set does not have a flat response down to the start frequency then the reduction in the F-D’s dynamic range towards f1 will cause an increase in the T-D’s noise floor, the resulting trace bounce, in the low-pass mode, can be improved by turning on T-D trace averaging. (2) Frequency-domain window errors. There is usually a choice of F-D window functions (e.g. Kaiser–Bessel) that can be applied prior to the IFT, for example, minimum (0th order), normal (6th order) and maximum (13th order). The minimum window has a rectangular function that produces the sin x/x impulse shape, having the minimum 6 dB impulse width and also the maximum sidelobe levels (with a minimum sidelobe suppression of only 13 dB in its power response). The other two window functions reduce the sidelobe levels (with a minimum suppression of 44 and 98 dB, respectively) at the expense of a wider impulse (by a factor of 1.6 and 2.4, respectively). It will be seen that a trade-off has to be made when choosing the F-D’s windowing function, between the desired resolution and dynamic range in the T-D. Note that this windowing function does not affect the displayed F-D response. (a) Time resolution errors: With narrow bandwidth VNAs, the impulse may be too wide. As a result, it may be difficult to resolve the MMIC and the connector/launchers features, down to the baseline, when the associated discontinuities are too close to one another. In practice, the MMIC should be separated by at least two 6 dB impulse widths from the connector/launcher.
224 Microwave measurements (b) Dynamic range errors: Impulse sidelobes limit the dynamic range of the T-D responses, since the sidelobes from a large impulse can hide a small adjacent target impulse. (c) Moding errors: If the bandwidth of the VNA is too high, such that overmoding in transmission lines or box mode resonances occur in the test jig, the T-D responses become un-interpretable. (d) Out-of-band response: The amplitude of the impulses represents the average value over the entire frequency-span. Therefore, the displayed amplitude of an impulse can be different from the expected value if the frequency-span includes an MMIC with a non-flat frequency response; for example, having highly abrupt out-of-band characteristics. (3) Discontinuity errors. (a) Masking errors: If the target discontinuity is preceded by other discontinuities that either reflect or absorb energy, then these other discontinuities may remove some of the energy travelling to and emanating from the target discontinuity. The trailing edge of earlier features can also obscure the target feature. (b) Multi-reflection aliasing errors: Multiple reflections between discontinuities can cause aliasing errors. For example, if a two-port MMIC is positioned midway between two connector/launchers, reflection from the furthest connector/launcher will be corrupted by multiple reflections between the MMIC and the nearest connector/launcher. (4) Time-domain window errors. In practice, a time filter having a non-rectangular response is used for gating, otherwise the sin x/x weighting would be conveyed to the F-D. There is usually a choice of T-D window functions that can be applied before the Fourier transform: minimum, normal, wide and maximum. The minimum window has the fastest roll-off and largest sidelobes, while the maximum window has the slowest roll-off and smallest sidelobes. (a) Baseline errors: The gate-start and gate-stop times, which define the −6 dB gate-span of the filter, must be set at the baseline if low frequency distortion in the F-D is to be minimised [14]. (b) Truncation errors: A limited gate width may truncate lengthy target features. To minimise truncation error, the wider gates are preferred. (c) Sidelobe errors: The time filter sidelobes may ‘see’ earlier or subsequent features. This could significantly corrupt the F-D response of the target feature. To minimise sidelobe errors, the wider gates are preferred. (d) Gate offset errors: F-D distortion can occur if the gate-centre is offset from the centre of the target feature(s). This is because a nearsymmetrical target response may lose its symmetry when applied to a time-offset gate that has significant in-gate attenuation. To minimise gate offset errors, the wider gate shapes are preferred.
RFIC and MMIC measurement techniques 225 (e) Minimum gate-span errors: The gate-span must be set wider than the minimum value, otherwise the gate will have no passband and may have high sidelobe levels. (f) Attenuation errors: For a fixed gate-span, the level and duration of in-gate attenuation may be excessive with wider gates. (g) Reflection/transmission switching errors: If gating is performed on a voltage reflection coefficient response then the associated return loss F-D measurement is valid. If the same gating times are applied to the voltage transmission coefficient response(s) then this may not be appropriate. For example, when a two-port MMIC is not placed midway between connectors, the transmission pulse may not be fully enclosed within the reflection response’s gate. The resulting insertion loss F-D measurement will not represent accurate de-embedding. As an example, a gallium arsenide (GaAs) MMIC with a 2.9 mm length of 55 0001 microstrip through-line was placed at the centre of a 25.4 mm alumina chip carrier. An Agilent Technologies 8510B VNA was calibrated with a 20 GHz bandwidth and 401 frequency points. The band-pass mode was selected with a minimum F-D windowing function. This combination provides a minimum response resolution and maximum range values of 60 ps and 20 ns, respectively. The F-D power responses are shown in Figure 11.2a. The corresponding T-D response of the input port’s voltage reflection coefficient is shown in Figure 11.2b. Here, the first and last peaks correspond to the impedance mismatches associated with the coaxial-to-microstrip transitions of the input and output ports, respectively. The two centre peaks correspond to the reflections associated with the microstrip-to-MMIC transitions. It will be apparent from Figure 11.2b that accurate de-embedding would not be possible using T-D gating. This is because the unwanted reflections cannot be resolved down to the baseline. If de-embedding was attempted in the above example then the ripples in the F-D responses would be smoothed out, as one would expect, although this would not constitute accurate de-embedded measurements. In order to achieve accurate deembedded measurements, a VNA with more bandwidth, or alternatively, a real-pulse TDR system having ultra-short impulses, can be used. 11.2.1.2 In-fixture calibration In general, a quality test fixture is much cheaper to buy than a probe station. Suitably designed quality test fixtures can be accurately characterised using in-fixture calibration techniques. As with coaxial calibration, the most appropriate algorithms use a combination of through, reflection and delay line standards, with common methods being through-reflect-match (TRL), TSD and line-reflect-line (LRL). The main reason for employing these types of calibration is that only one discrete impedance standard is required, such as an open or short, which is relatively easy to implement. The matched load is avoided; this is advantageous, as it is more difficult to fabricate non-planar 50 0001 loads to the same level of accuracy that can be
226 Microwave measurements achieved with low dispersion transmission lines. However, there are still significant disadvantages with in-fixture calibration: (1) Multiple delay lines may be required for wideband calibration (any one line must introduce between about 20 and 160 of electrical delay to avoid phase ambiguity, limiting the bandwidth contribution of each line to an 8:1 frequency range). (2) The use of multiple lines can add uncertainty to the measurements, since the launchers are continually being disturbed during calibration, although freely available software (called MultiCal™) can eliminate the effects of non-repeatability, by measuring either the same line a number of times or different lengths of line, in order to reduce the uncertainty [21]. (3) A frequency-invariant measurement reference impedance must be taken from the characteristic impedance, Z0 , of the delay lines, however, frequency dispersion in microstrip lines may not always be corrected for. In practice, the Z0 of the lines can be determined using TRL calibration [22,23] and then subsequent measurements can be renormalised to any measurement reference impedance. (4) The high level of accuracy is immediately lost with test fixtures that employ poor quality components and/or non-precision assembly. (5) The calibration substrates dictate and, therefore, restrict the location of the RF ports. (6) For devices with more than two ports the calibration procedure must be significantly extended and all the results from this routine must be easily stored and retrieved. (7) The microstrip-to-MMIC transition is not taken into account. 11.2.1.3 Equivalent circuit modelling Test fixtures made in-house tend to be simple in design, such as the type shown in Figure 11.1, and cost only a small fraction of the price of a good quality commercial test fixture. Unfortunately, these non-ideal test fixtures suffer from unwanted resonances [24], poor grounding [25] and poor measurement repeatability. The problem of unwanted resonances can be clearly seen in the F-D responses of Figure 11.2a. Here, the resonances at 3 and 12 GHz are attributed to the production grade coaxial connectors used in the test fixture. Because of poor repeatability, employing elaborate and expensive calibration techniques to characterise such fixtures would appear unjustified, because significant measurement degradation is inherent. As an alternative, equivalent circuit models (ECMs) can provide a crude but effective means of de-embedding. This ‘stripping’ process results in about the same level of degradation as would be found if in-fixture calibration was used with a non-ideal test fixture, but with minimal expense and greater flexibility. Also, ECMs based on the physical structure of the fixture have demonstrated a wide bandwidth performance. The ECMs can be easily incorporated into conventional F-D simulation software packages. They can also be employed to simulate packaged MMICs. An example of an ECM for a test fixture similar to the one in Figure 11.1 is shown in Figure 11.3. This model has
RFIC and MMIC measurement techniques 227 (a)
(b)
Figure 11.2
Embedded 55 0001 MMIC through-line: (a) frequency-domain power responses and (b) corresponding time-domain response for the input voltage reflection coefficient
228 Microwave measurements SMA connector/wedge-shaped launcher model
Coaxial connector
Lossy microstrip line model
Coax-to-microstrip transition C2
VNA reference plane
Figure 11.3
R1 TLINE 1 TLINE 2 TLINE 3
Z01 0001r1 00021 I1
Bond wire model
Z02 0001r2 00022 I2
Z03 0001r3 00023 I3
Wire 1 TLINE 4
R2 L1
Wire 2 L2 C1
Z04 0001r4
Im(i)
MMIC reference plane
Cf
I4
Equivalent circuit model of a microstrip test fixture
demonstrated a sufficient degree of accuracy from DC to 19 GHz for the popular Omni-Spectra SMA connector/wedge-shaped launcher [9], which is similar to the more popular SMA printed circuit board socket. The exact nature of the ECM, the element values and the microstrip parameter data are extracted from through-line measurements of the test fixture. Both a direct microstrip through-line and an MMIC through-line should be used in order to provide more information for the parameter extraction process, and to make it possible to model the microstrip-to-MMIC transition accurately. De-embedding can be carried out with most F-D CAD packages by converting the ECM into a series of negative elements connected onto the ports of the measured data. Some CAD packages provide a ‘negation’ function that allows the ECM sub-circuit to be directly stripped from the measured data. With either method, the order of the node numbers is critical, and the de-embedding routine should be verified. In addition to those already mentioned, de-embedding using equivalent circuit modelling has the following advantages: (1) dispersion in the microstrip lines does not have to be corrected for in the VNA’s calibration; (2) there is no restriction by the calibration procedure on the location of the RF ports; (3) systematic errors resulting from variations in the characteristic impedance of the chip carrier’s microstrip lines, due to relaxed fabrication tolerances, can easily be corrected for; (4) bond wires [26] and the microstrip-to-MMIC transition can be modelled [27]; (5) resonant mode coupling between circuit components, due to a package resonance, can also be modelled [24]. Better still, package resonances can, in some instances, be removed altogether [28,29].
RFIC and MMIC measurement techniques 229
Figure 11.4
Photograph of the Anritsu 3680V universal test fixture
11.2.2 One-tier calibration Improved contact repeatability and prolonged contact lifetime are two considerations that favour the two-tier process [6], as they are only assembled once with T-D gating and ECMs. In practice, however, to achieve the best performance, in-fixture TRL or line–network–network [30] calibration is applied directly to a quality test fixture, without the need for the two-tier coaxial calibration/de-embedding process. This onetier calibration procedure gives more accurate measurements than the two-tier method, since de-embedding is inherently prone to errors, and the propagation of measurement errors is reduced [6]. Using this approach, the Anritsu 3680 V universal test fixture, shown in Figure 11.4, can perform repeatable measurements up to 60 GHz. At the time of writing, a number of other companies produce test fixtures for accurate in-fixture calibration, including Agilent Technologies, Intercontinental Microwave, Argumens and Design Techniques. They are either split-block fixtures, with a removable centre section, or they use launchers attached to sliding carriages. With the high levels of accuracy that can be achieved using quality test fixtures, the poor characterisation of bond wires, due to the poor repeatability of conventional manually operated wire-bonding machines, becomes significant. Improvements in the modelling accuracy and physical repeatability of the microstrip-to-MMIC transition when using automatic wire-bonding assembly techniques have been reported [27]. In addition, flip-chip technology (also known as solder-bump technology) is now well established [31–39]. Here, a tiny bead of solder is placed on all the MMIC bond pads and the MMIC is placed upside down directly onto the chip carrier. When heated to the appropriate temperature, the solder flows evenly and a near perfect connection
230 Microwave measurements is made between the MMIC pad and its associated chip carrier pad. The advantages of this technology over bond wire technology, for the purposes of measurements, are its ultra-broad bandwidth, superior contact repeatability and high characterisation accuracy of the carrier’s transmission line-to-MMIC transition.
11.2.3 Test fixture design considerations The following guidelines are useful when selecting, designing or using a test fixture: (1) Split-block test fixtures [5,40] are ideal for two-port in-fixture TRL calibration, since they can provide good repeatability. Here, a short circuit standard is preferred, since significant energy may be radiated with an open circuit standard. (2) Side walls can form a waveguide or resonant cavity. The size of the waveguide/cavity should be made small enough so that the dominant mode resonant frequency is well above the maximum measurement frequency. Carefully placed tuning screws and/or multiple RF absorbing pads can eliminate or suppress unwanted modes [28,29]. (3) Poor grounding, due to excessively long ground paths and ground path discontinuities, must be avoided. (4) Avoid thick chip carrier substrates, wide transmission lines (sometimes used for off-chip RF de-coupling) and discontinuities, in order to minimise the effects of surface wave propagation and transverse resonances at millimetric frequencies. Transverse currents can be suppressed by introducing narrow longitudinal slits into the low impedance lines. (5) Use substrates with a high dielectric constant to avoid excessive radiation losses and to minimise unwanted RF coupling effects. (6) New precision connector/launchers should be used whenever possible, and measurements should be performed below the connector’s dominant TEM mode cut-off frequency. (7) Launchers should be separated from the DUT by at least three or four times the substrate thickness, so that any higher-order evanescent modes, generated by the non-ideal coax-to-microstrip transition, are sufficiently attenuated at the DUT.
11.3
Probe station measurements
Until relatively recently, the electrical performance of an MMIC was almost always measured using test fixtures. Nowadays, extremely accurate MMIC measurements can be achieved using probe stations. Such techniques were first suggested for use at microwave frequencies in 1980 [41], demonstrated experimentally in 1982 [42], and introduced commercially by Cascade Microtech in 1983. During the past two decades there have been rapid developments in probe station measurement techniques. Today, the partnership between Cascade Microtech and Agilent Technologies provides a total solution for on-wafer probing, which can perform repeatable
RFIC and MMIC measurement techniques 231 F-D measurements at frequencies as high as 220 GHz [43], although single-sweep measurements from 45 MHz to 110 GHz are routinely undertaken. When compared with test fixtures, commercial probe station measurements have the following advantages: (1) they are available in a single-sweep system from DC to 110 GHz; (2) they are more accurate and much more repeatable, since they introduce much smaller systematic errors; (3) they have a simpler calibration procedure, which can be automated with on-wafer calibration and verification standards [12,44]; (4) they enable the VNA measurement reference planes to be located at the probe tips or at some distance along the MMIC’s transmission line; in the latter case, transition effects can be removed altogether; (5) they provide a fast, non-destructive means of testing the MMIC, thus allowing chip selection prior to dicing and packaging; and (6) banded measurements are possible up to 220 GHz. Overall, the microwave probe station can provide the most cost effective way of measuring MMICs when all costs are taken into account.
11.3.1 Passive microwave probe design At frequencies greater than a few hundred megahertz, DC probe needles suffer from parasitic reactance components, due to the excessive series inductance of long thin needles and shunt fringing capacitances. If the needles are replaced by ordinary coaxial probes that are sufficiently grounded, measurements up to a few gigahertz can be achieved. The upper frequency is ultimately limited by the poor coax-to-MMIC transition. A tapered coplanar waveguide (CPW) probe provides a smooth transition with low crosstalk. Cascade Microtech have developed tapered CPW probes and microstrip hybrid probes (Infinity) that enable measurement to be made from DC to 110 GHz with a single coaxial input. With waveguide input, 50–75 GHz (V-band) or 75–110 GHz (W-band) [43] probes are available in both the tapered waveguide and Infinity versions, as shown in Figure 11.5. The Infinity probes are also available for 90–140 GHz (F-band), 110–170 GHz (D-band) and 140–220 GHz (G-band) operation. The maximum frequency limit for coaxial-input probes is imposed by the onset of higher-order modes propagating in the conventional coaxial cables and connectors. For W-band operation, Agilent Technologies developed a coaxial cable and connector that has an outer screening conductor diameter of only 1 mm, while Anritsu have their own 1.1 mm coaxial technology. A photograph illustrating the use of Agilent’s 1 mm coaxial technology to give state-of-the-art performance up to 110 GHz, with a Cascade Microtech Summit 12000 probe station, is shown in Figure 11.6. This arrangement uses the latest Agilent N5250 110 GHz VNA. Fully automatic calibration of the probing system can be performed up to 110 GHz. The D-band version is shown in Figure 11.7.
232 Microwave measurements
Figure 11.5
Photograph of a waveguide input Infinity probe
In the past, the tapered coplanar waveguide probe was made from an alumina substrate or an ultra-low-loss quartz substrate. The probe tips that made the electrical contacts consisted of hard metal bumps that were electroplated over small cushions of metal, allowing individual compliance for each contact. As the probes were overtravelled (in the vertical plane) the probe contacts wiped or ‘skated’ the MMICs’ probe pads (in the horizontal plane). One of the major limitations of these tapered CPW probes was their short lifetime, since the substrate had limited compliance and the probe contacts could wear down quite quickly. As a result, the more the probe was used, the more over-travel had to be applied to them. Eventually, either the probe substrate begins to crack or the probe tips fall apart. For this reason, GGB Industries developed the Picoprobe™. This coaxial probe is more compliant and can achieve operation between DC and 120 GHz, with a coaxial input, and between 75 and 120 GHz with a waveguide input [45]. From DC to 40 GHz, this probe has demonstrated an insertion loss of less than 1.0 dB and a return loss better than 18 dB. However, one potential disadvantage of coaxial probes is that the isolation between probes may be limited when operating above V-band. For even better compliancy, durability, ruggedness and flexibility, Cascade Microtech developed the Air Coplanar™ tipped coaxial probe [46]. This probe has demonstrated an insertion loss of less than 1.0 dB from DC to 110 GHz and can operate at temperatures from −65 to +200 ◦ C. A cross-sectional view and photograph can be seen in Figure 11.8.
RFIC and MMIC measurement techniques 233
Figure 11.6
Single-sweep, 10 MHz to 110 GHz, on-wafer probing system with Agilent’s N5250 110 GHz PNA series network analyser and the Summit 12971 probe
Cascade Microtech still produce the ACP probe, as it is useful for applications that require high power/bias use (above 500 mA), poor contact planarity, large pitches (above 250 µm) or temperatures above 125 ◦ C. Cascade Microtech’s latest generation of Infinity probes, shown in Figure 11.9, was initially designed to improve the contact resistance characteristics of probing onto aluminium pads but it also has significant advantages for probing onto gold pads. Figure 11.10 shows a comparison between the resistance characteristics of the tungsten ACP probe and Infinity probe, when probing onto aluminium. Inherent to the design is a coaxial-to-microstrip transition. This, in turn, uses vias to connect to extremely small contacts. The microstrip construction ensures vastly improved isolation between the underside of the probe and the measurement of the substrate underneath, allowing adjacent devices to be placed closer to the test structure. This design also dramatically improves the calibration and crosstalk characteristics. Moreover, as a result of the reduced contact size, as shown in Figure 11.11, the damage to the contact pads is also greatly reduced; this is very useful for tests that require multiple tests or with applications where very little pad damage is allowed.
234 Microwave measurements
Figure 11.7
Photograph of the banded, 110–170 GHz, on-wafer probing system Coaxial connector (b) (2.92, 2.4, 1.85 or 1mm)
(a)
Block
Hard absorber Absorber
Air coplanar waveguide
Figure 11.8
Soft absorber Low-loss cable
APC probe: (a) cross-sectional view of construction and (b) photograph
When selecting the type of microwave probe required, it is necessary to supply the vendor with the following specifications: (1) Footprint: Ground–signal–ground (GSG) is the most common for MMICs, although ground–signal (GS) probes are used below 10 GHz. (2) Probe tip contact pitch (i.e. distance between the mid-points of adjacent contacts): For microwave applications, 200 µm is very common, although
RFIC and MMIC measurement techniques 235 (a)
(b) Coax
Thin-film microstrip
Figure 11.9
Infinity tip: (a) illustration and (b) contact bumps in contact with wafer 0.25
Contact resistance, Ω
Conventional tungsten ACP
0.2 0.15 0.1 0.05
Infinity probe
0 0
1000
2000
3000
4000
5000
Figure 11.10
Variation of contact resistance with touchdowns for conventional tungsten ACP and Infinity probes
Figure 11.11
Contact damage from Infinity probes, typically 12 × 25µm2
236 Microwave measurements
(3) (4) (5) (6)
probes are commercially available with pitches ranging from 50 to 1250 µm. Smaller pads result in smaller extrinsic launcher parasitics. A 100 µm pitch is commonly used from applications in the 40–120 GHz frequency range, while 75 µm is used above 120 GHz. Probe tip contact width: 40 and 25 µm are typical for operation up to 65 and 110 GHz, respectively. Probe tip contact metal-plating: BeCu is optimised for GaAs chips (having gold pads) and tungsten is optimised for silicon and SiGe chips (having aluminium pads). Launch angle, φ. Coaxial connector type: The 3.5 mm Amphenol Precision Connector (APC3.5) is used for operation to 26.5 GHz; the Anritsu K-connector (2.92 mm), for single-mode operation to 46 GHz, is compatible with 3.5 mm connectors; the APC2.4 can be used for measurements up to 50 GHz, while the Anritsu V-connector (1.85 mm), for single-mode operation to 67 GHz, is compatible with 2.4 mm connectors; the Agilent Technologies 1 mm connector is used for operation up to 120 GHz, while the Anritsu W-connector (1.1 mm) has a cut-off frequency of either 110 or 116 GHz, depending on the coaxial dielectric used.
Cascade Microtech now sells probes that are capable of making on-wafer measurements in dual configurations, such as GSGSG. In the case of the dual infinity, this allows dual measurements up to 67 GHz. Such probes may be used in conjunction with modern four-port VNAs, such as Agilent’s N5230A PNA-L. If the launch angle is too small, unwanted coupling between the probe and adjacent on-wafer components may occur. For this reason, it is recommended that adjacent components have at least 600 µm of separation for 110 GHz measurements. On the other hand, if the angle is too large there will not be enough skate on the probe pads. It has been found analytically and empirically that the best angle occurs when the horizontal components of the phase velocity for the probe and MMIC transmission lines match one other [44]. Therefore 0006 0007 εeff . probe −1 φ = cos εeff . MMIC where εeff . probe is the effective permittivity of probe line and εeff . MMIC is the effective permittivity of MMIC line. For example, a CPW line on GaAs has εeff. MMIC ≈ 6.9 at 76.5 GHz and, therefore, φ = 68◦ with Air Coplanar™ probes, since εeff . probe = 1. However, in practice, the launch angle is approximately 20◦ . This may raise questions as to the possibility of launching unwanted parasitic modes, due to uncompensated velocity mismatches at the RF probe tip, and also fringe fields coupling from the RF probe tip into the wafer.
11.3.2 Probe calibration During the placement of probes onto an MMIC, there are two mechanisms by which the probe tips become soiled. First, since the probe tip contact’s metal-plating is
RFIC and MMIC measurement techniques 237 designed to be much harder than the MMIC probe pad ohmic contact’s metal, particles of either gold or aluminium will be deposited onto the respective BeCu or tungsten contacts. Second, it is not uncommon for the probe tip contacts to overshoot the unpassivated probe pads and scratch off some of the Si2 N3 (silicon nitride) passivation material surrounding the pads. Without regular cleaning, a build-up of gold/aluminium and Si2 N3 particles can form around the probe tip contacts. This build-up is likely to degrade the performance of measurements at millimetric frequencies. Therefore, prior to calibrating the measurement system, it is recommended that the probe tips be very gently cleaned. Here, forced-air can be blown onto the probe tip – in a direction parallel to the tip and towards its open contact end – in order to remove any particles. For more stubborn objects, a lint-free cotton bud, soaked in isopropanol (IPA), can be carefully brushed in a direction parallel to the tip and towards its open contact end. After the probe tips have been inspected for any signs of damage and cleaned, a planarity check must be made between the probes and the ultra-flat surface of the wafer chuck. A contact substrate, consisting of a polished alumina wafer with defined areas of patterned gold, is used to test that all three of the probe tip contacts (e.g. ground–signal–ground) make clear and even markings in the gold. Once this procedure is complete, the probe tip contacts can be cleaned of any residual gold by simply probing onto the exposed, un-metallised, areas of alumina. This is particularly important for tungsten contacts, because tungsten oxidises, and therefore the contact resistance would otherwise increase. However, this is not the case for BeCu contacts as they do not oxidise. Probe stations use a one-tier calibration procedure, with the standards located either on an impedance standard substrate (ISS) or on the test wafer. With a precision ISS, the standards can be fabricated to much tighter tolerances. For example, a pair of 100 0001 resistors are used to implement the CPW 50 0001 load reference impedance. Here, these resistors can be laser-trimmed to achieve an almost exact value of 50 0001, but at DC only. For D- and G-band operation, in order to reduce the effects of moding from the underside of the calibration substrate, Cascade Microtech produce a 250 µm thin ISS that, when used in conjunction with their ISS absorber blocks, drastically reduces the effects of substrate moding. It should be noted, however, that if a calibration is performed using a 635 µm thick alumina ISS and the verification is performed using 200 µm thick GaAs on-wafer standards (which is a realistic measurement scenario), then problems may be encountered at millimetric frequencies. This is because the probe-to-ISS interface is electromagnetically different from that of the probe-to-wafer interface. As a result, even though the specifications for corresponding calibration and verification standards may be identical, their measured characteristics may differ significantly. For this reason, the use of on-wafer standards is by far the best choice. This is because the probe-to-wafer interface can be electromagnetically the same for calibration, verification and all subsequent measurements. Moreover, on-chip launch transition discontinuities (e.g. probe pads and their transmission lines) can be treated as part of the overall measurement system to be calibrated. Ideally, the reference planes within the on-wafer standards should have the same line geometries as those at the on-chip
238 Microwave measurements DUT. The UK National Physical Laboratory (NPL) and the US National Institute of Standards and Technology (NIST) have developed GaAs ISS wafers with calibration standards and verification components of certified quality [47,48]. There are a number of calibration techniques that are used for on-wafer measurements [44,47–52]. The SOLT technique is not used at upper-microwave frequencies due to the poor quality of planar open standards. For TRL, the reflect standards (either an open or short circuit) must be identical at both ports, but they can be non-ideal and unknown. The TRL technique also requires a minimum of two transmission lines. The reference impedance is taken from the characteristic impedance, Z0 , of these lines [53]. Since a 50 0001 load is not required for TRL calibration, only transmission line standards are needed, and these are easily realisable on-wafer. In practice, in order to cover a useful frequency range, it is necessary to employ a number of different delay line lengths to overcome phase ambiguity at all the measurement frequencies. This means that the probe separation has to be adjusted during the calibration procedure. For many applications such as automated test systems this is a major limitation, and for these applications the line-reflect-match (LRM) calibration [49] is preferred to TRL. The multiple CPW delay lines required with the TRL calibration are effectively replaced by the CPW 50 0001 load, to theoretically represent an infinitely long delay line. This results in the following advantages: (1) (2) (3) (4) (5)
an ultra-wideband calibration can be achieved (e.g. DC to 120 GHz), the probes can be set in a fixed position, automatic calibration routines can be applied, reflections and unwanted modes in long CPW delay lines are avoided and a considerable saving of wafer/ISS area can be made.
With SOLT and LRM, the accuracy to which the load is known directly determines the accuracy of the measurement. In other words, perfect models are required for the load impedances. These loads inevitably have some parasitic shunt capacitance (which is equivalent to having negative series inductance), and furthermore, have frequencydependent resistance due to the ‘skin effect’. In addition, with microstrip technology there will be significant series inductance associated with the short and load standards. Cascade’s line-reflect-reflect-match (LRRM) calibration is a more accurate version of the standard LRM calibration, in which load-inductance correction is incorporated by including an extra reflection standard. NIST recently released some public domain software on the worldwide web called MultiCal™. This software provides a new method for the accurate calibration of VNAs [21–23]. Here, multiple and redundant standards are used to minimise the effects of random errors caused by imperfect contact repeatability. Moreover, with split-band methods (e.g. LRL and TRL), the calibration discontinuities at the frequency break points can be eliminated. With MultiCal™-TRL, only the physical lengths of the standards and the DC measurement of the line resistance per unit length (by applying a least-square error fit to the multiple shorted line lengths) are required. The Z0 of the lines can then be determined and subsequent measurements can be renormalised to the 50 0001 measurement reference impedance.
RFIC and MMIC measurement techniques 239 For the ultimate in ultra-wideband calibration, verification and measurement accuracy, there is strong support for having MultiCal™-TRL calibration for frequencies above a few gigahertz (say 1 GHz), combined with LRM for the frequencies below 1 GHz, using on-wafer standards. The LRM’s standards should be characterised at DC and at 1 GHz (using MultiCal™-TRL); conventional modelling techniques can be used to interpolate the results. A recent comparison was made between the calibration coefficients obtained from a NIST multiline calibration and those obtained from an assortment of other techniques; the results are shown in Figure 11.12. A two-port probe station traditionally uses a 12-term error model, although a 16-term error model has been introduced that requires five two-port calibration standards [54]. This more accurate model can correct for poor grounding and the additional leakage paths and coupling effects encountered with open-air probing. With the extremely high levels of accuracy that are possible with modern probe stations, the effects of calibration errors become more noticeable. Calibration errors can result from the following (in the order of greatest significance): (1) probe placement errors – position, pressure and planarity variations; (2) degradation with use in the probe tips and the standards’ probe pads surface wave effects on calibrations [55]; and (3) ISS manufacturing variations. It has been found that the effects of probe misplacement are greatly reduced when calibration is carried out on an automated probe. Cascade Microtech produce an automated calibration package, called WinCal, which allows full automation of the calibration on a Cascade semi-automatic probe station, such as the Summit 12000 or the 300 mm S300. Manual calibration is also possible. WinCal incorporates all the main family of calibrations (e.g. TRL, SOLT, LRM and also has LRM/LRRM
Figure 11.12
Comparison of calibration coefficients obtained from LRRM, LRM, SOLT and NIST multiline
240 Microwave measurements with auto load inductance compensation). Another routine, called Short Open Load Reflect, is included that allows accurate calibration to be conducted with non-ideal through-line standards. Such situations are almost unavoidable when device ports are orthogonal in nature. WinCal has the ability to measure, record and display S-parameters in a variety of formats and also carry out compensation to remove the effects of pad parasitics. A stability checker is also provided in order to determine the validity of the calibration at any given moment. With the extremely high level of measurement accuracy that can be achieved, the effects of on-chip launch transition discontinuities can be significant above a few gigahertz. So far, it has been assumed that the effects of probe pads and their associated transmission lines have been calibrated out. Here, the on-wafer calibration standards would have the same launch transition discontinuities as the on-chip DUT. However, effective de-embedding techniques can still be performed within the MMIC. If ECMs are to be employed, the foundry that fabricates the MMIC should provide very accurate models for probe pads and transmission lines. The metrologist must use these foundry-specific models to determine the actual measurements of the on-chip DUT. When de-embedding is performed using equivalent circuit modelling, these foundry-specific models can be easily incorporated into conventional F-D simulation software packages.
11.3.3 Measurement errors Even when the system has been successfully calibrated, measurement errors (or uncertainty) can still occur. Some of the more common sources of errors are as follows: (1) (2) (3) (4) (5) (6) (7)
probe placement errors, temperature variation between calibration and measurement, cable-shift induced phase errors between calibration and measurement, radiation impedance changes due to the probes/wafer chuck moving, matrix renormalisation not being performed with multiple port MMICs, resonant coupling of the probes into adjacent structures [56], low frequency changes in the characteristic impedance and effective permittivity of both microstrip and CPW transmission lines [56] and (8) optically induced measurement anomalies associated with voltage-tunable analogue-controlled MMICs [57].
11.3.4 DC biasing Depending on the nature and complexity of the device or circuit under test, DC bias can be applied to an MMIC in a number of ways: (1) through the RF probes, via bias-tees in the VNA’s test set; (2) through single DC needles mounted on probe station positioners; and (3) with multiple DC needles attached to a DC probe card, which may in turn be mounted on a positioner.
RFIC and MMIC measurement techniques 241 The DC probe needle has significant inductance, and as a result, provides RF de-coupling for the bias lines that helps to prevent stability problems. However, additional off-chip de-coupling capacitors and resistors can usually be added to the card to further minimise the risk of unwanted oscillations. With bias-tees and DC needles, the maximum DC bias voltage and current are approximately 40 V and 500 mA, respectively. With multiple DC needles, standard in-house DC footprints are recommended wherever possible, in order to provide card re-use. This will reduce measurement costs considerably. There is a limit to the maximum number of needles per card, but ten is typical. One needle is normally required to provide a ground reference.
11.3.5 MMIC layout considerations The foundry’s design guidelines will define a minimum distance between the centres of probe pad vias and the minimum distance from the vias to the edge of the MMIC’s active area. Generally, a particular company or institute may standardise on a certain pad size and pitch for a particular probe tip specification. In order to save expensive chip area, probing directly onto via-hole grounds is tempting. However, the probe tip contacts may puncture the gold pads on top of the via-holes, which could damage the probe tips and destroy the MMIC. While on-via probing can be used, in principle, it is likely that the chip would fail a subsequent QA inspection. As a result, when designing MMICs for on-wafer probed measurement, it is important to consult the foundry design guidelines for the probe pad specifications. The location and orientation of the probe pads must also be considered. If the pads associated with one port are too close to those of another port, the very fragile probe tips are at risk of severe damage if they accidentally touch one another during the probe alignment procedure. The minimum separation distance between probe tips is determined by the design rule on probe pad spacing (typically 250 µm with vias or 200 µm without vias, depending on the thickness of the chip). Moreover, if the spacing between port pads is less than 200 µm, there could be significant measurement errors due to RF crosstalk effects between probes. Finally, if three or four RF probe positioners are attached to the probe station then they will be oriented orthogonal to one another. As a result, the RF probe pads for a three- or four-port MMIC must also be orthogonal to one another. On the MMIC, launch transitions are required to interface between the probes and the DUT. In many cases, the DUT is in the microstrip medium, and so transitions from CPW-to-microstrip must be employed before and after the DUT. With reference to Figure 11.13a, microstrip launchers require through-GaAs vias to provide a low inductance earth path from the probe to the MMIC’s backside metallisation layer. A microstrip launcher should be long enough for the higher-order evanescent modes, resulting from the CPW-to-microstrip transition, to be sufficiently attenuated and have minimum interaction with the DUT. As a rule of thumb, the microstrip launchers should ideally have a length of three to four times the substrate thickness. With reference to Figure 11.13b, when the DUT is in the CPW medium, through-GaAs vias are not required and a matched taper from the probe pads to the DUT is used. Even though this taper is very short, if the 50 0001 characteristic impedance is not maintained throughout the transition, significant parasitic capacitance or inductance
242 Microwave measurements
Probe tip
G
Via to ground
G
G
S
S
S
G Source Drain
S
Source G
G (a)
Figure 11.13
G (b)
G (c)
Common launcher techniques: (a) microstrip, (b) coplanar waveguide and (c) direct probing onto a FET device
can be introduced. In special cases, launchers are not required at all for some devices. One example of this is with a simple FET structure, as shown in Figure 11.13c, where two GSG probes are placed directly onto the source–gate–source and source– drain–source pads. This approach eliminates the need for de-embedding the effects of launchers from the measurements, but the effects of the bond pads should still be considered. At this point, it is important to note that for frequencies above a few gigahertz, the equivalent circuit model of a device that has been characterised in one medium (e.g. microstrip or CPW) should only be used in circuits designed in the same medium. Single devices such as transistors and diodes can be biased through the bias-tees of the network analyser. However, in order to test a complete circuit using a probe station, special consideration has to be given to the layout of the DC bias pads and the design of the bias networks. When using DC needles to bias a circuit, the following points should be considered: (1) The foundry may impose minimum pad sizes and centre-to-centre pitch. (2) For ease of DC probe card fabrication and probe alignment, the DC probe pads should be arranged in a linear array along the edge of the chip’s active area, and should be kept away from the RF pads. A common method is to have the RF probe pads on the east and west edges of the chip, and the DC bias pads on the north and/or south edges. If layout constraints suggest that orthogonal RF inputs and outputs would be more convenient, first check that suitable positioners are available. (3) The bias networks of the circuit should be modelled separately to ensure that oscillations will not occur. Off-chip de-coupling capacitors cannot always be placed as near to the chip as they can be in a test fixture. (4) High-value resistors can be added on-chip to prevent RF leakage and catastrophic failure resulting from excess forward biasing of diodes and transistors. With varactor diodes, cold-FETs and switching-FETs, a trade-off may have to be made in the value of these bias resistors. If the resistance is too small there may not be enough RF isolation. If the resistance is too high the maximum switching speed may not be reached, due to an excessive R-C time
RFIC and MMIC measurement techniques 243 constant. In practice, a minimum resistance value of approximately 300 0001 should suffice for most applications.
11.3.6 Low-cost multiple DC biasing technique Conventional DC probe cards may need to be replaced for every new MMIC design, unless standard DC probe footprints can be used. This throwaway approach is very costly, especially when the DC probe cards are supplied by a commercial vendor (as automated and precision manufacturing techniques generally have to be used for aligning multiple needles). Moreover, the cost of the cards increases with the number of needles, as the individual needles are themselves precision-made components. A flexible, low-cost technique has been developed for providing an experimental active filter with multiple DC bias connections [58]. The MMIC is attached to a gold-plated chip carrier using conductive epoxy glue. An array of single-layer microwave capacitors is then attached to the chip carrier in close proximity to the MMIC. BAR-CAPS™, made by Dielectric Labs Inc., are ideal for this purpose since they are available as single-chip strips of three, four or six 100 pF shunt capacitors, each having a probeable area of approximately 650 × 325 µm2 and separated by approximately 170 µm. A gold bond wire is then used to connect the MMIC’s DC probe pad to its off-chip capacitor. As an example of this technique, a microphotograph of the experimental MMIC, requiring 15 DC bias lines, is shown in Figure 11.14. It has been found that this low-cost solution has a number of important advantages for use in the R & D laboratory. (1) The high-inductance bond wires and off-chip de-coupling capacitors minimise the risk of unwanted oscillations. (2) When designing the MMIC layout, the DC probe pads do not need to be arranged in a linear array along the edges of the chip. This provides greater design layout flexibility. (3) The linear array of off-chip capacitors automatically provides a standard in-house DC footprint, reducing long-term measurement costs considerably. (4) The probeable area of the off-chip capacitors is approximately 15 times larger than that of the MMIC probe pads and the capacitors can withstand greater mechanical forces. As a result, in-house DC probe cards can be made by hand because of the relaxation in manufacturing precision, reducing short-term costs considerably.
11.3.7 Upper-millimetre-wave measurements The past few years have seen considerable developments in the proposed uses of the millimetric frequency range above 75 GHz for new civil applications; for example, collision avoidance radar at 77 GHz. Also, the 94 GHz band is no longer dominated by military applications. High-resolution radiometric imaging at 94 and 140 GHz has a number of important applications, including aircraft landing systems, finding victims trapped in fires and locating concealed weapons without the use of X-rays. Ultra-high
244 Microwave measurements
Figure 11.14
Microphotograph of an experimental MMIC with multiple DC biasing using the low-cost technique [58]
data rate optical communications – using a ‘radio-fibre’ system at 180 GHz – could transform the way domestic computer networks are distributed. Future EC directives on environmental air pollution monitoring will require cheap high-performance terahertz sensors to be mass-produced. Sensors for sub-cellular probing are opening up new areas of medical research. Finally, passive tagging/identification systems are possible, which are both easy to conceal and extremely difficult to forge. With most (if not all) of these applications, monolithic technology will be sought. To this end, there have been major advances in both high electron mobility transistor (HEMT) and heterojunction bipolar transistor (HBT) technologies, both of which have attained values of fmax greater than 500 GHz [59,60]. Today, VNAs are commercially available that can operate in either broadband or banded configurations up to 110 GHz. The Agilent Technologies N5250 and the Anritsu ME7808B are examples of two broadband VNAs that are able to measure small-signal S-parameters from about 45 MHz to 110 GHz in a single-sweep. Both systems use coaxial cables between the test-sets and the probes. As frequency increases, the combined losses of all the components between the test-sets’ reflectometers and the MMIC under test (e.g. test-set combiners, transmission lines, probes, transitions and connectors) also increase. As a result, the overall system suffers from a reduction in both accuracy and stability [61]. The Anritsu 360B employs two test-sets: one rack-mounted (operating from 40 MHz to 67 GHz) and the other mounted on the probe station (operating from 67 to 110 GHz). Here, a test-set
RFIC and MMIC measurement techniques 245 combiner (or forward wave MUX coupler) is used to combine the signals from both test-sets. The drawback with this approach is the considerable losses associated with test-set combiners, which will degrade the effective directivity, source match and frequency tracking of the system at W-band. Ultimately, this will have an impact on the quality of calibrations and the system’s ability to hold a calibration in the presence of drift. The Agilent Technologies 8510XF minimises this problem by removing the need for a test-set combiner. Here, ultra-broadband (45 MHz to 110 GHz) directional couplers are utilised to create a single test-set [61]. In order to minimise the losses between the test-set’s reflectometer and the MMIC under test, a banded VNA is preferred. This can utilise coaxial cables up to W-band and metal-pipe rectangular waveguides at and/or above W-band. The UK’s National Physical Laboratory has recently established a new primary national standard measurement facility for S-parameters with rectangular waveguide operating over the frequency range of 75–110 GHz, using such a banded VNA system [62]. This facility represents a significant extension to the existing UK national standards for S-parameter and impedance measurements [63]. To date, there are still no traceable standards for on-wafer measurements above 75 GHz, from either NPL or NIST. This is due to a multitude of issues (e.g. mechanical precision, multi-moding, radiation effects, dielectric and surface wave propagation, ohmic losses in the dielectric and anomalous skin-effect losses in the conductors) associated with accurate calibration and verification measurements using non-ideal standards. However, there is a great deal of experimental work being undertaken to find the optimum calibration strategy for W-band [64–66]. With the ever-increasing interest in performing on-wafer measurements above 110 GHz, Oleson Microwave Laboratories Inc. can now supply frequency extension modules for the commercial market to include the following waveguide bands: WR-8 for F-band (90–140 GHz) [67]; WR-5 for G-band (140–220 GHz); and WR-3 for H-band (220–325 GHz). Cascade Microtech and GGB Industries supply the Infinity and Picoprobe™ on-wafer probes, respectively, for frequencies up to 220 GHz. In addition to these commercial systems, the University of Kent has developed an experimental passive on-wafer probing system. Here, ultra-low loss PTFE dielectric waveguides are used to avoid the problem of the skin-effect altogether [68–72]. The dielectric waveguide has been used to implement the multistate reflectometer, interconnecting transmission lines, and even the on-wafer probes. In principle, this system can operate from 118 to 178 GHz [72]. However, the ultimate challenge is to remove all the losses between the test-set’s reflectometer and MMIC under test. In an experimental set-up, a full two-port VNA has been implemented with active probes, enabling S-parameter measurements to be made from DC up to 120 GHz [73]. Here, high-speed non-linear transmission line (NLTL)-gated directional T-D reflectometers (which are essentially directional samplers) were realised using GaAs MMIC technology [74]. More recently, a 70–230 GHz VNA has been demonstrated that also employs MMIC reflectometers located on the on-wafer probes [75,76]. The NLTL-based active probes serve as S-parameter test-sets for the Agilent Technologies 8510 VNA. Using the Agilent Technologies 8510XF system, good agreement has been demonstrated from 70 to 120 GHz [75].
246 Microwave measurements
11.4
Thermal and cryogenic measurements
11.4.1 Thermal measurements In real-life applications, microwave circuits can be exposed to temperatures other than ambient room temperature (i.e. 23 ◦ C or approximately 296 K). For example, some components in geostationary orbiting satellites (e.g. within the antenna subsystem) may be periodically exposed to temperatures ranging from −150 to +80 ◦ C, depending on the amount of visible sunlight, the levels of localised heat generated within the satellite and the effectiveness of the thermal control sub-system. Also, Gunn diodes can have junction temperatures in excess of +200 ◦ C. At the other extreme, cryogenically cooled LNAs can operate at −196 ◦ C, with a liquid nitrogen cryogen having a boiling point temperature of 77 K. During the development of a sub-system, the levels of performance degradation while operating over a predefined temperature range must be known. Therefore, the temperature-dependent characteristics of all the MMIC components that make up a sub-system must be determined. Once the complete sub-system has been assembled, temperature-cycling is performed so that the measured levels of performance degradation can be compared with those predicted during simulation. The Cascade Microtech Summit S300-863 semi-automatic probing system, in conjunction with the Microchamber™ enclosure, enables very fast set-up and measurements to be performed up to 110 GHz in a dark, temperature controlled and electromagnetic interference-isolated environment. The Summit S300-973 thermal probing system [77] can be seen in Figure 11.15. The MMIC under test sits on a temperature controlled wafer chuck, which can be subjected to temperatures ranging from −65 to +200 ◦ C or from 0 to +300 ◦ C. Across these temperature ranges, the parameter values within, say, a FET’s equivalent circuit model exhibit a linear temperature dependency. Here, all the resistive and capacitive elements have a positive temperature coefficient, while Ids , gm and fT have negative temperature coefficients. Also, as the temperature drops, the gain of an active device can increase significantly. Therefore, to ensure linear operation, and thus avoid oscillation, the input RF power levels need to be reduced accordingly. Also, if the RF probes and cables exhibit large temperature gradients, significant phase changes will be found, even at low microwave frequencies. As a result, an air flow purge is introduced into the chamber in order to minimise the thermal coupling between the chuck and the probe/connector/cables. The air-flow purge also creates a dry, frost-free environment. The system is calibrated for every new wafer chuck temperature setting. An LRRM calibration is used, with the ISS located on a separate thermally isolated stage. The at-temperature calibration procedure can be performed 15 min after the chuck temperature has been changed. This short wait corresponds to approximately three thermal time constants for the probe/connector/cable assembly. Since all but the matched load impedance standards are insensitive to temperature, the ISS chuck temperature can be set at −5 ◦ C, for a wafer chuck temperature of −65 ◦ C. This approach results in less than a 1 per cent error in measurements between DC and 65 GHz.
RFIC and MMIC measurement techniques 247
Figure 11.15
Photograph of the Summit S300-973 thermal probing system, capable of over temperature measurements from −65 to 200 ◦ C
As a wafer chuck changes temperature it expands or contracts. For example, the total chuck expansion, from −65 to +200 ◦ C, can be about 230 µm. As a result, probe placement errors will become significant. Therefore, at each temperature, the overtravel of the probe tips may need to be adjusted. In addition, as the wafer diameter changes with temperature, there will be small changes in the spacing between devices. Cascade Microtech’s Summit series of semi-automatic thermal probe stations include control software that automatically compensates for such changes. This minimises the impact of measurement accuracy. Cascade Microtech now has a new microscopy system called Evue. This enables the contact height to be adjusted dynamically to ensure that the chuck is maintained at a constant height. This has the potential to enable fully automatic over temperature probing. Moreover, the technology employed in this system allows for an extremely large field of view that can be zoomed into a far smaller field of view at a single software command.
11.4.2 Cryogenic measurements Cryogenic hybrid MICs, employing high-performance active semiconductor and passive superconductor components, are being more widely used in applications ranging from radio astronomy, to space communications, to medical nuclear magnetic
248 Microwave measurements resonance scanners. Therefore, it is important to be able to determine the cryogenic temperature characteristics of these components [3–5,78–82]. At cryogenic temperatures, the noise figures of conventional GaAs transistors are reduced dramatically from their ambient room temperature values. For example, at 10 GHz the measured noise figure of a typical 0.6 × 100 µm MESFET is 0.8 dB at 300 K and only 0.4 dB at 35 K [80]. With HEMT technology, electron mobility can increase by a factor of 5 when the lattice temperature is reduced from 300 to 77 K [80], resulting in a considerable improvement in gain and noise performance. Furthermore, measurements made at temperatures as low as 10 K may provide information that can give a unique insight into the physics of experimental devices. Also, in addition to the advances being made in new semiconductor devices, there is considerable interest in the developments of ultra-low loss high temperature superconducting microwave components that currently have to be refrigerated below around 100 K. The first microwave test fixture to be used in cryogenic measurements was reported in 1976 [3]. The fixture was designed to be immersed in liquid nitrogen (LN2 ), which has a boiling point of 77 K. This approach suffers from the problems of poor accuracy and poor repeatability due to the changing temperature gradients exhibited by the cable/connector/launcher assembly, and requires a complicated calibration procedure. Accurate measurements have been reported using a TRL calibrated split-block test fixture mounted on the cold-head of an RMC Cryosystems™ LTS-22-IR helium refrigerator [5]. This approach enables small-signal S-parameter measurements to be made at 300 and 77 K. Cryogenic probe stations have either the MMIC under test and the probes immersed in liquid nitrogen or a liquid cryogen-cooled copper stage with a dry nitrogen vapour curtain. The former approach suffers from poor repeatability (due to varying amounts of LN2 ), a short measurement duration (in order to limit the build-up of ice formation) and a limited lifetime due to the degradation of the probes in contact with the LN2 . With the latter approach, accuracy is limited by mechanical stress, caused by the large thermal gradients between the microwave hardware and the MMIC under test. Also, reliability is limited by moisture and the build-up of ice, which increases the wear and tear on manipulators and requires extensive re-planarisation of the mechanical apparatus. Researchers at the University of Illinois have, however, demonstrated the design and operation of a cryogenic vacuum microwave probe station, for the measurement of S-parameters from DC to 65 GHz, which minimises the problems of limited accuracy and repeatability [80]. Within a vacuum chamber, the vacuum probe station has high-frequency CPW probes connected to cable feeds via a custom bellows and manipulator system. A liquid helium cryogen, with a boiling point temperature of 4.2 K, enables measurements to be performed at temperatures as low as 20 K. The copper stage is continually fed with liquid cryogen, and the system is then left to stand for 15–20 min in order to achieve temperature equilibrium. Once the at-temperature calibration has been performed, the actual device measurements can be taken for up to 4 h before having to recalibrate. Today, complete on-wafer cryogenic characterisation (from 20 to 300 K) can be performed for S-parameters, noise parameters and load-pull measurements [82].
RFIC and MMIC measurement techniques 249
11.5
Experimental field probing techniques
So far only invasive MMIC measurement techniques have been discussed, which generally do not perform internal function and failure analysis. However, one simple technique that can perform such tasks is to realise a coaxial probe with a highimpedance tip. Here, a 500 0001 resistor is used to create a potential divider with the 50 0001 oscilloscope. The internal node voltage can be measured without perturbing the operation of the circuit. This technique has been demonstrated on an MMIC power amplifier [83]. Alternatively, non-contacting methods also exist. Again, all the RF ports of the MMIC under test are terminated with matched loads. An RF signal is injected into the MMIC’s input port and a micron-level probing system is used to detect the internal signal strength. In the case of non-contacting techniques, different types of field are detected along transmission lines and at discontinuities. Field probing can detect current crowding, standing waves and unwanted modes of propagation, and S-parameters can be determined from T-D network analysis measurements.
11.5.1 Electromagnetic-field probing The simplest method of field detection uses a semiconductor diode. At microwave frequencies, however, it becomes difficult to match the diode because its impedance varies with power level. At low power levels, bolometers are traditionally employed for use above 1 GHz. The device is similar to a thin-film resistor, where a highresistivity bismuth film is evaporated onto metallic electrodes. When exposed to microwave radiation, the bolometer absorbs the electromagnetic energy and converts it into heat energy. As the film heats up, its resistivity decreases. Since the bolometer is inherently a square law detector, the measured voltage change across the device is proportional to the change in incident RF power. In practice, however, since the signal levels are so small, the incident microwave signal must be pulsed. This causes the resistance of the bolometer to change at the pulse repetition frequency, which is usually below 100 kHz. With a DC bias current applied, the low-frequency voltage signal across the bolometer is applied to a lock-in amplifier that acts as a coherent detector. This technique exhibits a high degree of sensitivity; as an example, a 4 × 5µm device with a noise equivalent power of 160 pW/Hz1/2 has been reported [84]. With the use of conventional probe microfabrication techniques, microbolometers can be employed to detect power levels as low as a few nanowatts along MMIC transmission lines. A microbolometer probe that can be used for microstrip and CPW transmission lines is illustrated in Figure 11.16. With a perfectly symmetrical probe positioned directly above a CPW line, the wanted CPW (or even) mode will be detected and the unwanted slotline (or odd) mode will not. As well as their simple fabrication and calibration, microbolometer probes can be designed to operate in the terahertz frequency range. Unfortunately, the attainable stability and uniformity of the resistive film does not yet appear to be sufficient for the commercial production of these probes. A more recent development uses a dielectric rod probe, with a thin copper strip at its end face that helps to pick up the electromagnetic field and couple it to the dielectric
250 Microwave measurements
Ι
Ι
To bias and lock-in amplifier
Bolometer
Figure 11.16
Illustration of an electromagnetic-field probe
waveguide [85]. Using this technique, measured results have been demonstrated between 200 and 220 GHz to show standing wave patterns on a mismatched dielectric waveguide [85].
11.5.2 Magnetic-field probing The simplest magnetic-field probing technique is to connect a conventional spectrum analyser to a magnetic-field probe. Using wafer probe microfabrication techniques, a miniature magnetic quadrupole antenna can be configured to match the magnetic fields associated with microstrip and CPW transmission lines, as illustrated in Figure 11.17. Placed directly above the transmission line, the lines of magnetic flux will come up through one loop and back down through the other loop. As a result, the induced signals add. From a distance, the probe sees a near uniform magnetic field which induces signals that tend to cancel each other out. In addition to amplitude, phase measurements can also be measured. A reference signal at the same frequency, with a variable amplitude and phase, is combined with the measured signal. The measured phase is equal to the reference phase when the amplitude displayed on the spectrum analyser is at its peak. Therefore, the probe can be used to measure the amplitude and phase of currents at any node within an MMIC. An experimental system has been reported that can operate in the 26.5–40 GHz frequency range [86]. Here, a 25–50 µm separation distance provides sufficient coupling and discrimination, while providing a negligible effect on the MMIC under test. One of the major sources of error is electrostatic pickup. Increasing the width of the loops increases the ratio of magnetic to electric coupling, but it also increases the random radiation picked up from other circuit elements. Reducing the width of the metal conductors reduces capacitive pickup, but increases the conductor’s resistance and self-inductance. In practice, an effective method of limiting the errors due to electrostatic pickup is to rotate the probe and average the measurements. This problem can be avoided by having just a single-loop probe [87].
RFIC and MMIC measurement techniques 251 To spectrum analyser
CPW feed line
Dielectric Quadrupole antenna
Figure 11.17
Illustration of a magnetic-field probe
11.5.3 Electric-field probing The simplest electric-field probing technique is to connect a conventional spectrum analyser to a near electric-field (i.e. capacitive) probe. This technique was first demonstrated on MICs in 1979 [88], but it is still being used today [89]. The probe can be simply realised by removing a small section of the outer screening conductor and dielectric from the end of the analyser’s coaxial feed line. Unfortunately, these probes have significant unwanted parasitic reactances at high microwave frequencies, which can severely perturb the operation of the circuit under test, thus causing measurement errors. However, micromachining techniques can be adopted to limit this problem, to realise dipole and monopole antennas [90]. In practice, this technique is only accurate when used with shielded transmission lines. As a result, it is unsuitable for micron-level features found in MMICs. Over the past decade, a number of alternative electric-field probing techniques have been investigated, with varying degrees of success. 11.5.3.1 Electron beam probing The voltage-contrast scanning electron microscope (SEM) was developed in the late 1960s for detecting voltages on the conductor tracks of integrated circuits. A pulsed electron beam stimulates secondary electron emissions from the irradiated surface of metals. For conductors at a negative potential, the secondary electrons have more energy than for conductors at a more positive potential. Commercial SEMs suffer from a poor millivolt potential sensitivity and limited bandwidths of only a few gigahertz [91], although larger bandwidths have been reported [92]. Also, apart from its very high complexity and cost, the electron beam may affect the operation of GaAs MMICs due to charging of deep levels in the GaAs substrate. However, the major advantage of this technique is that the attainable spatial resolution that can be achieved is in the order of a few angstroms.
252 Microwave measurements 11.5.3.2 Photo-emissive sampling Instead of using an electron beam to stimulate secondary electron emissions, another approach uses a high-intensity pulsed laser beam to illuminate the surface of the metals [91]. This T-D sampling technique offers an improved potential sensitivity and a greatly extended bandwidth. However, as with the SEM, the performance of GaAs MESFETs may be affected by charging of deep level traps. 11.5.3.3 Opto-electronic sampling Time-domain network analysis can be performed using opto-electronic sampling techniques. Here, electrical pulses can be generated on an MMIC by illuminating DC biased photoconductive switches with a pulsed laser beam. The optical excitation of a photoconductive switch can also perform signal sampling. By comparing the Fourier transforms of the sampled incident and reflected or transmitted waveforms, the complex two-port S−parameters can be determined for the DUT [91,93–99]. Sub-picosecond electrical pulse generation with a photoconductive switch has been reported, enabling terahertz measurement bandwidth [100]. This T-D opto-electronic sampling technique (also known as photoconductive sampling) requires the DUT to be embedded in a single-chip GaAs test fixture. Each RF port of the DUT is connected to a test structure consisting of a 50 0001 matched load termination, photoconductive switches, DC bias lines and a length of transmission line. These test components are not only wasteful of expensive chip space, but they must also be de-embedded from the measurements. In addition, the fabrication process of the photoconductive switches must be compatible with that of the MMIC under test. However, a DC to 500 GHz measurement system has been demonstrated [99]using this technique. 11.5.3.4 Electro-optic sampling The most promising electric-field probing technique is electro-optic sampling. A variety of non-centrosymmetric crystals, such as gallium arsenide and indium phosphide, exhibit Pockel’s electro-optic effect. The presence of an electric field will induce small anisotropic variations in the crystal’s dielectric constant, and therefore, its refractive index. If a laser beam passes through this material it will experience a voltage-induced perturbation in its polarisation, which is directly proportional to the change in the electric-field strength. As a result, this linear electro-optic effect can be used to provide a non-invasive means of detecting electric fields [91,93,94,101–111]. With internal (or direct) electro-optic probing the laser beam penetrates the GaAs MMIC in a reflection mode, as illustrated in Figure 11.18a, giving good beam access and requiring only a single focusing lens [91,93,94,101–103,107–111]. However, optical polishing of the MMIC substrate is required for best results. With front-side probing, the beam is reflected off the back-side ground plane metallisation, adjacent to the circuit conductor. With back-side probing, the beam is reflected off the back of the circuit conductor itself, making this scheme ideal for conventional CPW or coplanar strip lines and slotlines. Today, internal electro-optic sampling can achieve a spatial resolution down to less than 0.5 µm [110]. Centrosymmetric crystals, such as silicon and germanium, do not exhibit the linear electro-optic effect. Therefore, silicon MMICs must employ external (or indirect)
RFIC and MMIC measurement techniques 253 Back-side probing Slotline
Front-side probing
Electric-field lines
Probe beam
Ground plane
Microstrip line GaAs substrate
Probe beam
Ground plane (a) Probe beam
Fused silica needle Electro-optic crystal
(b)
Figure 11.18
Illustration of electric-field probe: (a) internal and (b) external
electro-optic probing [91,93,104–106]. This technique uses an extremely small electric field sensor, consisting of a 40 × 40 µm2 electro-optic crystal (lithium tantalate) at the end of a fused silica needle, placed in close proximity to the circuit conductor, as shown in Figure 11.18b. Sending a laser beam down the needle and measuring the induced change in the refractive index of the crystal from the returning beam can detect the conductor’s fringing fields. Since the beam can be focused down to a spot size of 3–5 µm in diameter, excellent spatial resolution is achieved. Also, there is no need for MMIC substrate polishing. With electro-optic probing, picosecond optical pulses (generated by a laser with an output power level that is lower than the band-gap energy of the MMIC’s semiconductor) pass through the electric fields associated with the MMIC’s circuit conductors. After being passed through a common beam splitter, the incident and return beams are combined, before being passed through a polarising beam splitter. Two photodiodes detect the intensity of the orthogonally polarised components and lock-in amplifiers are then used to determine the electric-field vectors. As a result, internal node voltage measurements can be determined and impressive two-dimensional mappings of the amplitude [105,107–109] and phase angles [109]
254 Microwave measurements of microwave fields within the MMIC can be obtained. T-D network analysis can also be performed using electro-optic sampling. Here, picosecond electrical pulses are applied to the input port of the MMIC under test, with the generator connected to the MMIC using traditional invasive techniques. By comparing the Fourier transform of the detected incident and reflected or transmitted waveforms, the complex two-port S-parameters can be determined. To date, a 50–300 GHz network analyser has been demonstrated using this technique [106]. A European consortium (which includes NPL and the Fraunhofer Institute for Applied Solid State Physics) has developed the first optical instrument capable of testing terahertz circuits and tracing the measurements back to international standards [111]. 11.5.3.5 Electrical sampling scanning-force microscopy A number of non-invasive measurement techniques have been introduced that can perform internal function and failure analysis of MMICs. The electron beam probing technique is well established and has excellent spatial resolution, but the temporal resolution is limited because of electron transit time effects. Optical probing techniques have a superior temporal resolution, but because of the micron-beam diameters they have a limited spatial resolution. Scanning-force microscopy, in the electrical sampling mode, is a relatively new non-contacting measurement technique that has high spatial, temporal and voltage resolutions [112,113]. Here, an atomically sharp needle is mounted on one end of a cantilever. When the needle is placed at a fixed working distance of between 0.1 and 0.5 µm above the MMIC, it will be subjected to attraction or repulsion forces, causing a detectable bending of the cantilever. This very experimental technique has so far demonstrated a spatial resolution of 0.5 µm and a bandwidth of 40 GHz [112].
11.6
Summary
A wide range of techniques has been briefly introduced for the measurement of MMICs. A summary of the main features associated with the most practical invasive techniques is given in Table 11.2. In general, the level of accuracy and repeatability Table 11.2
Comparison of the invasive measurement technologies Commercial test fixture
On-wafer probe station
1-tier
1-tier
1-tier
High Moderate Wideband Poor Low
High High Wideband Poor High
Very high Very high Ultra-wideband Poor Very high
In-house test fixture Calibration Accuracy Repeatability Bandwidth Flexibility Cost
2-tier with ECM de-embedding Moderate Moderate Wideband Excellent Very low
RFIC and MMIC measurement techniques 255 obtainable is proportional to the initial investment costs of the measurement system. Compared with traditional invasive on-wafer measurement techniques, optical systems have so far demonstrated a lower dynamic range and inferior frequency resolution. In addition, optical techniques have complicated and lengthy calibration procedures. However, with its excellent spatial resolution and extremely wide bandwidth capabilities, electro-optic probing may become commonplace in the not too distant future.
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258 Microwave measurements 48 Pence, J. E.: ‘Technique verifies LRRM calibrations on GaAs substrates’, Microwaves & RF, 1994, 505–07 49 Eul, H. J., and Schiek, B.: ‘Thru-match-reflect: one results of a rigorous theory for de-embedding and network analyzer calibration’, Proceedings of 18th European Microwave Conference, 1988 50 Pradell, L., Caceres, M., and Purroy, F.: ‘Development of self-calibration techniques for on-wafer and fixtured measurements: a novel approach’, Proceedings of 22nd European Microwave Conference, 1992, pp. 919–24 51 Ferrero, A., and Pisani, U.: ‘Two-port network analyzer calibration using an unknown ‘thru’, IEEE Microwave and Guided Wave Letters, 1992;2 (12):505–7 52 Purroy, F., and Pradell, L.: Comparison of on-wafer calibrations using the concept of reference impedance’, Proceedings of 23rd European Microwave Conference, 1993, pp. 857–859 53 Marks, R. B., and Williams, D. F.: ‘A general waveguide curcuit theory’, Journal of Research of the National Institute of Standards and Technology, 1992;97 (5):533–62 54 Silvonen, K. J.: ‘Calibration of 16-term error model’, Electronics Letters, 1993;29 (17):1544–5 55 Godshalk, E. M.: ‘Wafer probing issues at millimeter wave frequencies’, Proceedings of 22nd European Microwave Conference, 1992, pp. 925–30 56 Miers, T. H., Cangellaris, A., Williams, D., and Marks, R.: ‘Anomalies observed in wafer level microwave testing’, IEEE MTT-S International Microwave Symposium Digest, 1991, pp. 1121–24 57 Lucyszyn, S., and Robertson, I. D.: ‘Optically induced measurement anomalies with voltage-tunable analog-control MMIC’s’, IEEE Transactions on Microwave Theory and Techniques, 1998;MTT-46 (8):1105–14 58 Lucyszyn, S., and Robertson, I. D.: ‘Monolithic narrow-band filter using ultrahigh-Q tunable active inductors’, IEEE Transactions on Microwave Theory and Techniques, 1994;MTT-42 (12):2617–22 59 Smith, P. M., Liu, S.-M. J., Kao, and M.-Y. et al.: ‘W-band high efficiency InPbased power HEMT with 600 GHz fmax’, IEEE Microwave and Guided Wave Letters, 1995;5:230–2 60 Lee, Q., Martin, S. C., Mensa, D. et al.: ‘Deep submicron transferred-substrate heterojunction bipolar transistors’, Proceedings of Device Research Conference, 1998 61 Gibson, J.: ‘New capabilities for enhancing mm-wave network measurements’, Microwave Journal, 1998; 86–94 62 French, G., and Ridler, N.: ‘A primary national standard millimetric waveguide S-parameter measurements’, Microwave Engineering Europe, 1999; 29–32 63 Ridler, N. M.: ‘A review of existing national measurement standards for RF and microwave impedance parameters in the UK’, IEE Colloquium Digest, 1999, no. 99/008, pp. 6/1–6 64 Kok, Y.-L., DuFault, M., Huang, T.-W., and Wang, H., ‘A calibration procedure for W-band on-wafer testing’, IEEE MTT-S International Microwave Symposium Digest, 1997, pp. 1663–66
RFIC and MMIC measurement techniques 259 65 Marks, R. B.: ‘On-wafer millimeter-wave characterization’, Gallium Arsenide and its Applications Symposium Digest, 1998, pp. 21–6 66 Edgar, D. L., Elgaid, K., Williamson, F. et al.: ‘W-band on wafer measurements of active and passive devices’, IEE Colloquium Digest, 1999, pp. 2/1–6 67 Anritsu Co.: ‘140 GHz extender modules for vector network analyzers’, Microwave Journal, 1998; 148–50 68 Collier, R. J., and Boese, I. M.: ‘Microwave measurements above 100 GHz’, Proceedings of Microwaves and RF Conference, 1995, pp. 147–151 69 Boese, I. M., and Collier, R. J.: ‘Novel measurement system within 110–170 GHz using a dielectric multistate reflectometer’, Proceedings of 26th European Microwave Conference, 1996, pp. 806–10 70 Boese, I. M., Collier, R. J., Jastrzebski, A. K., Ahmed, H., Cleaver, J. R., and Hasko, D.: ‘An on wafer probe for measurements at 140 GHz’, IEE Colloquium Digest, 1997, pp. 9/1–7 71 Collier, R. J.: ‘Measurements of impedance above 110 GHz’, IEE Colloquium Digest, 1998, pp. 1/1–6 72 Boese, I. M., and Collier, R. J.: ‘Measurements on millimeter wave circuits at 140 GHz’, IEE Proceedings – Science, Measurement and Technology, 1998;145 (4):171–6 73 Yu, R., Reddy, M., Pusl, J., Allen, S., Case, M., and Rodwell, M.: ‘Full two-port on-wafer vector network analysis to 120 GHz using active probes’, IEEE MTT-S International Microwave Symposium Digest, 1993, pp. 1339–42 74 Rodwell, M., Allen, S., Case, M., Yu, R., Bhattacharya, U., and Reddy, M.: ‘GaAs nonlinear transmission-lines for picosecond and millimeter-wave applications’, Proceedings of 23rd European Microwave Conference, 1993, pp. 8–10 75 Wohlgemuth, O., Rodwell, M. J. W., Reuter, R., Braunstein, J., and Schlechtweg, M.: ‘Active probes for network analysis within 70–230 GHz’, IEEE Transactions on Microwave Theory and Techniques; 1999; 47 (12):2591–8 76 Wohlgemuth, O., Agarwal, B., Pullela, R. et al.: ‘A NLTL-based integrated circuit for a 70–200 GHz VNA system’, Microwave Engineering Europe, 1999; 35–39 77 D’Almeida, D., and Anholt, R.: ‘Device characterization with an integrated on-wafer thermal probing system’, Microwave Journal, 1993; 94–105 78 Laskar, J., and Kolodzey, J.: ‘Cryogenic vacuum high frequency probe station’, Journal of Vacuum Science Technology, 1990; 1161–5 79 Meschede, H., Reuter, R., Albers, J. et al.: ‘On-wafer microwave measurement setup for investigations on HEMT’s and high Tc superconductors at cryogenic temperatures down to 20 K’, IEEE Transactions on Microwave Theory and Techniques, 1992;MTT-40 (12):2325–31 80 Laskar, J., and Feng, M.: ‘An on-wafer cryogenic microwave probing system for advanced transistor and superconductor applications’, Microwave Journal, 1993, 104–14 81 Laskar, J., Lai, R., Bautista, J. J. et al.: ‘Enhanced cryogenic on-wafer techniques for accurate InxGa1-xAs HEMT device models’, IEEE MTT-S International Microwave Symposium Digest, 1994, pp. 1485–88
260 Microwave measurements 82 Laskar, J., Murti, M. R., Yoo, S. Y., Gebara, E., and Harris, H. M.: ‘Development of complete on-wafer cryogenic characterization: S-parameters, noise-parameter and load-pull’, Gallium Arsenide and its Applications Symposium Digest, 1998, pp. 33–38 83 Wei, C.-J., Tkachenko, Y. A., Hwang, J. C. M., Smith, K. R., and Peake, A. H.: ‘Internal-node waveform analysis of MMIC power amplifiers’, IEEE Transactions on Microwave Theory and Techniques, 1995;MTT-43 (12):3037–42 84 Schwarz, S. E., and Turner, C. W.: ‘Measurement techniques for planar highfrequency circuits’, IEEE Transactions on Microwave Theory and Techniques, 1986;MTT-34 (4):463–7 85 Basu, A., and Itoh, T.: ‘A new field-probing technique for millimeter-wave components’, IEEE MTT-S International Microwave Symposium Digest, 1997, pp. 1667–70 86 Osofsky, S. S., and Schwarz, S. E.: ‘Design and performance of a non-contacting probe for measurements on high-frequency planar circuits’, IEEE Transactions on Microwave Theory and Techniques, 1992;MTT-40 (8):1701–8 87 Gao, Y., and Wolff, I.: ‘A new miniature magnetic field probe for measuring three-dimensional fields in planar high-frequency circuits’, IEEE Transactions on Microwave Theory and Techniques, 1996;MTT-44 (6):911–18 88 Dahele, J. S., and Cullen, A. L.: ‘Electric probe measurements on microstrip’, IEEE Transactions on Microwave Theory and Techniques, 1980;MTT-28 (7):752–5 89 Gao, Y., and Wolff, I.: ‘Electric field investigations on active microwave circuits’, Proceedings of 26th European Microwave Conference, 1996, pp. 662–4 90 Budka, T. P., Waclawik, S. D., and Rebeiz, G. M.: ‘A coaxial 0.5–18 GHz near electric field measurement system for planar microwave circuits using integrated probes’, IEEE Transactions on Microwave Theory and Techniques, 1996;MTT-44 (12):2174–82 91 Bloom, D. M., Weingarten, K. J., and Rodwell, M. J. W.: ‘Probing the limits of traditional MMIC test equipment’, Microwaves & RF, 1987; 101–06 92 Kubalek, E., and Fehr, J.: ‘Electron beam test system for GHz-waveform measurements on transmission-lines within MMIC’, Proceedings of 22nd European Microwave Conference, 1992, pp. 163–8 93 Bierman, H.: ‘Improved on-wafer techniques evolve for MMIC testing’, Microwave Journal, 1990; 44–58 94 Lee, T. T., Smith, T., Huang, H. C., Chauchard, E., and Lee, C. H.: ‘Optical techniques for on-wafer measurements of MMICs’, Microwave Journal, 1990; 91–102 95 Huang, S.-L. L., Chauchard, E. A., Lee, C. H., Hung, H.-L. A., Lee, T. T., and Joseph, T.: ‘On-wafer photoconductive sampling of MMICs’, IEEE Transactions on Microwave Theory and Techniques, 1992;MTT-40 (12):2312–20 96 Kim, J., Son, J., Wakana, S. et al.: ‘Time-domain network analysis of mm-wave circuits based on a photoconductive probe sampling technique’, IEEE MTT-S International Microwave Symposium Digest, 1993, pp. 1359–61
RFIC and MMIC measurement techniques 261 97 Golob, L. P., Huang, S. L., Lee, C. H. et al.: ‘Picosecond photoconductive switches designed for on-wafer characterization of high frequency interconnects’, IEEE MTT-S International Microwave Symposium Digest, 1993, pp. 1395–98 98 Armengaud, L., Gerbe, V., Lalande, M., Lajzererowicz, J., Cuzin, M., and Jecko, B.: ‘Electromagnetic study of an electronic sampler for picosecond pulse measurements’, Proceedings of 23rd European Microwave Conference, 1993, pp. 751–4 99 Frankel, M. Y.: ‘500-GHz characterization of an optoelectronic S-parameter test structure’, IEEE Microwave and Guided Wave Letters, 1994;4 (4):118–20 100 Valdmanis, J. A., and Mourou, G.: ‘Subpicosecond electrooptic sampling: principles and applications’, IEEE Journal of Quantum Electronics, 1986;QE-22: 69–78 101 Bloom, D. M., Weingarten, K. J., and Rodwell, M. J. W.: ‘Electrooptic sampling measures MMICs with polarized light’, Microwaves & RF, 1987; 74–80 102 Mertin, W., Bohm, C., Balk, L. J., and Kubalek, E.: ‘Two-dimensional field mapping in MMIC-substrates by electro-optic sampling technique’, IEEE MTT-S International Microwave Symposium Digest, 1992, pp. 1443–6 103 Lee, C. H., Li, M. G., Hung, H.-L. A., and Huang, H. C.: ‘On-wafer probing and control of microwave by picosecond optical beam’, Proceedings of IEEE Asia-Pacific Microwave Conference, 1992, pp. 367–370 104 Wu, X., Conn, D., Song, J., and Nickerson, K.: ‘Calibration of external electro-optic sampling using field simulation and system transfer function analysis’, IEEE MTT-S International Microwave Symposium Digest, 1993, pp. 221–4 105 Mertin, W., Roths, C., Taenzler, F., and Kubalek, E.: ‘Probe tip invasiveness at indirect electro-optic sampling of MMIC’, IEEE MTT-S International Microwave Symposium Digest, 1993, pp. 1351–54 106 Cheng, H., and Whitaker, J. F.: ‘300-GHz-bandwidth network analysis using time-domain electro-optic sampling’, IEEE MTT-S International Microwave Symposium Digest, 1993, pp. 1355–58 107 Hjelme, D. R., Yadlowsky, M. J., and Mickelson, A. R.: ‘Two-dimensional mapping of the microwave potential on MMIC’s using electrooptic sampling’, IEEE Transactions on Microwave Theory and Techniques, 1993;MTT-41 (6/7):1149–58 108 David, G., Redlich, S., Mertin, W. et al.: ‘Two-dimensional direct electro-optic field mapping in a monolithic integrated GaAs amplifier’, Proceedings of 23rd European Microwave Conference, 1993, pp. 497–99 109 Mertin, W., Leyk, A., David, G. et al.: ‘Two-dimensional mapping of amplitude and phase of microwave fields inside a MMIC using the direct electro-optic sampling technique’, IEEE MTT-S International Microwave Symposium Digest, San Diego, 1994, vol. 3, pp. 1597–1600 110 David, G., Tempel, R., Wolff, I., and Jager, D.: ‘Analysis of microwave propagation effects using 2D electro-optic field mapping techniques’, Optical and Quantum Electronics, 1996;28:919–31
262 Microwave measurements 111 ‘Maps of electric fields traced back to standards’, Optics and Laser Europe (OLE) Magazine, 1997; 31–2 112 Bohm, C., Roths, C., and Kubalek, E.: ‘Contactless electrical characterization of MMICs by device internal electrical sampling scanning-force microscopy’, IEEE MTT-S International Microwave Symposium Digest, 1994, pp. 1605–8 113 Mueller, U., Boehm, C., Sprengepiel, J., Roths, C., Kubalek, E., and Beyer, A.: ‘Geometrical and voltage resolution of electrical sampling scanning force microscopy’, IEEE MTT-S International Microwave Symposium Digest, 1994, pp. 1005–8
Chapter 12
Calibration of automatic network analysers Ian Instone
12.1
Introduction
Network analysers are very complex instruments so it is important to define terms such as calibration to avoid confusion. The two dictionary definitions of calibration that can be applied to network analysers are ‘to mark (a gauge) with a scale of readings’ [1], and ‘to correlate the readings of (an instrument, etc.) with a standard to find the calibre of’ [1]. Unfortunately neither of these expressions defines the term calibration as it is applied to network analysers, instead they relate better to verification which is the process where the network analyser’s measurements are compared with those performed in a higher level laboratory.
12.2
Definition of calibration
Calibration in the network analyser sense is the process by which the errors within the instrument are compensated for, whereas verification checks that the resultant corrections have been properly assessed and applied. The extent of calibration used will depend on the desired measurement accuracy and the type of network analyser employed. To a large extent the available time will influence the type of calibration. There are two basic types of network analyser, both of them having their own advantages and limitations.
12.3
Scalar network analysers
The scalar network analyser usually consists of a source, display/processor and a transducer. Earlier scalar network analysers rarely included a receiver, instead they
264 Microwave measurements
Figure 12.1
Photograph of a typical wideband detector based scalar network analyser and accessories
normally employ wide band diode detectors that have the advantage of being able to make measurements over a very wide frequency range at high speed (Figure 12.1). Because this type operates over such a wide range the noise floor usually limits their low amplitude response to around −70 dBm. Diode detectors do not have a linear response to amplitude so the display/processor will also include a table of corrections (within the memory) that are applied to the measured values before being displayed. A very useful application of the scalar network analyser is its ability to characterise the transmission properties of mixers where the incident signal will be at a different frequency to the output signal. Filters might need to be selected to reject any unwanted signals generated by the mixer. More modern scalar network analysers are based on spectrum analysers (with one or more inputs) with a tracking generator (or two) included (Figure 12.2). With the rapidly decreasing costs of electronic equipment both the sources and receiver sections of these instruments are usually synthesised. A scalar network analyser of this design will be similar in complexity to its vector cousin, although it will lack many of the useful features (due to it being unable to measure the phase component of any signal). It will often have the advantage that it can be used as a standalone source or spectrum analyser, in some cases making it a more cost-effective solution.
Calibration of automatic network analysers 265
Figure 12.2
Photograph of a high-performance spectrum analyser based scalar network analyzer, which uses a high-performance external source as the tracking generator
Figure 12.3
Network, spectrum, impedance analyser combined with a test-set used for making a wide range of RF and LF measurements
Due to it using a spectrum analyser as the detector this type of scalar network analyser will usually have a very large dynamic range, and depending on the quality of the included spectrum analyser, will often have a good linearity characteristic. With the inclusion of digital filters this type of scalar network analyser can have a speed performance similar to that obtained using wideband detectors, but with a linearity and selectivity performance similar to that of the vector network analyser. Fully integrated analysers (Figure 12.3) are now available combining vector network, spectrum, impedance, gain, phase, group delay, distortion, harmonics, spurious
266 Microwave measurements and noise measurements in one instrument. When combined with a test set, these instruments provide reflection measurements, such as return loss, VSWR, voltage reflection coefficient and S-parameters in both real and imaginary units that can be displayed as magnitude and phase if desired. These instruments combine tremendous dynamic range (>140 dB is normal) with good linearity and full vector or scalar error-correction creating the ability to perform accurate measurements very quickly. At present these, due their complexity, useful instruments are limited to radio frequencies (RFs).
12.4
Vector network analyser
The vector network analyser consists of a display/processor, source, test set and receivers. Modern vector network analysers are usually encompassed in one compact enclosure (Figure 12.4). They are capable of measuring all of the small signal scattering parameters of a two-port device connected to it in near real time. Because the instrument employs a receiver (often with an adjustable bandwidth) it is able to make reliable measurements over a much wider amplitude range than with the wide band detector based scalar network analyser. The term ‘vector’ also demonstrates that the analyser is able to measure the quantity in terms of phase and magnitude. By using vector measurements we are able to fully characterise the analyser and then apply corrections when an item is measured. The major part of any errors introduced by the loading effects of the item being measured, or the analyser itself, can be effectively removed by calculation thereby producing very accurate values with reasonable speed. Modern analysers are able to display the measurements in a variety of formats including phase and magnitude, real and imaginary, impedance co-ordinates, etc. Despite their relatively high-cost vector network analysers are employed to make a variety of measurements where accuracy and speed are important.
Figure 12.4
Modern vector network analyser covering the frequency range 10 MHz to 67 GHz
Calibration of automatic network analysers 267
12.5
Calibration of a scalar network analyser
12.5.1 Transmission measurements Because scalar network analysers are unable to measure the phase component of any signal the calibration process is much simpler and faster than that necessary with the vector network analyser. Calibration for transmission measurements is simply a process of establishing a reference level to which the measured values will be referred. This is accomplished by connecting the detector to the source, allowing the instrument to sweep through the range of frequencies, and storing the values in the instrument’s memory. The device to be measured is then connected between the source and the detector and the instrument swept through the range of frequencies again. The difference between the first set of measurements (stored in memory) and the second set will be due to the device being tested plus any errors within the measurement system. Large potential errors with this type of measurement occur due to the mismatch loss uncertainties where the detector is connected to the source, and where the device being measured is connected to the source and detector. These uncertainties can be reduced by performing measurements through well-matched attenuators or couplers, but it is still likely that the mismatch loss uncertainties will dominate the uncertainty budget. In addition, where attenuators or couplers are used their value has to be chosen very carefully. High-value attenuators often have the best match and provide the best isolation against re-reflections and mismatch effects, but they also allow less of the signal to pass through, therefore reducing the effective dynamic range of the measurement. It is usually not practical to increase the source power as the higher power attenuators required to improve the match at the insertion point are often a poorer match than their lower power counterparts. Another alternative is to use a second detector and a power splitter. The ratio of the power appearing at the output ports of the power splitter is recorded (in the analyser’s memory) and the device to be measured is connected between one output port and its detector. The measurements are performed again and the difference between the first and the second measurements will be due to the device being tested. Using this configuration and by connecting an appropriate attenuator between the reference detector and the power splitter, and then, perhaps by using an amplifier increasing the signal generator’s amplitude between the first and second measurement it is possible to make measurements using the analyser over a much wider amplitude range than is specified. Spectrum analyser based instruments will enable a wider variety of attenuators or couplers to be used in the matching process as this type of analyser has a much wider dynamic range which copes with the additional losses much better.
12.5.2 Reflection measurements Calibrating prior to making reflection measurements follows a similar process of setting a reference and performing measurements relative to it. The input port of the bridge is connected to the generator and a short circuit connected to the bridge’s test port. The generator is swept through the range of desired frequencies and the values stored in the scalar network analyser’s memory.
268 Microwave measurements The short circuit is then replaced with an open circuit and the source is swept again through the range of desired frequencies and the values stored again in the analyser’s memory. The mean of these two sets of measurements is used as a reference and all measured values of reflection referred to it. It is important that the open circuit and short circuit are exactly 180◦ apart throughout the frequency range or further errors will be present in the measurement. Because an open circuit will always have a capacitance term associated with it and a short circuit effectively shunts any capacitance it is not normally possible to satisfy this requirement over the entire frequency range. The resultant errors are normally included as contributions to the uncertainty budget, having the most effect on the bridge’s source match estimate. As with transmission measurements, compromises are often made to ensure that the best quality measurement is performed without compromising speed or cost, etc. For instance, it is good practice to include a power splitter at the input to the bridge and connect a detector to the other output port of the power splitter. The scalar network analyser is then set to measure the ratio of the bridge over the detector’s output. The power splitter and detector perform three functions: (1) They measure and compensate for any variations in the generator’s output power which may not have been compensated for with the generator’s automatic level control. (2) When the directional bridge output port is loaded with different impedance devices connected to it (such as the short and open circuits and device being tested) it may cause the generator’s output amplitude to change. This phenomenon is almost eliminated by this arrangement. (3) The mismatch looking into the directional bridge’s test port is a contribution to the measurement uncertainties; if it can be improved the uncertainties will reduce. A typical microwave generator has a fairly poor mismatch, whereas power splitters have a fairly good mismatch in comparison. The mismatch of the generator or power splitter is transmitted through the bridge and will have an effect upon the resultant measurement uncertainties. When used in this configuration the effective output match of the power splitter is at its best, therefore transferring the best measurement conditions through the bridge. Unfortunately, as with transmission measurements, there is a downside. Every power splitter has loss and inserting more loss into the measuring system will reduce the dynamic range thereby increasing the noise floor. Power splitters and detectors also cost money and each item will have a maintenance cost associated with it so including additional items in the measurements will increase costs. Inserting a good quality attenuator between the directional bridge and the source will also improve the ‘effective source match’. To be effective the attenuator will need to have at least 20 dB transmission loss so it will not be suitable for most wideband detector systems. This method could be the most cost-effective for the spectrum analyser based system. A reasonably high value of attenuator will perform exactly the same function as the power splitter above but at a fraction of the cost.
Calibration of automatic network analysers 269
12.6
Problems associated with scalar network analyser measurements
The scalar network analyser measurement system consists of a microwave generator, detector (or a bridge and detector) and a scalar network analyser. The scalar network analyser is very similar to an oscilloscope in construction and operation. It has an input for the x-scale and several inputs for the detectors which display on the y-axis. The time base or x-axis is usually derived from the sweep output of the signal generator. Modern scalar network analysers also have a digital connection to the signal generator so that the display can be annotated with the start and stop frequencies, enabling easier control of the instruments. In addition, the digital connection is often used to connect to printers, plotters and disk drives to provide a permanent record of the test results. It can also be used to connect a computer so that the entire measurement process, presentation and archiving of results can be automated. The biggest problem with any measurement system employing diode type detectors is that they have different responses depending on the applied power level. At low powers (less than −30 dBm) they typically have a response proportional to the square of the applied power. As the power level increases their response becomes closer to a linear response. The designers of the early scalar network analysers tried to compensate for this effect by having active feedback loops in the conditioning amplifiers in the analyser; more modern instruments compensate for these effects digitally. Another problem is the limited dynamic range when compared to network analyser with a tuned front end. The diode detector often has a very wide frequency response (10 MHz to 26.5 GHz is common and 10–50 MHz is becoming more popular) which results in its ability to detect and add many very small signals across its operating spectrum. Where each of these signals might have a very small amplitude when they are all combined they effectively produce a noise floor of around −70 dBm. At this level the random component in the measurements is usually too large for sensible measurements to be performed so scalar network analyser measurements are often limited to −60 dBm. At the higher powers the detectors might suffer from being over loaded so most diode detectors are limited to a maximum input power of about +16 dBm.
12.7
Calibration of a vector network analyser
The vector network analyser as the name suggests also has the capability to measure the relative phase of the signals. The measurement system employs several receivers (usually three or four) to make the measurements as fast as possible without the need for extensive switching of the signals. On modern instruments the ‘resolution bandwidth’ is switchable allowing the user to make compromises between accuracy and speed. A process known as ‘accuracy enhancement’ is usually employed to reduce the errors in measurement due to the network analyser. Expressed simply, accuracy enhancement is the process whereby the network analyser is characterised using known standards so the errors within the measurement are removed mathematically. Each device, which is used for this characterisation, is manufactured to be excellent
270 Microwave measurements for only one parameter or purpose (e.g. a short should have 100 per cent reflection or a load should have 100 per cent absorption) so it is a lot easier to manufacture these ‘simple’ devices than the perfect couplers which might otherwise be required. A potential confusion in terms often occurs, the term ‘calibration’ when applied to vector network analysers is usually intended to describe the ‘accuracy enhancement’ process. The following paragraphs are taken from the Agilent Technologies 8722ES operating manual [2] and the Hewlett-Packard HP8753A operating manual [3] and describe in some detail the process of ‘accuracy enhancement’.
12.8
Accuracy enhancement
12.8.1 What causes measurement errors? Network analysis measurement errors can be separated into systematic, random and drift errors. Correctable systematic errors are the repeatable errors that the system can measure. These are errors due to mismatch and leakage in the test setup, isolation between the reference and test signal paths, and system frequency response. The system cannot measure and correct for the non-repeatable random and drift errors. These errors affect both reflection and transmission measurements. Random errors are measurement variations due to noise and connector repeatability. Drift errors include frequency drift, temperature drift, and other physical changes in the test setup between calibration and measurement. The resulting measurement is the vector sum of the test device response plus all error terms. The precise effect of each error term depends on its magnitude and phase relationship to the actual test device response. In most high-frequency measurements the systematic errors are the most significant source of measurement uncertainty. Since each of these errors can be characterised, their effects can be effectively removed to obtain a corrected value for the test device response. For the purpose of vector accuracy enhancement, these uncertainties are quantified as directivity, source match, load match, isolation (crosstalk) and frequency response (tracking). The description of each of these systematic errors follows. Random and drift errors cannot be precisely quantified, so they must be treated as producing a cumulative uncertainty in the measured data.
12.8.2 Directivity Normally a device that can separate the reverse from the forward travelling waves (a directional bridge or coupler) is used to detect the signal reflected from the test device. Ideally the coupler would completely separate the incident and reflected signals, and only the reflected signal would appear at the coupled output (Figure 12.5). However, an actual coupler is not perfect. A small amount of the incident signal appears at the coupled output due to leakage as well as reflection from the termination in the coupled arm (Figure 12.6). Also, reflections from the coupler output connector appear at the coupled output, adding uncertainty to the signal reflected from the device.
Calibration of automatic network analysers 271 Coupled output
Main coupler output
Input
Incident Reflected
Figure 12.5
Diagrammatic representation of an ideal directional coupler or directional bridge Coupled output
Main coupler output
Input Incident Reflected
Figure 12.6
Diagrammatic representation of an actual directional coupler or directional bridge showing the various error paths
The figure of merit for how well a coupler separates forward and reverse waves is directivity. The greater the directivity of the device, the better the signal separation. System directivity is the vector sum of all leakage signals appearing at the analyser receiver input. The error contributed by directivity is independent of the characteristics of the test device and it usually produces the major ambiguity in measurements of low reflection devices.
12.8.3 Source match Source match is defined as the vector sum of signals appearing at the analyser receiver input due to the impedance mismatch at the test device looking back into the source, as well as to adapter and cable mismatches and losses (Figure 12.7). In a reflection measurement, the source match error signal is caused by some of the reflected signal from the test device being reflected from the source back towards the test device and re-reflected from the test device. In a transmission measurement, the source match error signal is caused by reflection from the test device that is re-reflected from the source.
272 Microwave measurements Coupled output
Main coupler output
Input
DUT
Re-reflected
Reflected from the source
Reflected Incident
Figure 12.7
Diagrammatic representation of the constituent parts in the formation of source match
Input
Reflected Incident
Port 1
Port 2 DUT Reflected from load match Transmitted
Figure 12.8
Diagrammatic representation of the constituent parts in the formation of load match
The error contributed by source match is dependent on the relationship between the actual input impedance of the test device and the equivalent match of the source. It is a factor in both transmission and reflection measurements. Source match is a particular problem in measurements where there is a large impedance mismatch at the measurement plane (e.g. reflection devices such as filters with stop bands).
12.8.4 Load match Load match error results from an imperfect match at the output of the test device. It is caused by impedance mismatches between the test device output port and port 2 of the measurement system. Some of the transmitted signal is reflected from port 2 back to the test device. A portion of this wave may be re-reflected to port 2, or part may be transmitted through the device in the reverse direction to appear at port 1. If the test device has low insertion loss (e.g. a filter pass band), the signal reflected from port 2 and re-reflected from the source causes a significant error because the test device does not attenuate the signal significantly on each reflection (Figure 12.8). The error contributed by load match is dependent on the relationship between the actual output impedance of the test device and the effective match of the return port (port 2). It is a factor in all transmission measurements and in reflection measurements of two-port devices.
Calibration of automatic network analysers 273 The interaction between load match and source match is less significant when the test device insertion loss is greater than about 6 dB. However, source match and load match still interact with the input and output matches of the DUT, which contributes to transmission measurement errors (these errors are largest for devices with highly reflective ports).
12.8.5 Isolation (crosstalk) Leakage of energy between analyser signal paths contributes to error in a transmission measurement, much like directivity does in a reflection measurement. Isolation is the vector sum of signals appearing at the analyser samplers due to crosstalk between the reference and test signal paths. This includes signal leakage within the test set and in both the RF and IF sections of the receiver. The error contributed by isolation depends on the characteristics of the test device. Isolation is a factor in high-loss transmission measurements. However, analyser system isolation is more than sufficient for most measurements, and correction for it may be unnecessary. For measuring devices with high dynamic range, accuracy enhancement can provide improvements in isolation that are limited only by the noise floor. Generally, the isolation falls below the noise floor, therefore, when performing an isolation calibration the performer should use a noise reduction function such as averaging or reducing the IF bandwidth.
12.8.6 Frequency response (tracking) This is the vector sum of all test setup variations in which magnitude and phase change as a function of frequency. This includes variations contributed by signal π separation devices, test cables, adapters, and variations between the reference and test signal paths. This error is a factor in both transmission and reflection measurements.
12.9
Characterising microwave systematic errors
12.9.1 One-port error model In a measurement of the reflection coefficient (magnitude and phase) of a test device, the measured data differs from the actual, no matter how carefully the measurement is made. Directivity, source match and reflection signal path frequency response (tracking) are the major sources of error (Figure 12.9). To characterise the errors, the reflection coefficient is measured by first separating the incident signal (I) from the reflected signal (R), then taking the ratio of the two values. Ideally, (R) consists only of the signal reflected by the test device (S11A , for S11 actual) (Figure 12.10). However, all of the incident signal does not always reach the unknown. Some of (I) may appear at the measurement system input due to leakage through the test set or through a signal separation device. Also, some of (I) may be reflected by imperfect adapters between a signal separation device and the measurement plane. The vector
274 Microwave measurements
Measurement errors Directivity Frequency tracking Source match
S11M
S11A
Measured data
Figure 12.9
Unknown
Sources of error in reflection measurement
Incident power (I) R S11m = — I
S11A Reflected power (R)
Unknown
Figure 12.10
Reflection coefficient model
Effective directivity I
EDF
S11A
R
Unknown
Figure 12.11
Effective directivity (EDF ) model
sum of the leakage and the miscellaneous reflections is the effective directivity, EDF (Figure 12.11). Understandably, the measurement is distorted when the directivity signal combines with the actual reflected signal from the unknown, S11A. Since the measurement system test port is never exactly the characteristic impedance (50 0003), some of the reflected signal bounces off the test port, or other
Calibration of automatic network analysers 275
Source match I
EDF
S11A
ESF
R
Unknown
Figure 12.12
Source match (ESF ) model ERF frequency tracking
S11M
EDF
ESF
S11A
I
Figure 12.13
Reflection tracking (ERF ) model
impedance transitions further down the line, and back to the unknown, adding to the original incident signal (I). This effect causes the magnitude and phase of the incident signal to vary as a function of S11A and frequency. Levelling the source to produce a constant incident signal (I) reduces this error, but since the source cannot be exactly levelled at the test device input, levelling cannot eliminate all power variations. This re-reflection effect and the resultant incident power variation are caused by the source match error, ESF (Figure 12.12). Frequency response (tracking) error is caused by variations in magnitude and phase flatness versus frequency between the test and reference signal paths. These are mainly due to coupler roll off, imperfectly matched samplers, and differences in length and loss between the incident and test signal paths. The vector sum of these variations is the reflection signal path tracking error, ERF (Figure 12.13). These three errors are mathematically related to the actual data, S11A , and measured data, S11M , by the following equation: S11M = EDF +
(S11A ERF ) (1 − ESF S11A )
(12.1)
276 Microwave measurements
50 Ω
S11M = 0 EDF +
Figure 12.14
S11A = 0
(0) (ERF) 1–ESF (0)
‘Perfect load’ termination model
If the value of these three ‘E’ errors and the measured test device response were known for each frequency, this equation could be solved for S11A to obtain the actual test device response. Because each of these errors changes with frequency, their values must be known at each test frequency. These values are found by measuring the system at the measurement plane using three independent standards whose S11 is known at all frequencies. The first standard applied is a ‘perfect load’, which assumes S11 = 0 and essentially measures directivity (Figure 12.14). ‘Perfect load’ implies a reflection-less termination at the measurement plane. All incident energy is absorbed. With S11A = 0 the equation can be solved for EDF , the directivity term. In practice, of course, the ‘perfect load’ is difficult to achieve, although very good broadband loads are available in the compatible calibration kits. Since the measured value for directivity is the vector sum of the actual directivity plus the actual reflection coefficient of the ‘perfect’ load, any reflection from the termination represents an error (Figures 12.15 and 12.16). System effective directivity becomes the actual reflection coefficient of the near ‘perfect load’. In general, any termination having a return loss value greater than the uncorrected system directivity reduces reflection measurement uncertainty. Next, a short circuit termination whose response is known to a very high degree is used to establish another condition (Figures 12.17 and 12.18. The open circuit gives the third independent condition (Figures 12.19 and 12.20). In order to accurately model the phase variation with frequency due to fringing capacitance from the open connector, a specially designed shielded open circuit is used for this step (the open circuit capacitance is different for each connector type). Now the values for EDF , directivity, ELF , source match, and ERF , reflection frequency response, are computed and stored. This completes the calibration procedure for one-port devices.
12.10 One-port device measurement The unknown one-port device is measured to obtain values for the measured response, S11M , at each frequency.
Calibration of automatic network analysers 277 Actual directivity before correction (DA)
Γ of load (ΓL)
(–DM) Measured directivity before correction (DM) Effective directivity after correction (DA–DM = –ΓL)
Figure 12.15
Vector diagram showing how effective directivity (EDF ) is resolved
Figure 12.16
Network analyser display with a sliding load on port 1 (S11 ) and a lowband load connected to port 2 (S22 )
This is the one-port error model equation solved for S11A (Figure 12.21). Since the three errors and S11M are now known for each test frequency, S11A can be computed using the following equation: S11A =
(S11M − EDF ) ESF (S11M − EDF ) + ERF
(12.2)
278 Microwave measurements
S11A = 1∠180°
S11M = EDF +
(−1) (ERF) 1–ESF (−1)
Figure 12.17
Short circuit termination model
Figure 12.18
Network analyser display with short circuits connected to both ports (S11 and S22 )
S11A = 1∠
S11M = EDF +
Figure 12.19
(1∠
fc)
(ERF)
1–ESF (1∠
fc)
Open circuit termination model
fc
Calibration of automatic network analysers 279
Figure 12.20
Network analyser display with open circuits connected to both ports (S11 and S22 )
S11A
S11M = EDF +
Figure 12.21
S11A =?
(S11A) (ERF) 1–ESFS11A
Flow diagram representing the individual constituents of an S11 reflection measurement
For reflection measurements on two-port devices, the same technique can be applied, but the test device output port must be terminated in the system characteristic impedance. This termination should have as low a reflection coefficient as the load used to determine directivity. The additional reflection error caused by an improper termination at the test device’s output port is not usually incorporated into the one-port error model.
12.11
Two-port error model
The error model for measurement of the transmission coefficients (magnitude and phase) of a two-port device is derived in a similar manner. The potential sources of
280 Microwave measurements
Measurement errors Tracking
S21M Source match
S21A
Load match Measured value
Isolation Directivity Unknown
Figure 12.22
Major sources of error in transmission measurements of a two-port device (I)
(T)
Forward
S21M S21A
ETF
S12A =
S12M S12A
S21M ETF
(I) Reverse
(T)
Figure 12.23
S21A =
ETR
S12M ETF
Constituent parts of the transmission coefficient model
error are frequency response (tracking), source match, load match and isolation as shown in Figure 12.22. On a two-port network analyser these errors are effectively removed using the full two-port error model. The transmission coefficient is measured by taking the ratio of the incident signal (I) and the transmitted signal (T) (Figure 12.23). Ideally, (I) consists only of power delivered by the source and (T) consists only of power emerging at the test device output. As in the reflection model, source match can cause the incident signal to vary as a function of test device S11A . Also, since the test setup transmission return port is never exactly the characteristic impedance, some of the transmitted signals are reflected from the test set port 2, and from other mismatches between the test device output and the receiver input, to return to the test device. A portion of this signal may be re-reflected at port 2, thus affecting S21M , or part may be transmitted through the device in the reverse direction to appear at port 1, thus affecting S11M . This error term, which causes the magnitude and phase of the transmitted signal to vary as a function of S22A , is called load match, ELF (Figure 12.24). The measured value, S21M , consists of signal components that vary as a function of the relationship between ESF and S11A as well as ELF and S22A , so the input and
Calibration of automatic network analysers 281 Port 1
Port 2
S21
(I)
ESF
S11
(T)S21M
S22
Load match
Source match
ERF
Figure 12.24
ELF
S12
Load match error model
output reflection coefficients of the test device must be measured and stored for use in the S21A error-correction computation. Thus, the test setup is calibrated as described for reflection to establish the directivity, EDF , source match, ESF , and reflection frequency response, ERF , terms for reflection measurements on both ports. Now that a calibrated port is available for reflection measurements, the thru is connected and load match, ELF , is determined by measuring the reflection coefficient of the thru connection. Transmission signal path frequency response is then measured with the thru connected. The data are corrected for source and load match effects, then stored as transmission frequency response, ETF . Note: It is very important that the exact electrical length of the thru be known. Most calibration kits assume a zero length thru. For some connection types such as Type-N, this implies one male and one female port. If the test system requires a non-zero length thru, for example, one with two male test ports, the exact electrical delay of the thru adapter must be used to modify the built-in calibration kit definition of the thru.
Isolation, EXF , represents the part of the incident signal that appears at the receiver without actually passing through the test device (Figures 12.25 and 12.26). Isolation is measured with the test set in the transmission configuration and with terminations installed at the points where the test device will be connected. Since isolation can be lower than the noise floor, it is best to increase averaging by at least a factor of 4 during the isolation portion of the calibration. Note: If the leakage (isolation) falls below the noise floor, it is best to increase averaging before calibration. If it is not possible to increase the averaging it will be better to omit the isolation measurement.
Thus there are two sets of error terms, forward and reverse, with each set consisting of six error terms, as follows: • Directivity, EDF (forward) and EDR (reverse) • Isolation, EXF and EXR • Source match, ESF and ESR
282 Microwave measurements EXF
Isolation
EFT S21M
(I)
Port 1
Port 2
Figure 12.25
Isolation error model
Figure 12.26
Typical network analyser display during the isolation measurement
• • •
Load match, ELF and ELR Transmission tracking, ETF and ETR Reflection tracking, ERF and ERR
Network analysers equipped with S-parameter test sets can measure both the forward and reverse characteristics of the test device without the performer having to manually remove and physically reverse the device. A full two-port error model is illustrated in Figure 12.28. This illustration depicts how the analyser effectively removes both the forward and reverse error terms for transmission and reflection measurements.
Calibration of automatic network analysers 283
Figure 12.27
Typical network analyser display during the ‘through’ measurement Forward
EXF 1
S21A
ETF
S11A S22A
ELF
ESF ERF
S12A
RF IN
EDF S11M
Port 1 Reverse
Port 2
S21A S11A
S12M
ELR ETR
S21M
ERR ESR
S22A S12A
1
S22M EDR RF IN
EXR
Figure 12.28
Full two-port error model
The equations for all four S-parameters of a two-port device are shown in Figure 12.29. Note that the mathematics for this comprehensive two-port error model use all forward and reverse error terms and measured values. Thus, to perform full error-correction for any one parameter, all four S-parameters must be measured.
284 Microwave measurements
Figure 12.29
Mathematical representation of the full two-port error model algorithms
12.12 TRL calibration 12.12.1 TRL terminology Notice that the letters TRL, LRL, LRM etc. are often interchanged, depending on the standards used. For example ‘LRL’ indicates that two lines and a reflect standard are used and LRM indicates that a reflection and match standards are used. All of these refer to the same basic method. TRL∗ calibration is a modified form of TRL calibration. It is adapted for a receiver with three samplers instead of four samplers. The TRL∗ calibration is not as accurate as the TRL calibration because it cannot isolate the source match from the load match, so it assumes that load match and source match are equal. 12.12.1.1 How TRL∗ /LRL∗ calibration works The TRL/LRL calibration used in the network analyser relies on the characteristic impedance of simple transmission lines rather than on a set of discrete impedance
Calibration of automatic network analysers 285
R
B
A
Error adapter
(SA)
Error adapter
8 Error terms
Figure 12.30
Functional block diagram for a two-port error corrected network analyser measurement system employing only three receivers
standards. Since transmission lines are relatively easy to fabricate (e.g. in microstrip or co-axial), the impedance of these lines can be determined from the physical dimensions and substrate’s dielectric constant. For the analyser TRL∗ two-port calibration, a total of ten measurements are made to quantify eight unknowns (not including the two isolation error terms). Assume the two transmission leakage terms, EXF and EXR are measured using the conventional technique. The eight error terms are represented by the error adapters shown in Figure 12.30. Although this error model is slightly different from the traditional Full two-port 12-term model, the conventional error terms may be derived from it. For example, the forward reflection tracking (ERF ) is represented by the product of ε10 and ε01 . Also notice that the forward source match (ESF ) and reverse load match (ELR ) are both represented by ε11 while both the reverse source match (ESR ) and forward load match (ELF ) are represented by ε22 . In order to solve for these eight unknown TRL error terms, eight linearly independent equations are required. The first step in the TRL∗ two-port calibration process is the same as the transmission step for a full two-port calibration. For the thru step, the test ports are connected together directly (zero length thru) or with a short length of transmission line (non-zero length thru) and the transmission frequency response and port match are measured in both directions by measuring all four S-parameters. For the reflect step, identical high-reflection coefficient standards (typically open or short circuits) are connected to each test port and measured (S11 and S22 ). For the line step, a short length of transmission line (different in length from the thru) is inserted between port 1 and port 2 and the frequency response and port match are measured in both directions by measuring all four S-parameters.
286 Microwave measurements In total, ten measurements are made, resulting in ten independent equations. However, the TRL error model has only eight error terms to solve for. The characteristic impedance of the line standard becomes the measurement reference and, therefore, has to be assumed ideal (or known) and defined precisely. At this point the forward and reverse directivity (EDF and EDR ), transmission tracking (ETF and ETR ) and reflection tracking (ERF and ERR ) terms may be derived from the TRL error terms. This leaves the isolation (EXF and EXR ), source match (ESF and ESR ) and load match (ELF and ELR ) terms to discuss. 12.12.1.2 Isolation Two additional measurements are required to solve for the isolation terms (EXF and EXR ). Isolation is characterised in the same manner as the full two-port calibration. Forward and reverse isolation are measured as the leakage (or crosstalk) from port 1 to port 2 with each port terminated. The isolation part of the calibration is generally only necessary when measuring high-loss devices (greater than 70 dB). 12.12.1.3 Source match and load match A TRL calibration assumes a perfectly balanced test set architecture as shown by the term which represents both the forward source match (ESF ) and reverse load match (ELR ) and by the (ε22 ) term which represents both the reverse source match (ESR ) and forward load match (ELF ). However, in any switching test set, the source and load match terms are not equal because the transfer switch presents a different terminating impedance as it is changed between port 1 and port 2. In network analysers based on a three-sampler receiver architecture, it is not possible to differentiate the source match from the load match terms. The terminating impedance of the switch is assumed to be the same in either direction. Therefore, the test port mismatch cannot be fully corrected. An assumption is made, such that Forward source match (ESF ) = reverse load match (ELR ) = ε11 Reverse source match (ESR ) = forward load match (ELF ) = ε22 For a fixture, TRL∗ can eliminate the effects of the fixture’s loss and length, but does not completely remove the effects due to the mismatch of the fixture. Note: Because the technique relies on the characteristic impedance of transmission lines, the mathematically equivalent method (for line-reflect-match) may be substituted for TRL. Since a well matched termination is, in essence, an infinitely long transmission line, it is well suited for low-frequency calibrations. Achieving a long line standard for low frequencies is often physically impossible.
Most of the latest network analysers are equipped with four receiver test-sets. In this configuration they are able to implement the full TRL algorithm.
12.12.2 True TRL/LRL Implementation of TRL calibration with a network analyser which employs four receivers requires a total of fourteen measurements to quantify ten unknowns as
Calibration of automatic network analysers 287 opposed to only a total of twelve measurements for TRL∗ (both include the two isolation error terms). Because of the four-sampler/receiver architecture, additional correction of the source match and load match terms is achieved by measuring the ratio of the two ‘reference’ receivers during the thru and line steps. These measurements characterise the impedance of the switch and associated hardware in both the forward and reverse measurement configurations. They are then used to modify the corresponding source and load match terms (for both forward and reverse). The four receiver configuration with TRL calibration establishes a higher performance calibration method over TRL∗ , because all significant error terms are systematically reduced. With TRL∗ , the source and load match terms are essentially that of the raw, ‘uncorrected’ performance of the hardware where as with TRL the source and load match terms are reduced in line with the quality of calibration kit components used.
12.12.3 The TRL calibration procedure When building a set of standards the requirements for each of the standard types specified in Table 12.1 must be satisfied. Table 12.1
TRL calibration procedure: requirements for each of the standard types
Standard types
Requirements
Thru
No loss Impedance (Z0 ) need not be known S21 = S12 = 1∠0◦ S11 = S22 = 0
Thru (non-zero length)
Z0 of the thru must be the same as the line. Attenuation of the thru need not be known. If the thru is used to set the reference plane, the insertion phase or electrical length must be well known and specified
Reflect
Reflection coefficient 0007 magnitude is optimally 1.0, but need not be known. Phase of 0007 must be known and specified to be within ±1/4 wavelength or 90◦ . 0007 must be identical on both ports. If the reflect is used to set the reference plane, the phase response must be well known and specified.
Line/match (line)
Z0 of the line establishes the impedance of the measurement (i.e. S11 = S22 = 0). Insertion phase of the line must be different from the thru. Difference between thru and line must be >20◦ and <160◦ . Attenuation need not be known. Insertion should be known
Line/match (match)
Z0 of the match establishes the reference impedance of the measurement. 0007 must be identical on both ports
288 Microwave measurements When calibrating a network analyser, the actual calibration standards must have known physical characteristics. For the reflect standard, these characteristics include the offset in electrical delay (seconds) and the loss (0003 per second of delay). The characteristic impedance, Z0 , is not used in the calculations in that it is determined by the line standard. The reflection coefficient magnitude should optimally be 1.0, but need not be known since the same reflection coefficient magnitude must be applied to both ports. The thru standard may be a zero ss-length or known length of transmission line. The value of length must be converted to electrical delay, just like that done for the reflect standard. The loss term must also be specified. The line standard must meet specific frequency-related criteria, in conjunction with the length used by the thru standard. In particular, the insertion phase of the line must not be the same as the thru. The optimal line length is 14 wavelength (90◦ ) relative to a zero length thru at the frequency of interest, and between 20◦ and 160◦ of phase difference over the frequency range of interest. (Note: these phase values can be ±N × 180◦ , where N is an integer.) If two lines are used the difference in electrical length of the two lines should meet these optimal conditions. Measurement uncertainty will increase significantly when the insertion phase nears zero or is an integer multiple of 180◦ , and this condition is not recommended. For a transmission medium that exhibits linear phase over the frequency range of interest, the following expression can be used to determine a suitable line length of 1 4 wavelength at the frequency (which equals the sum of the start frequency and stop frequency divided by 2): Electrical length (cm) = (Line − Zero length thru) Electrical length (cm) =
(15,000 × VF) f1 (MHz) + f2 (MHz)
(12.3)
where f1 = 1000 MHz, f2 = 2000 MHz and VF = Velocity Factor = 1. Thus the length to initially check is 5 cm. Next, use the following to verify the insertion phase at f1 and f2 (1000 and 2000 MHz): (360 × f × l) (12.4) v where f is the frequency (MHz), l is the length of line (cm) and v = velocity = speed of light × velocity factor, which can be reduced to the following: Phase (degrees) =
0.012 × f (MHz) × l (cm) (12.5) VF So for an airline (velocity factor is approximately 1) at 1000 MHz, the insertion phase is 60◦ for a 5 cm line; it is 120◦ at 2000 MHz. This line would be suitable as a line standard. Where the standard is fabricated in other media (microstrip for instance) the velocity factor is significant. For example, if the dielectric constant for a substrate is 10, and the corresponding ‘effective’ dielectric √ constant for microstrip is 6.5, then the ‘effective’ velocity factor equals 0.39 (1 + 6.5). Phase (degrees) approximately =
Calibration of automatic network analysers 289 Using the above a potential problem using TRL becomes evident. The lengths of airline required at low frequencies become so long that they are difficult to fabricate.
12.13 Data-based calibrations Traditionally the calibration standards used in any network analyser calibration routine have been defined in terms of the way in which their parameters vary in relation to the measurement frequency; for instance, the open circuit would be defined in terms of capacitance. Three or four frequency terms would be employed, f , f 2 , f 3 and sometimes f 4 . Open circuits would be defined in a similar manner, in terms of inductance. As correction algorithms progressed some standards were defined in terms of both capacitance and inductance. Loads were usually considered as perfect. These definitions are usually excellent providing that it is possible to define the standards using smooth curves. As processors and particularly memory have become cheaper another method of defining the calibration standards has become available, the data-based calibration. Each standard is measured across the frequency range of interest using the best equipment and techniques available. These measured values are entered into the network analyser’s database and used in the correction algorithms. At frequencies where data are not available the network analyser uses interpolation, thus if measurements are made at more frequencies on the standards, the resulting network analyser measurements will become more accurate. Electronic calibration units, where the standards are in one enclosure and a switch matrix employed to apply them to the network analyser, often use a data-based calibration routine. The accuracy available from the data-based calibration employing the electronic calibration units approaches the best available from TRL calibrations, but without needing the same level of skilled operator.
References 1 J.M. Hawkins (ed.): The Oxford Reference Dictionary. (Oxford University Press, Oxford, 1987, reprinted 1989) 2 8719ET/20ET/22ET, 8719ES/20ES/22ES Network Analysers User’s Guide, Agilent Technologies, Inc. 2000 3 HP8753A Network Analyser Operating and Programming Reference–0875390015, Hewlett-Packard Company, 1986. Now Agilent Technologies, Inc.
Chapter 13
Verification of automatic network analysers Ian Instone
13.1
Introduction
Network analysers are complex instruments that can combine many different instruments within one measurement system. With this in mind it is easy to make apparently similar measurements with a variety of different instrument settings. Each setting may enhance one particular aspect of the measurement, but this is often traded off in another area. For example, to improve repeatability we might increase the averaging or decrease the bandwidth or use a combination of both. The resulting improvement in repeatability will usually be at the expense of the considerably increased measurement time. This chapter discusses different types of verification which may be applied to network analyser measurements to enable the user to assess or confirm the most appropriate choice of settings on the network analyser for their particular measurement scenario.
13.2
Definition of verification
As with calibration, it is important to understand the interpretation of the word ‘verification’. The Oxford Reference Dictionary (1989) defines the word ‘verify’ as ‘to establish the truth or correctness of by examination or demonstration; (of an event etc.) to bear out, to fulfil (a prediction or promise)’. This dictionary definition exactly describes the process of verification as applied to automatic network analysers; the quality of measurements which the analyser is capable of making is verified by comparing them with values obtained from another source, whereas calibration characterises the network analyser prior to ‘corrected’ measurements being performed.
292 Microwave measurements
13.3
Types of verification
There are several different methods of verification so the method chosen needs to address the particular requirements of the user. In all cases the method chosen or designed should provide the user with at least acceptable confidence that the measurements being made with the network analyser meet the user’s minimum quality requirements. Verification limits are set using a combination of the measurement uncertainties and the acceptable product quality. Uncertainties should be assessed using an accepted method such as that described in EA-10/12, Guidelines on the Evaluation of Vector Network Analysers, available free from http://www. euromet.org/docs/calguides/index.html
13.3.1 Verification of error terms As described in the previous chapter, the corrected network analyser’s display is made up of the following elements: (1) (2) (3) (4)
parameters of the device under test (DUT), errors contributed by the measurement system, corrections applied to the measurements and residual errors present after correction.
Verification of the network analyser’s residual errors after correction involves measuring and quantifying the residual errors present after the error correction has been applied. This method is perhaps one of the most difficult to perform, is the most time consuming, and requires the highest skill levels, but will enable the user to determine exactly which components may require attention without any additional measurements having to be performed. Typically, this type of verification provides the greatest insight into the characteristics of the network analyser and calibration kit used.
13.3.2 Verification of measurements This verification scheme involves calibrating the network analyser (usually as part of the normal measurement process) and then measuring a known artefact(s). Appropriate acceptance limits must be set when using this method as it is often possible for one parameter showing poor performance to be masked by other parameters where performance exceeds minimum expectations. Whilst this method provides the best assessment of all the contributors combining in the uncertainty budget, the danger is that one component in the calibration kit or network analyser which is beginning to deteriorate is masked by other parameters that are still exceeding expectations. This method, however, is one of the easiest to implement, easiest to understand and quickest to perform so warrants consideration on these points alone. On a production line this method might be implemented by periodically taking a ‘sample’ DUT and re-testing it on a different network analyser or measurement system. If the measurements from both systems are compared and the results found
Verification of automatic network analysers 293 to fall within the user’s acceptable quality limits it can be assumed that both systems are making acceptable measurements. This method is often used by network analyser manufacturers and their service agents when maintaining customer’s equipment at the customer’s site.
13.4
Calibration scheme
It should be possible to perform verification of the network analyser irrespective of the calibration scheme used. The correction coefficients employed as a result of the calibration may affect the acceptance limits used for the verification but should have little or no influence on the method of verification. Ideally the calibration scheme employed will be identical to that used for measurements, and might even be exactly the same calibration. As the verification verifies the satisfactory operation of the network analyser, test port leads, adapters and calibration kit, it is essential to ensure that all of these items are used in the calibration and verification process.
13.5
Error term verification
For a full two-port measurement seven dominant error terms that could be checked are as follows: (1) (2) (3) (4) (5) (6) (7)
effective directivity, effective source match, effective load match, effective isolation, effective tracking, effective linearity and repeatability.
The term ‘effective’ as used in the list above refers to the parameter after error correction has been applied. These terms are often referred to as the residual errors, which are also contributors to the uncertainty of measurement. Methods for checking most of these terms are shown in EA-10/12.
13.5.1 Effective directivity Directivity refers to the ability of a directional device, such as a coupler or directional bridge, to separate the forward and reverse signals. Where the bridge or coupler is embedded in a network analyser the most convenient way to measure this parameter is to first reflect all of the signal using a short or open circuit (the mean between the short and open circuit is considered the most accurate in this simplistic case) and set as a reference. The short or open circuit is then replaced with a fixed termination of the correct characteristic impedance. Where the fixed termination has a good match (negligible voltage reflection coefficient) the network analyser’s display will be
294 Microwave measurements
Figure 13.1
Typical network analyser display of the voltage reflection coefficient of a fixed broadband load
predominantly composed of the effective directivity. Since the perfect termination rarely exists, we need some method of separating the network analyser’s own errors from those generated by the fixed termination. These errors tend to increase as the measurement frequency increases. Two methods of ‘signal separation’ are discussed below (Figure 13.1). 13.5.1.1 Sliding load method A sliding load can be used to separate the directivity from the terminating load. Where possible the network analyser should be set to display the measurements in ‘linear mode’. After the reference has been recorded the sliding load is connected in place of the open or short circuits. If the load element is positioned furthest away from the input connector the network analyser will display a curve representing the match of the sliding load’s load element with ripple superimposed upon the measurement. The majority of ripple is produced by the directivity either adding ‘in phase’ or ‘anti-phase’ with the load element measurement. There will also be a small error produced in this measurement contributed by the effects of imperfect source match and an imperfect sliding load element; however, this error is often so small that it is neglected. The directivity may be assessed by measuring the height of the ripples: directivity will be one-half the ripple amplitude. Sometimes the transitions in match of the sliding load make the measurement of the superimposed ripple difficult or impossible. In these cases it will be necessary to make a continuous waves (CW) measurement. The network analyser’s marker is placed at the frequency of interest. The sliding load is adjusted so that a maximum value is observed using the marker and the value noted. The sliding load is now adjusted so that a minimum value is observed using
Verification of automatic network analysers 295 the marker and the value noted. The directivity is one-half of the difference between the two marker values. The major problem in using a sliding load is that measurements on sliding loads are difficult to perform and traceability for these measurements may not be easy to obtain. 13.5.1.2 Offset load or airline method This method works in a very similar way to the sliding load method. After the reference has been recorded the airline and fixed termination are connected in place of the open or short circuits. The network analyser will display a curve representing the match of the fixed termination with ripple (from the directivity) superimposed upon the measurement. Half of the amplitude of the ripple is the directivity. This method has the same problem as the sliding load method regarding the effects of source match. Providing the fixed termination has a small reflection coefficient this problem will be kept to a minimum (Figures 13.2 and 13.3). Where the fixed termination shows a rapid transition between two values of reflection coefficient it may not be possible to make an accurate measurement of directivity. Since this method should be independent of the fixed termination used, it will be perfectly valid to select another fixed termination with a different reflection coefficient profile to provide more reliable directivity measurements at these more difficult frequencies. The calibration devices used to characterise the effective directivity term are the low-band load (at lower frequencies), and the sliding load or short airline(s) at high frequencies except in broadband load calibrations where the broadband load is used
Figure 13.2
Ripple superimposed on the fixed load response caused by the interaction of directivity and the broadband load
296 Microwave measurements
Figure 13.3
Using another broadband load with a different profile can make the ripples easier to determine
exclusively to define the directivity term. The types of measurement most affected by directivity errors are low-reflection measurements; high-reflection measurements will often appear as normal.
13.5.2 Effective source match This term refers to the impedance of the directional bridge or coupler and associated cables and adapters as they are presented to the DUT. Methods of measurement are very similar to those used to measure effective directivity. However, since we need to measure source match we must feed a reasonable amplitude signal back into the directional bridge or coupler. This task is performed best using either a short or open circuit. The short or open circuit is usually connected to the directional bridge or coupler via an airline, which provides some phase shift enabling the source match to be shown as ripple superimposed on the reflection characteristics of the short or open circuit. One problem in trying to present these data is that the loss of the airline used is often a major part of the displayed measurement. This can make it difficult to determine the ripple amplitude when the source match is fairly small. Shorter airlines will reduce the loss and will also reduce the quantity of ripples observed so a suitable compromise must be achieved. Note in the following plots that there are some ripples of very short period which can be ignored as they are probably generated by other effects within the measurement system (Figures 13.4 and 13.5). As with directivity, the peak to peak height of the ripple is twice the source match. Note also that this measured source match also contains the directivity, which at any
Verification of automatic network analysers 297
Figure 13.4
Ripple caused by the interaction of the source match and an open circuit
Figure 13.5
Ripple caused by the interaction of the source match and a short circuit
given frequency may either add to or subtract from the source match. Since we have no easy way of separating the source match and directivity, we usually consider directivity as one of the sources of uncertainty when making source match measurements. Directivity is usually much smaller than source match so this assumption causes few problems. Time-domain gating (explained below) can be used to effectively separate these interacting terms. Unfortunately, it has not been possible to provide traceability for
298 Microwave measurements
Figure 13.6
Ripple caused by the interaction of the source match and short and open circuits
any measurements in the time-domain so this function is best left to the development laboratories where it provides useful improvements in test development times. One neat trick that can be employed to provide reliable and easy to read source match measurements is to either store or plot the display with a short circuit connected, then connect the open circuit. Assuming the short and open circuits are approximately 180◦ apart in reflection phase, the resultant display will be one of two traces where the ‘peaks and troughs’ occur at approximately the same frequencies (looking similar to the envelope on an Amplitude Modulated signal). The peaks and troughs can now be read at the same frequency, producing a more accurate value of source match at a particular frequency (Figure 13.6). It is also possible to use a sliding short circuit to determine source match at any particular frequency, using a similar technique as described for the sliding load in the measurement of directivity. Unfortunately, sliding short circuits fitted with co-axial connectors are now getting harder to obtain. This technique is still useful where rectangular waveguide is employed as the transmission medium because sliding short circuits in rectangular waveguide are still supplied by several manufacturers. The calibration items used to characterise the effective source match term are the short and open circuits. A poor connection of either of these devices will affect the effective source match. Further, open circuits usually have a centre pin supported with a delicate piece of dielectric; if this dielectric fractures and the centre pin is misplaced the effect on the source match will be massive. The measurements most affected by source match errors are high-reflection measurements and transmission measurements of highly reflective devices. Poor cables can cause both the directivity
Verification of automatic network analysers 299 and source match terms to vary as the cable is flexed. The effect of this variation is that there will be errors in the measured values .
13.5.3 Effective load match Effective load match is the effective impedance of the load presented to the DUT. For a full two-port measurement the load would be represented by the ‘receiving signal port’. As there appear to be no ‘classical’ methods for measuring load match it is usually assumed that it has a similar value to the source match. Refer to Network Analyser Uncertainty Computations for Small Signal Model Extractions by Jens Vidkjær [1] for more detailed information on this subject. The measurements most affected by effective load match are all transmission and reflection magnitude measurements of low insertion loss two-port devices.
13.5.4 Effective isolation Isolation is a measure of how much signal passes from one channel to the other when both channels are terminated in their characteristic impedance. Although the error correction routines are designed to compensate for some degree of poor isolation it is good practice to maintain as ideal a value as possible. The simplest way to measure isolation is to connect the two test port cables together and set a transmission reference in each direction on the screen. Then connect reasonably well-matched terminations to the DUT ends of the test port cables and repeat the transmission measurement. The screen display will be very noisy and should consist of a combination of the network analyser noise floor and the network analyser’s isolation. Poor isolation may be caused by loose connectors within the test set or poor or worn screening throughout the measurement system. In particular, look at the test port extension cables as these are often subjected to plenty of flexing and plenty of wear and tear at the connector. Whilst connectors in poor condition will be obvious to the experienced eye, there will be few visible signs of any deteriorating screening making regular testing desirable. Where isolation is found to be a constant value at any particular frequency corrections are applied. With modern network analysers having very good isolation, often in the same area as the instrument’s noise floor, there is often a danger that the values due to the noise floor become entered into the isolation corrections causing further errors rather than correcting them. Poor isolation would affect both reflection and transmission measurements where the test channel signal is at a very low level, that is, reflection measurements and also transmission measurements where the insertion loss of the DUT is large (i.e. greater than a 50 dB attenuator).
13.5.5 Transmission and reflection tracking This correctable error includes the effects of the insertion loss of the signal separation devices, detectors (or samplers), cables, signal paths and any other items in the signal paths. Residual errors after correction may be analysed by connecting the test port cables together and examining the transmission trace. Any deviation from 0 dB may be
300 Microwave measurements due to tracking. Also, there may be an amplitude-dependent tracking error; this would be checked in the same way, but in addition the source power would be varied and the trace deviation from the 0 dB level noted. The calibration devices used to characterise transmission tracking are the transmission measurements of the ‘thru’ connection. Large variations in the tracking terms might indicate a problem in the reference or test signal path in the test set or poor connections during the calibration process. All transmission measurements are affected by transmission tracking errors. The calibration devices used to characterise reflection tracking are the short and open circuits. As with transmission tracking large variations in the tracking term might indicate a problem in the reference or test signal path in the test set or poor connections during the calibration process. All reflection measurements are affected by transmission tracking errors.
13.5.6 Effective linearity Deviation from linearity may be checked by measuring a previously calibrated stepattenuator. Providing the step-attenuator has been calibrated with a sufficiently low measurement uncertainty, and the step-attenuator has a good match in each direction, it can be assumed that any deviations noted are due to the network analyser’s deviation from ideal linearity. Effective linearity is a significant contributor in the uncertainty budget and needs to be assessed with the signal travelling in either direction. Linearity is not a term characterised using the calibration kit. Some network analysers have corrections for linearity which may be updated when a routine maintenance check is performed. All measurements are affected by linearity. 13.5.6.1 Time-domain and de-embedding Many of the higher frequency network analysers are capable of performing fast Fourier transforms (FFTs). Where implemented this process allows measurements of components within complex networks to be displayed using a process known as ‘time-domain gating’. The component under test or evaluation is mathematically de-embedded from its surrounding network and its response displayed on the screen of the network analyser. This function can be employed to provide values of directivity and source match providing a suitable reference (usually an airline in same characteristic impedance as the coupler or directional bridge) is available. Unfortunately, traceability of measurement has not been developed for this type of time-domain function, so these measurement methods are best left for routine maintenance and diagnostic tasks rather than the task of ensuring traceability of measurement. The concept of time-domain gating refers to mathematically removing a portion of the time-domain response, and then viewing the result in the frequency domain. The intent is to remove the effects of unwanted reflections, say from connectors and transitions leaving just the response of the device being measured. An experienced operator will be able to perform measurements of directivity, source match and load match much faster using time-domain gating rather than using any of the alternative methods described above.
Verification of automatic network analysers 301
13.6
Verification of measurements
This method of verification is perhaps easier to understand and provides a much easier visualisation of the general health of the network analyser, calibration kit and test port cables. The method involves calibrating the network analyser then measuring an artefact or artefacts. The measurements are then compared either with measurements performed earlier, or if it is desired to obtain traceability this way they would be compared with measurements performed on the same artefacts at a laboratory operating at a higher echelon in the traceability chain. For this method to be effective the artefacts used for the verification need to be stable with both time and temperature. For these reasons ‘simple’ devices such as fixed attenuators, fixed terminations and certain types of coupler are often chosen. Sometimes an artefact similar to that which it is desired to measure is chosen so that if an error occurs within the measuring system its effect can be seen and assessed immediately.
13.6.1 Customised verification example To improve throughput on one of the production lines it was decided to use an electronic calibration module with the network analyser testing input impedance. It was also desired to calibrate or check the e-cal module on site as the only alternative was to have it sent overseas to its manufacturer which would cause unacceptable downtime. The specification of the e-cal module is excellent so straightforward testing of it could not be performed to the desired level. It was decided that an artefact which was representative of the manufactured product could be used to access the ‘general health’ of the complete measuring system. The artefact chosen was a programmable attenuator with a short circuit connected to one port (Figure 13.7). This provides a range of mismatch that can be adjusted using software so maintaining the level of automation. It was not considered necessary to have all steps of the attenuator measured as this would provide too much information, much of which may never be looked at, hence, the following were chosen: (1) (2) (3) (4) (5)
highest mismatch, approximate upper specification of DUT, approximate centre of specification of DUT, approximate lower specification of DUT and lowest mismatch.
Figure 13.7
Artefact chosen for the comparison, an Agilent 84904K programmable step-attenuator with a type N adapter and short circuit fitted
302 Microwave measurements 8719ES and 8510C iPIMMS measurement comparison using ET54021 18 June 2004 0.095 8719ES
iPIMMS
Voltage reflection coefficient
0.090
0.085
0.080
0.075
0.070 36
2.
Hz G
Hz
38 2.
G
Hz
40 2.
G
Hz
42 2.
G
Hz
44 2.
G
Hz
46 2.
G
Hz
Hz
48 2.
G
50
Hz
G
2.
52
2.
Hz
G
54
G
2.
Measurement frequency
Figure 13.8
Plot produced from the results of a customised verification example showing all of the uncertainty bars overlapping
This list provides plenty of measurements in the range where it is essential for the network analyser to provide the most accurate measurements possible, and some supplementary measurements (highest and lowest mismatch) which could be used to provide some rudimentary diagnosis should the need arise. The attenuator was calibrated using the best and most accurate and traceable equipment possible. The attenuator was then transferred to the production line where it was measured using the network analyser and electronic-calibration system. A graphical representation of the two sets of results obtained is shown in Figure 13.8. The process is fully automated so it can be used each time the network analyser is re-calibrated. Since accurate measurements can take a long time to obtain there were only 51 points measured by the ‘accurate’ network analyser. This is adequate in this case because the attenuator is a linear resistive device so there is a high probability that linear interpolation can be used between measurement points, if necessary. The production line network analyser, however, is normally measuring active devices so measurements are made at considerably more frequencies, albeit with slightly greater uncertainties in places. In order to make this quantity of measurements within the very short times demanded by production processes they must be made faster, with the trade-off being slightly increased measurement uncertainties. Note in Figure 13.8 that the reference measurements are performed at considerably fewer frequencies. This is quite normal as ‘quality measurements’ can be expensive to perform. Sufficient measurements have been performed showing that linear interpolation between measured values is valid.
13.6.2 Manufacturer supplied verification example Many manufacturers supply verification procedures with their network analysers. The user will normally need to buy a verification kit which is often supplied with a disk containing measurements made on the component parts of the kit. Verification
Verification of automatic network analysers 303 kits and associated procedures are usually designed to provide a quick ‘health check’ on the network analyser. Testing that the network analyser (and calibration kit) meet their specification will often involve adjusting the settings on the network analyser resulting in the measurements taking far longer. The process begins with the operator performing an appropriate calibration (error correction). Test devices from the verification kit are then measured and the results compared with measurements that were made using a reference measurement system (Figures 13.9 and 13.10). If the comparison reveals that the results fall within prescribed limits the network analyser (and appropriate calibration kit) are said to be verified. This type of verification is intended as a routine ‘health check’ and is used by some manufacturers as a routine check for equipment installed at a customer’s location. To this end the software required to automate this process and therefore improve consistency is often included within the operating firmware of the network analyser.
Figure 13.9
Printed output from a typical verification program. A sheet similar to this is produced for both phase and magnitude for each S-parameter of each device tested
304 Microwave measurements
Figure 13.10
Another example from the same verification routine, this time displaying a transmission parameter
The major problem with these types of verification (manufacturer supplied and customised) is that all of the ‘errors’ and measurements are lumped together, the measured values contain both and there is no easy way to separate them. Degraded items can be offset by items still in their prime. This makes it very difficult to identify any one device in the calibration kit or network analyser which may be starting to drift into a problem state, but at least has the advantage of allowing the user to quickly estimate if their system is in a suitable state for measurements. Presentation of the results can be difficult in certain circumstances, particularly transmission phase where the phase vector often rotates through its full 360◦ and the test limit can be less than 1◦ .
References Vidkjær, J.: Network Analyser Uncertainty Computations for Small Signal Model Extractions, Technical University of Denmark, R549, Feb 1994
Chapter 14
Balanced device characterisation Bernd A. Schincke
14.1
Introduction
For decades high frequency circuits were developed using unbalanced (non-symmetrical) structures. Typical line systems, representing this kind of structure, are coaxial or coplanar line systems. Each unbalanced system consists of a signal line and a ground. The measurable signal is referenced to the ground. Balanced (or symmetrical) structures are not used that often. A typical balanced structure is a parallel line system (Lecher line), a Low Voltage Differential Signal Line (LVDS-line) or balanced amplifiers and filters. Typically such a structure consists of two lines (simply said, a ‘plus’ and a ‘minus’) and a signal can be measured between these two lines. In practice, these structures create some additional phenomena compared to unbalanced systems which must be analysed in detail. In an unbalanced system only the non-symmetrical TEM mode is present and it can be compared to the so-called common mode, which we will discuss later. In a coaxial system the inner conductor is the signal line and the outer conductor represents the ground. In addition this ground functions as a shield. Unbalanced line systems are normally connected to unbalanced circuits. Under the condition of power matching the measured voltage U1 against ground is U01 /2. We can conclude that such an unbalanced system offers very high noise immunity, it generates less radiation, the integration density is high and the losses are acceptable. If such a line is connected to, for example, a non-shielded circuit, a signal generated by an interferer (like ground noise or general electromagnetic interference) can be induced on the signal and will be present on the signal at the load. A fundamental disadvantage of an unbalanced structure is its susceptibility against an interferer (Figure 14.1). By using a balanced system (two-line-system), in an ideal case only one signal between the two lines can be measured. Here, the differential TEM mode is the only
306 Microwave measurements
Figure 14.1
Unbalanced system
Figure 14.2
Balanced system
one which is present. Analogous to the balanced line system the circuits are performed as balanced structures, too. A disadvantage by using balanced structures is that more components are needed compared with unbalanced structures. Under the condition of power matching a voltage U2 can be measured between the two lines which can be expressed by U02 /2. An important advantage is that the original signal is (theoretically) not influenced by electromagnetic radiation. A balanced system can be performed by using a transformer to transform the signal with 0◦ phase shift to the ‘upper’ line and by using a BALUN (BALanced–UNbalanced) to transform the signal with 180◦ phase shift to the ‘lower’ line. If an interferer occurs, the signals on both lines are interfered in the same way. Using the same transformer/BALUN structure at the output of the circuit the 0◦ phase shifted, interfered signal will be superimposed on the 180◦ phase shifted signal and the interference will be shortened (Figure 14.2). If a ground is present, again under the condition of power matching, the signal that can be measured between each signal line (upper and lower) and the ground is U02 /4. Between the two lines U2 = U02 /2. The signals have the same amplitude, but they are 180◦ phase shifted. This means that the needed voltage amplitudes to generate a desired power are half of the needed amplitudes working with an unbalanced structure. The advantage is that components with a lower breakdown voltage can be used. For narrow band applications especially in the higher GHz range (e.g. low noise converter (LNC)) the band-pass filtering offers sufficient interference suppression. Such a system will in the future also serve as an unbalanced system.
14.1.1 Physical background of differential structures An essential problem when working with differential structures is that we cannot regard a differential structure as a pure ‘two-line-system’. Every balanced system
Balanced device characterisation 307
Figure 14.3
Three-line-system
must be regarded together with a ground. When, for example, a twisted pair line is used in an instrument, the instrument wall is normally grounded. A multilayer board needs ground layers in order not to influence each other. Because of the ground (‘third line’) in practice such a differential structure must be regarded as a ‘three-line-system’ (Figure 14.3). In a three-line-system two different TEM modes of propagation are possible and must be analysed. On the right-hand side the (wanted) differential energy propagates through the device under test (DUT), on the left-hand side the common mode energy. Especially electromagnetic radiation and ground noise are typical common mode signals. On a board the two modes are quasi-TEM modes with different field distributions in the air and in the dielectric material. This can result in different propagation velocities and the characteristic impedances of the two modes are typically different. To perform an exact measurement and dimensional design in the RF, an S-parameter description is needed taking both modes into account. 14.1.1.1 Ideal device An ideal balanced device is characterised by ideal symmetry of, for example, the two lines. This means in detail the same electrical length, same attenuation, same dielectric, etc. In this case only the differential mode signal is transmitted and the common mode signal is suppressed. This is valid for pure differential structures (balanced input/balanced output) and for balanced to single-ended structures (e.g. balanced input/single-ended output) (Figure 14.4). 14.1.1.2 Real device Caused by asymmetries such an ideal balanced structure is normally not given. Very often it is possible to measure a common mode at the output of a DUT even though the device is powered by a pure differential mode signal. In this case a common mode signal is generated from the differential mode signal. Such a common mode signal can be described as an electromagnetic interferer. This procedure is called ‘Differential Mode to Common Mode Conversion’. If the device is powered only by a common mode signal, it is possible to measure a differential mode signal at the output. Here, from an electromagnetic interferer at the input, a differential mode signal at the output is generated which will be superimposed the original differential signal. Caused by this ‘Common Mode to Differential Mode Conversion’ the structure becomes susceptible to an EMI (Figure 14.5).
308 Microwave measurements Gain = 1 Differential-mode signal Fully balanced
Common-mode signal (EMI or ground noise) Gain = 1 Differential-mode signal
Balanced to single ended
Common-mode signal (EMI or ground noise)
Figure 14.4
Ideal device Differential to common mode conversion +
Generates EMI
Susceptible to EMI
Common-mode to differential conversion
Figure 14.5
Real device, transmission characteristic
These facts are valid for the transmission characteristic of the DUT as well as for the reflection characteristic of the DUT. We can conclude that real devices are normally non-ideal devices. Non-ideal devices convert differential mode energy into common mode energy and common mode energy into differential mode energy. This conversion can be measured at the input of a DUT (converted, reflected energy) and at the output (converted, transmitted energy). The complete description of a non-ideal device is shown in the signal-flow diagram in Figure 14.6. Using this model the balanced device is described by two separate systems, a pure common mode system and a pure differential mode system. The pure common mode S-parameters are the connection between the common mode stimulus signals and the measured common mode responses. The pure differential mode S-parameters are described by the connection between differential mode stimulus signals and measured differential responses. The conversion parameters, caused by the interaction between the two systems, are also shown in this model.
Balanced device characterisation 309
Common mode
Differential mode Common mode Differential mode Ground
Figure 14.6
14.2
Ground
Signal-flow diagram
Characterisation of balanced structures
The typical parameters to be tested are (1) (2) (3) (4)
performance in the pure differential mode, performance in the pure common mode, conversion from differential mode to common mode (in both directions) and conversion from common mode to differential mode (in both directions).
To be able to do all these measurements the unbalanced two-port model must be extended to a balanced two-port model. Such a balanced two-port model has by definition four unbalanced physical ports. To measure the pure differential mode and the pure common mode behaviour as well as the conversion parameters we must be able to generate differential mode and common mode signals and to measure the desired responses. These measurements must be done in both directions. The connection between the stimulus signals and the measured responses are described by the so-called Mixed Mode S-parameters Matrix. bDD,1 SDD,11 SDD,12 SDC,11 SDC,12 aDD,1 bDD,2 SDD,21 SDD,22 SDC,21 SDC,22 aDD,2 (14.1) bCC,1 = SCD,11 SCD,12 SCC,11 SCC,12 · aCC,1 bCC,2 SCD,21 SCD,22 SCC,21 SCC,22 aCC,2 The differential mode stimulus signals are labelled with aDD at port one and at port two and the common mode stimulus signals with aCC . The differential mode and the common mode response signals are described by bDD and bCC (Figure 14.7).
310 Microwave measurements Differential ports
bDD,1
aDD,2
Symmetrical two-port
aCC,1
bDD,2 aCC,2
Port-pair_2
Port-pair_1
aDD,1
bCC,2
bCC,1
Common ports
Figure 14.7
Balanced two-port
The S-parameters shown with the indices ‘DD’ and ‘CC’ are called selfparameters. These parameters are comparable to the unbalanced S-parameters, because by these the reflection quantity and the transmission quantity for the common mode and for the differential mode operation are described. The S-parameters shown with the indices ‘CD’ and ‘DC’ are the conversion parameters. These parameters describe the reflection behaviour and the transmission behaviour of the DUT under the condition that mode conversion happens. If possible, the conversion parameters must be as low as possible. Ideally the common mode system is completely separated from the differential mode system. Then the conversion parameters are zero. The conversion parameters of differential structures become very low, whenever the lines are symmetric. This means that each line offers the same attenuation, same electrical length, etc.
14.2.1 Balanced device characterisation using network analysis Network analysers are in general not developed to characterise balanced devices because they are unbalanced and normally only have two ports. They are working with CW (continuous wave) signals and do not generate common mode signals and differential mode signals. In addition, the hardware structure is not designed to measure the common mode and the differential mode response and characterise the common mode and the differential mode behaviour of the DUT. In addition for balanced devices, balanced calibration standards and a normalised reference impedance (Z0 ) are not available.
14.2.2 Characterisation using physical transformers By using physical transformers it is possible to transform a single-ended signal into a balanced common mode signal and using a BALUN it is possible to generate a balanced differential mode signal. Normally line impedances of 50 0002 against ground are used. In this case a common mode impedance of 25 0002 and a differential mode impedance of 100 0002 are generated (Figure 14.8). By using a four-port network analyser it is possible to connect one transformer at port 1 and one BALUN at port 3 to feed the balanced input of the balanced DUT with a common mode signal and a differential mode signal. Using both, the differential mode and the common mode response can also be measured. At port 2 of the DUT the second transformer and the second BALUN can be connected to measure the transmitted common mode and differential mode signal (Figure 14.9).
Balanced device characterisation 311 Balanced common mode signal
Balanced differential mode signal 10
25 Ω
0Ω
V2
2) (Z
) 22) (Z
2 VV
50 Ω
Figure 14.8
I) (ZZ II ( VV
I) Z I( VV
Uunsym.
50 Ω
50 Ω
50 Ω
Uunsym.
Physical transformer and BALUN
DUT balanced
Figure 14.9
BALUN setup
Using such a setup the conversion parameters can be measured as well, because it is possible to generate a differential mode stimulus signal at port 1 and to measure the differential mode and the common mode response at port 1 (reflection characteristics) and at port 2 (transmission characteristics). These measurements can be done bidirectionally. This simple test setup needs four physical ports and additional external equipment. Caused by this external equipment some disadvantages are known which make it impossible to use this configuration in the range of super high frequencies (SHF range) and partly in the VHF range (very high frequencies). An important disadvantage is that the calibration plane is different from the measurement plane because of the unavailability of balanced calibration standards. A calibration can be performed at the single-ended ports on the basis of coaxial calibration tools. The measurement results after such a calibration are results of the DUT including the characteristics of the used transformers and BALUNs. Especially, the poor RF performance of a normal BALUN degrades the measurement accuracy. In addition the RF performance is responsible for the limited frequency range. These problems can be compensated by using the so-called Virtual Ideal Transformers.
312 Microwave measurements 16 measured unbalanced S-parameters
Description of virtual ideal transformers
Calculated mixed mode S-parameters
Figure 14.10
Modal decomposition method, principle Test fixture Port 1
a b
Port 3
DUT
Port 4
Port 2
a1 a2 a3 a4 Figure 14.11
S11 S12 S13 S14 =
S21 S22 S23 S24 S31 S32 S33 S34 S41 S42 S43 S44
a b
b4 .
b3 b2
(14.2)
b1
Unbalanced measurement
14.2.3 Modal decomposition method The principle is to measure 16 unbalanced S-parameters and to calculate with the help of (virtual) ideal transformers, the Mixed Mode S-parameters. The whole theory and procedure are given by Bockelman and Eisenstadt [1] (Figure 14.10). First, measure the 16 unbalanced S-parameters of the balanced two-port model using a four-port analyser (Figure 14.11). As S-parameters can be converted into all other parameters it is possible to convert the S-parameters into Z-parameters which connect – according to Ohm’s law – voltages with currents (Figure 14.12). [V ] = [Z] · [I ]
(14.3)
The next step is to express the unbalanced measured currents and voltages by balanced currents and voltages. This connection can be shown for two coupled lines (14.5) using the Kirschoff laws. The principle is shown only for the balanced port 1. For the balanced port 2 it can be demonstrated in the same way. The current at the physical port 1 can be expressed by the sum of the differential mode current at the balanced port 1 and half of the common mode current at the balanced port 1. Respectively the current at the physical port 4 can be expressed
Balanced device characterisation 313 I1 Port 1
V1
Port 2
V2 V3
I2
I4
V3
Port 3
V4
Port 4
Z11 Z12 Z13 Z14 =
V4 Figure 14.12
DUT
V2
V1
I3
Z21 Z22 Z23 Z24 Z31 Z32 Z33 Z34 Z41 Z42 Z43 Z44
I1 .
I2
(14.4)
I3 I4
Conversion S-parameters → Z-parameters
by the sum of the negative differential mode current and half of the common mode current (14.5). Port 1: 1 I1 = Idiff .1 + Icom.1 2 1 I4 = Idiff .1 + Icom.1 2 1 (I1 − I4 ) 2 = I1 + I4
Idiff .1 = Icom.1
(14.5)
(14.6)
Using this connection the differential mode and the common mode currents at the balanced (or logical) port 1 and the balanced (or logical) port 2 can be expressed by the measured (unbalanced) currents (Figure 14.13). The voltage at the physical port 1 can be expressed by the sum of the differential mode voltage at the balanced port 1 and the voltage U4 at the unbalanced port 4. Respectively, twice the common mode voltage at the balanced port 1 can be expressed by the sum of U1 and U4 (Figure 14.14). Port 1: U1 = Udiff .1 + U4 2.Ucom.1 = U1 + U4 Udiff .1 = U1 − U4 1 Ucom.1 = (U1 + U4 ) 2
(14.7)
(14.8)
314 Microwave measurements 2
I2
I3
P_2
P_3 U3
U2
−Idiff 2
Idiff 2
½ Icom2
½ Icom1 −Idiff 1 Idiff 1 P_4
P_1 I4
I1
U4
U1
1
Figure 14.13
Nodal → modal, currents at port 1
I2
2
P_2
P_3 Udiff 2
Ucom 2
Udiff 1
Ucom1 P_4
P_1 I4
I1
U4
U1
1
Figure 14.14
I3
Nodal → modal, voltages at port 1
U2
U3
Balanced device characterisation 315 To give a total description according to the (14.5) and (14.7) the following matrixes can be used: 1 0 0 1 2 Idiff .1 1 I1 I2 0 0 −1 2 Icom.1 · = (14.9) I I3 1 0 0 diff .2 1 I4 2 Icom.2 1 −1 0 0 2 I = Q · Im
(14.10)
U1 U2 U3 U4
1 1 0 0 2 Udiff .1 1 0 0 − 2 1 Ucom.1 = · U 1 0 0 diff .2 1 2 Ucom.2 1 − 1 0 0 2
(14.11)
U = P · Um
(14.12)
At this point the calculation can be done using the following procedure. As the mixed mode voltages and currents are directly connected to the measured unbalanced voltages and currents it is possible to show the measured quantities by the mixed mode quantities virtually linked to ‘ideal transformers’ (Q, P-matrix). The quotient Um /Im is equal to the mixed mode impedances Zm . The last step is to convert the mixed mode impedance matrix into the mixed mode S-parameters matrix. V = [P] · Vm I = [Q] · Im V = [Z] · I V = [Z] · [Q] · Im [P] · Vm = [Z] · [Q] · Im Vm = [P −1 ] · [Z] · [Q] · Im Zm = [P −1 ] · [Z] · [Q] → Sm Calculation 1: calculation of Sm using Z-parameter.
316 Microwave measurements Another possibility to explain the calculation of the mixed mode S-parameters is to proceed directly using the wave quantities. Then the differential/common currents and voltages must be expressed according to (14.6) and (14.8) 1 1 0 0 − Idiff .1 I1 2 2 1 1 Idiff .2 0 − I2 0 · = (14.13) 2 2 I I3 com.1 0 0 1 1 Icom.2 I4 0 1 1 0 Im = Mi · I
1
(14.14) 0
0 −1 Udiff .2 = 1 U 0 com.1 2 Ucom.2 1 0 2 Udiff .1
0 1 0 1 2
−1 U1 0 U2 1 · U 3 2 U4 0
Um = Mu · U
(14.15)
(14.16)
Wave quantities are normalised to the root square of the impedance. By unbalanced system the reference impedance is normally 50 0002. 0007 Ui ii = Ii Z0 ; ui = √ (14.17) Z0 Because of the differential mode impedance normally being twice the reference impedance and the common mode impedance normally being half of the reference impedance according to Bockelman and Eisenstadt [1] the normalisation shown in the following equation is common (Figure 14.15). Form 2 (Bockelmann a.o.) idiff .i = Idiff .i · icom.i
√
2Z0 ;
→ Zdiff =2Z0 Z0 = Icom.i · ; 2 Z0 → Zcom = 2
Udiff .i udiff .i = √ 2Z0 Ucom.i ucom.i = √ Z0 /2
(14.18)
The calculation of the mixed mode S-parameters is based on the ratio between the measured wave quantities. Using a normalisation according to (14.17), the measured
Balanced device characterisation 317 ad2 ac2
P_2
bd2 bc2
P_3 P_2
P_1 P_4
P_1
ad1
ac1
Figure 14.15
bd1
bc1
Balanced two-port description
mixed mode response can be shown by mixed mode S-parameters multiplied with a mixed mode stimulus signal: bm = Sm · am ui = ai + bi ;
ii = ai − bi
1 (ui − ii ) 2 1 ai = (ui + ii ) 2 bi =
Using the Mi and the Mu matrix, it is possible to calculate the mixed mode wave quantities from the single-ended wave quantities and the measured (unbalanced) S-parameters. The ratio between the mixed mode stimulus and response wave quantities describes the mixed mode S-parameters. Using the normalisation according to (14.18) it can be shown that Mu = Mi 1 (um − im ) = 2 1 am = (um + im ) = 2 M · S · a = Sm · M · a bm =
1 M (u − i) = 2 1 M (u + i) = 2
1 1 M ·b= M ·S ·a 2 2 1 M ·a 2
318 Microwave measurements Port Port33 Port Port 11
Port Port 22 Port44 Port
Logical ports
DUT Port 1
Figure 14.16
Physical ports
Port 2
Port configuration
Smode res.;mode stim.;port res.;port stim. Figure 14.17
Naming convention
Sm = M · S · M −1 S = M −1 · Sm · M Calculation 2: calculation using form 2. Important for all calculations is that the port numbering must be known because two single-ended physical ports are combined to a logical (balanced) port 1 and the other two single-ended physical ports are combined to a logical (balanced) port 2 (Figure 14.16). Especially, the calculations which are based on form 2 are referred to differential mode impedance which is twice the single-ended impedance and a common mode impedance which is half of the single-ended impedance.
14.2.4 Mixed-mode-S-parameter-matrix The resulting S-parameters matrix, called mixed mode S-parameters matrix, contains S-parameters describing the reflection and the transmission characteristics of a DUT using differential and common mode stimulus signals and measuring differential and common mode responses. The naming convention is related to the naming convention of the S-parameters. The first letter shows the TEM mode of the measured signal (response) and the second letter the TEM mode of the stimulus signal (Figure 14.17). The first number names the logical port where the response is measured and the second number names the logical port where the generator is working. The mixed mode S-parameters matrix describes in the upper left quadrant (or ‘DD-quadrant’) the fundamental performance of the DUT in pure differential mode operation and the lower right quadrant (or ‘CC-quadrant’) in pure common mode operation. Each of the four S-parameters represents reflection coefficients at logical port 1 and port 2 and the forward/reverse transmission coefficients between the logical ports (Figure 14.18).
Balanced device characterisation 319
Figure 14.18
Figure 14.19
Sdd11
Sdd12
Sdc11
Sdc12
Sdd21
Sdd22
Sdc21
Sdc22
Scd11
Scd12
Scc11
Scc12
Scd21
Scd22
Scc21
Scc22
Pure differential and pure common modes
Sdd11
Sdd12
Sdc11
Sdc12
Sdd21
Sdd22
Sdc21
Sdc22
Scd11
Scd12
Scc11
Scc12
Scd21
Scd22
Scc21
Scc22
Mode conversion parameter
The upper right and the lower left quadrant provide the information about the conversion parameter. In the upper right quadrant (or ‘DC-quadrant’) the conversion of a common mode stimulus signal to a differential mode response is described. A conversion of a differential mode stimulus signal to a common mode response is described in the lower left quadrant (or CD-quadrant). It is obvious that these reflection and transmission parameters are equal to zero in the case of ideal symmetry (Figure 14.19). As the DC-quadrant shows the part of differential mode energy generated from a common mode stimulus signal, this quadrant describes directly the susceptibility to an EMI. However, the CD-quadrant describes the amount of produced common mode energy from a differential mode stimulus signal. Therefore the information of this quadrant is related to the generation of EMI.
14.2.5 Characterisation of single-ended to balanced devices Such a typical three-port device is a surface acoustic wave (SAW)-filter. The mixed mode S-parameters of a three-port device can also be calculated from the unbalanced measured S-parameters using the same theory (Figure 14.20).
320 Microwave measurements Single-ended
Port 1 (unbalanced)
Figure 14.20
Figure 14.21
Differential-mode common-mode DUT
Port 2 (balanced)
Three-port device
Sss11
Ssd12
Ssc12
Sds21
Sdd22
Sdc22
Scs21
Scd22
Scc22
Nine-parameter mixed mode matrix
The difference to a fully balanced DUT is the single-ended input and the balanced output. A structure containing a balanced input and a single-ended output is also possible. Here the resulting mixed mode S-parameters matrix is a nine S-parameters matrix. At the single-ended port only the normal reflection coefficient can be measured (labelled with Sss ). The mode conversion parameters in the transmission paths describe the mode conversion from the single-ended signal into a common mode signal and into a differential mode signal in the forward and in the reverse direction. At the logical port 2 the reflection coefficients in the pure common mode and the pure differential mode operation can be measured, as well as the mode conversion parameters of the reflected energy at port 2 (Figure 14.21).
14.2.6 Typical measurements The measurement parameters directly give some information about the differential and common mode insertion loss and the differential and common mode return loss. By using external hardware or network analysers providing more than four ports it is also possible to make Near End Crosstalk (NEXT) and Far End Crosstalk (FEXT) measurements. Other very popular quality parameters are the amplitude imbalance and the phase imbalance because this information is directly related to the symmetry of the structure and therefore to the mode conversion characteristic of the DUT. The imbalance parameters can be calculated using (14.19). Using the unbalanced MAG-information it is possible to show the amplitude imbalance and using
Balanced device characterisation 321
Port b Port a Port c Logical port 1
Figure 14.22
Logical port 2
Imbalance and CMRR measurement
the unbalanced phase measurements it is possible to show the phase imbalance (Figure 14.22). IMB =
Sba Sca
(14.19)
The common mode rejection ratio (CMRR) is the relation between the Sds21 parameter and the Scs21 parameter and provides information about the rejected common mode energy . CMRR =
Sds21 Scs21
(14.20)
Modern network analysers with powerful Math-functions are able to calculate these results immediately and show the results in an additional trace.
14.3
Measurement examples
14.3.1 Example 1: Differential through connection This simple example shows the influence of the symmetry on the conversion parameters, and thus on the pure differential and pure common mode parameters. Two coaxial lines connected at physical port 1 and physical port 2 of the analyser are combined to a logical port 1. The other two coaxial lines are connected at physical port 2 and physical port 4 of the analyser and combined to a logical port 2. The two logical ports are directly connected (through connection). To avoid measurement errors caused by different lengths or different attenuations of the coaxial lines, a coaxial full four-port calibration is recommended (Figure 14.23). The diagrams in Figure 14.24 show all the 16 mixed mode S-parameters. The traces 1, 2, 5 and 6 show the results under pure differential mode operation. We see that the DUT is well matched at both ports and that the differential mode energy does transmit the DUT with negligible losses. The traces 3, 4, 7, 8, 9, 10, 13 and 14 display the conversion parameters. It is evident that the mode conversion from differential mode energy to common mode energy and the conversion from common mode energy to differential mode energy are very low.
322 Microwave measurements
Port 3
Port 1
Port 4
Port 2
SMA
Logical port 1
Logical port 2 Reference planes
Figure 14.23
Test setup, example 1
The pure common mode behaviour of the DUT is shown in the traces 11, 12, 15 and 16. To show the influence of the symmetry on the structure of a balanced device, we will change the symmetry in two different ways. (1) Change of the electrical length of one part (line) of the balanced device by implementing an additional small piece of line between ports 2 and 3. (2) Creation of two different attenuations, by implementing a 3 dB attenuator between ports 2 and 3 and by implementing a 6 dB attenuator between ports 1 and 4. It is essential to use two different attenuators because, otherwise, the electrical length will be changed significantly. First, change of the electrical length between the ports (Figure 14.25). As we are using a very small piece of line, the influence in the lower frequency range is lower to the mode conversion than in the higher frequency range. This happens due to the relation between the dimension of the additional line and the wave length (Figure 14.26). As expected, the mode conversion, especially in the higher frequency range, becomes higher. This is shown in the lower two diagrams. For comparison with the ideal results, these are traced. Another point of interest is that the converted energy (differential to common mode) will no longer be transmitted as differential mode energy. In the higher frequency range the transmitted differential mode energy seems to be attenuated. The next exercise is to use different attenuations in the two parts of the balanced device (Figure 14.27). Because of the attenuator being a broadband working device, the influence of the symmetry change in this way will be the same during the whole frequency range. Compared with the ideal (traced) results the mode conversion becomes higher during the whole frequency range. The transmitted differential mode energy is once again attenuated, because a part of the differential mode energy is converted into common mode energy. In other words, an EMI is produced from the differential mode energy at the input (Figure 14.28).
Figure 14.24
0 dBrr Stop
8 GHz
Ch1
Start
0 dBrr Stop
0 dBrr Stop
Ch1
Sdd11
8 GHz
Ch1
−70
−50
−30
0 −10
Sdd21
100 Trc15
8 GHz
dB Mag 10 dB/Ref
Pwr
Sdd22
Pwr
Ch1
100 Trc11
8 GHz
−70
−50
−30
0 −10
Sdd21
60 Trc7
Start
8 GHz
Ch1
−70
−50
−30
0 −10
−2
2
−5
5
0 dBrr Stop
−1
0.5 1
1
8 GHz
Ch1
−70
−50
−30
0 −10
Sdd12
Pwr
0 dBrr Stop
8 GHz
Ch1
Sdd22
Sdd12
Start
0
0 dBrr Stop
Pwr
−0.5
0.2
−2
2
−5
5
0 dBrr Stop
−1
0.5 1
1
120
8 GHz
120
8 GHz 10 dB/Ref
0 dBrr Stop dB Mag
Pwr
80
8 GHz
10 dB/Ref
dB Mag 10 dB/Ref
Pwr
dB Mag
40
8 GHz
10 dB/Ref
0 dBrr Stop
dB Mag
Pwr
0.5
Sdd22
Start
Sdd12
Start
Sdd22
Start
Sdd22
70 Trc8
dB Mag 10 dB/Ref 110 Trc15
Pwr
−0.5
0.2
Sdd21
Start
0
0.5
0 dBrr Stop
10 dB/Ref
dB Mag 10 dB/Ref 110 Trc12
Pwr
dB Mag
Ch1
−70
−50
−30
0 −10
Sdd12
30 Trc4
8 GHz
10 dB/Ref
0 dBrr Stop
dB Mag
Pwr
Sdd11
Start
Sdd21
Start
Sdd11
Measurement of mixed mode S-parameters acc. to example 1
Pwr
−70
−70
Start
−50
−50
Ch1
−30
Trc14
−2
−5
5
0 dBrr Stop
−1
0.5 1
2
dB Mag 10 dB/Ref
Pwr
−0.5
0.2
Sdd12
Start
−30
90
Ch1
0 −10
Ref 1 U
8 GHz
0 −10
Smith
0 dBrr Stop
Sdd22
Sdd21
Pwr
Sdd21
Trc13
Start
−70
−70
Ch1
−50
0
1
10 dB/Ref
Ch1
−70
−50
−30
0 −10
Sdd11
20 Trc3
8 GHz
10 dB/Ref
0 dBrr Stop
dB Mag
Pwr
dB Mag
0.5
Sdd22
Start
Sdd12
Trc10
−30
90
Ch1
Sdd12
Start
Sdd22
Trc6
−50
Ref 1 U
8 GHz
50
Ch1
−30
Smith
0 dBrr Stop
Ref 1 U
8 GHz
−70
−50
−30
0 −10
Sdd12
Trc2
0 −10
Sdd11
Trc9
Pwr
Smith
0 dBrr Stop
−2
−5
5
C1a
Sdd11 0 −10
Start
Ch1
−70
−50
−30
0 −10
Sdd21
Sdd21
Trc5
Pwr
−1
2
Ref 1 U
0.2 0.5 1
1
Smith
−0.5
Start
0
0.5
Sdd11
Ch1
Sdd11
Trc1
Balanced device characterisation 323
324 Microwave measurements
Port 3
Port 1
Port 4
Port 2
SMA
Logical port 1
Logical port 2 Add. line
Figure 14.25
Trc1 Sdd11 Smith
Change of electrical length
Ref 1 U
Cal
1
1
Sdd11
2
0.5
Sdd21 dB Mag 10 dB / Ref 0 dB Trc5 Mem14[Trc5] Sdd21 dB Mag 10 dB / Ref 0 dB Sdd21
Cal
5
10 0 5
0
0.2
0.5
1
2
−10 10 −20 20
5
30 −30 −40 40 −5
0.5 −0.5
50 −50 −60 60
−2
70 −70
−1 Ch1 Start 300 kHz
Pwr 0 dBm
Sdc21 dB Mag 10 dB / Ref 0 dB Mem15[Trc7] Sdc21 dB Mag 10 dB / Ref 0 dB Trc7
Stop 8 GHz Cal
7
Sdc21 10
Ch1 Start 300 kHz
0
0
10 −10
10 −10
20 −20
20 −20
30 −30
30 −30
−40 40
−40 40
50 −50
50 −50
−60 60
−60 60
−70 70
70 −70
Ch1 Start 300 kHz
Figure 14.26
Pwr 0 dBm
Stop 8 GHz
Pwr 0 dBm
S Trc13 cd21 dB Mag 10 dB / Ref 0 dB Mem16[Trc13] Scd21 dB Mag 10 dB / Ref 0 dB S cd21 10
Ch1 Start 300 kHz
Mode conversion with additional line
Pwr 0 dBm
Stop 8 GHz Cal
13
Stop 8 GHz
Balanced device characterisation 325
Port 3
Port 1
Port 4
Port 2
SMA 6-dB 3-dB Logical port 1
Logical port 2 Attenuators
Figure 14.27
Trc1 Sdd11 Smith
Change of the attenuation
Ref 1 U
Cal
1
1
Sdd11 0.5
2
Sdd21 dB Mag 10 dB / Ref 0 dB Trc5 Mem14[Trc5] Sdd21 dB Mag 10 dB / Ref 0 dB Sdd21
Cal
5
10 0 5
0
0.2
0.5
1
2
−10 −20
5
−30 −40 −5
−0.5 0.5
−50 −60
−2
−70
−1 Ch1 Start 300 kHz
Pwr 0 dBm
Sdc21 dB Mag10 dB / Ref 0 dB Trc7 Mem15[Trc7] Sdc21 dB Mag10 dB / Ref 0 dB S dc21 10
Stop 8 GHz Cal
7
Ch1 Start 300 kHz
0
−10
−10
−20
−20
−30
−30
−40
−40
−50
−50
−60
−60
−70
−70
Figure 14.28
Pwr 0 dBm
Stop 8 GHz Cal
13
10
0
Ch1 Start 300 kHz
Pwr 0 dBm
Scd21 dB Mag 10 dB / Ref 0 dB Trc13 Mem16[Trc13] Scd21 dB Mag10 dB / Ref 0 dB Scd21
Stop 8 GHz
Ch1 Start 300 kHz
Mode conversion by different attenuation
Pwr 0 dBm
Stop 8 GHz
326 Microwave measurements Trc1 Sds21 dB Mag 5 dB / Ref 0 dB
Trc2 Ssd12 dB Mag 5 dB / Ref 0 dB
1
S
sd12
0
−5 −10 −15 −20 −25 −30 −35 −40 Ch1 Center 1.85 GHz SdS21 T dB Mag 10 dB / Ref 0 dB rc3
Pwr 0 dBm Trc5
SCS21
Span 195 MHz 2
dB Mag 10 dB / Ref 0 dB
SCS21
10
0 −10 −20 −30 −40 −50 −60 −70 Ch1 Center 1.85 GHz
Figure 14.29
Pwr 0 dBm
Span 195 MHz
Transmission behaviour of the SAW-filter
14.3.2 Example 2: SAW-filter measurement A SAW-filter is a typical three-port device with one single-ended input and a balanced output. When measuring a SAW-filter it is of importance that most of the single-ended input energy is converted into differential mode energy. It is not intended to receive common mode energy. This type of energy must be rejected because otherwise an interferer is produced from the single-ended signal (Figure 14.29). To calculate the CMRR we can use (14.20) and using the User Defined Math Editor the result can be shown directly (Figure 14.30).
14.4
(De)Embedding for balanced device characterisation
By working with single-ended 50 0002 systems, the differential mode impedance is 100 0002 and the common mode impedance is 25 0002. These impedance values are not the normalised reference values. A SAW-filter, for example, provides differential output impedances different from 100 0002 (e.g. 150–240 0002 or other), but the calculation routine works with 25 and 100 0002. By working with such a real device a mismatching happens. This mismatching can be reduced by using physical matching networks. Disadvantages of physical matching networks are the poor reproducibility, their being normally restricted to lower frequencies and the possibility to only use them in the narrow band. Another disadvantage is that using physical networks the user cannot operate as flexibly as possible.
Balanced device characterisation 327 CMRR Scs21 dB Mag 7.5 dB / Ref 15 dB Math
3 of 3 (Max)
Scs21 45.0
37.5
30.0
22.5
15.0
7.5
0.0 −7.5 −15.0
Ch1 Center1.85 GHz
Figure 14.30
Pwr 0 dBm
CMRR of a SAW-filter
P1
P2
Physical ports
Impedance transformer
−R
R
Figure 14.31
Span 195 MHz
L
C
P3
100 to 150 Ω
Matching network parallel L
L
R
−R
C
Virtual matching
The use of virtual (theoretically) matching networks provides a high range of flexibility with no frequency restriction. Using these virtual networks both embedding and de-embedding are possible.
328 Microwave measurements To provide the impedance transformation from 100 to 150 0002 a virtual transformer must be embedded. In general, ‘Embedding’ is used to implement virtual additional components and circuits and to show the S-parameters with the influence of these virtual networks. The de-embedding functionality can be used to remove virtually an influence caused by the hardware, for example, the characteristics of a test fixture when it is possible to give a complete S-parameters description of the fixture. When, for example, a DUT with 150 0002 output impedance is placed in a test fixture with an RC-characteristic the structure can be matched using a virtual network shown in Figure 14.31. Virtual embedding and de-embedding are possible for single-ended and for balanced structures at all used physical and logical ports. It is possible to use predefined structures and vary the parameters of the given lumped elements or to import the S-parameters to describe the networks.
Further Reading 1 Bockelman, D. E., and Eisenstadt, W. R.: ‘Combined differential and common mode scattering parameters: theory and simulation’, IEEE Transactions on Microwave Theory and Techniques, 1995;43(70): 1530–9 2 Simon, J.: Measuring balanced components with vector network analyzer ZVB, Rohde and Schwarz Application Note 1EZ53, September 2004 3 Heuermann H.: 7.10.2003, Grundlagen der Hoch- und Höchstfrequenztechnik, Umdruckversion 1.1, Fachhochschule Aachen (script from studies at university) 4 Concepts in Balanced Device Measurements, Multiport and Balanced Device Measurement Application Note AN1373-2, Agilent Technologies 5 Martius S.: January 2002, Nodale und Modale Streumatrizen (Dreileiteranordnungen), Lehrstuhl für Höchstfrequenztechnik Universität Erlangen-Nürnberg (script from studies at university)
Chapter 15
RF power measurement James Miall
15.1
Introduction
This is a brief introduction to guided-wave power measurements in the approximate range of a few MHz to several hundreds of GHz, some devices that can be used to measure RF power and the techniques for calibrating these devices.
15.2
Theory
15.2.1 Basic theory The instantaneous incident power due to an electromagnetic field can be written as [1] 0001 1 P= E0002t × H0002t dS 2 0002 t and H 0002 t are the electric and magnetic fields at a time t, and S is the surface where E over which the power is being measured. In terms of voltage (V ) and current (I ) in a transmission line, power can be written as Pinstantaneous = V (t) × I (t) Paverage = VRMS × IRMS × cos(φ) where φ is the phase angle between the voltage and current waveforms. In many situations V (t) and I (t) are sinusoids and in this case the instantaneous power will vary at twice the frequency of the sinusoid. However, these are not particularly useful definitions at RF and microwave frequencies because the instantaneous voltage, current and field distributions are not easily measured. At RFs and above power becomes the only convenient measure of signal strength.
330 Microwave measurements In practice RF and microwave power is usually measured using substitution techniques based on its heating effect, or by rectification. The unit of power is Watt (W), where 1 W = 1kg m2 s−3 Power ratios are often more conveniently expressed in decibels where given Power bel = log10 (Power Ratio) and 1 decibel =
1 bel 10
the power ratio in decibels is therefore 0002 0003 Power 1 Power dB = 10 × log10 Power 2 A power in dBm is defined as the ratio with respect to 1 mW, that is 0003 0002 Power Power dBm = log10 1 mW That is, 0 dBm corresponds to 1 mW, 20 dBm to 100 mW and −50 dBm to 10 nW. Often ‘power’ refers to CW power, that is, the average power produced by a constant sinusoid waveform at a single frequency. It should be assumed that these notes are dealing with this case unless otherwise specified. Discussion of non-CW power occurs in section 15.9. In general, in power measurements, a source of power will be connected via a transmission line to a load (Figure 15.1). Both the source and the load will reflect some of the incident electromagnetic field and therefore the power delivered into the load will be dependent on the reflection coefficients of both devices. If we define, at the connection to the load, the forward voltage wave (a), reflected voltage wave (b), reflection coefficient of the load 0004, incident power (Pi ), reflected power (Pr ) and the power delivered to the load (Pd ) then we can write the
a
b Γ
Generator
Pi
Figure 15.1
10.05 mW
Pr
Pd
Incident, reflected and delivered power from source to load in a general power measurement situation
RF power measurement 331 following relations: Pi =
|a|2 Z0
|b|2 Z0 |b| |0004| = |a| Pr =
|0004|2 =
|b|2 |a|2
Pr = Pi |0004|2 Pd = Pi − Pr Pd = Pi − Pi |0004|2 Pd = Pi (1 − |0004|2 ) The power delivered to the load is never greater than the incident power. Until now this treatment has ignored the power source. Any generator can be thought of as an idealised source with available power Pa and an internal impedance Z0 (cf. the DC case) (Figure 15.2). The power dissipated into a load with impedance Z is PZ . The Z0 -available power, PZo , is the power available to a load with impedance Z0 . The maximum power that can be dissipated in a load occurs when the load has the complex conjugate impedance of the source internal impedance. Pd = Pa
(1 − |0004G |2 )(1 − |0004L |2 ) |1 − 0004G 0004L |2
PZo = Pa (1 − |0004G |2 ) PZo = Pd
|1 − 0004G 0004L |2 1 − |0004L |2
As expected if 0004L = 0 the power delivered to the load is the Z0 -available power, PZo . In general we can measure Pi or Pd with a power sensor but often we wish to know PZo , the power available to a perfectly matched load, which can be found, for example, by using (15.1). A more comprehensive description of the relationship between powers in different points in microwave circuits can be found in Reference 22. PZ0 = Pi |1 − 0004G 0004L |2
(15.1)
No power sensor is a perfect indicator of the delivered power. There will always be losses within the sensor and systematic errors within the measurement process that will mean that the measured power is not the same as the power delivered (Figure 15.2).
332 Microwave measurements
10.05 mW Generator
ΓG
ΓL
Pa Pz
o
Figure 15.2
Effect of generator match
The Effective Efficiency (ηe ) of a power sensor can be defined as the ratio of the measured power to the RF absorbed power ηe =
Pmeas Pd
and the calibration factor (K) as the ratio of the measured power to the RF incident power K=
Pmeas Pi
(15.2)
so the two definitions are related by K = ηe (1 − |0004L |2 ) In a power sensor calibration certificate, K would usually be quoted for each frequency (either relative to absolute power or often relative to the figure at 50 MHz).
15.2.2 Mismatch uncertainty By combining equations (15.1) and (15.2) we can write Pmeas |1 − 0004G 0004L |2 K and if our power meter supplies a reading Prdg , corrected for the sensor calibration factor, as is often the case, then PZo =
PZo = Prdg |1 − 0004G 0004L |2 this has a maximum and minimum given by PZo = Prdg (1 ± |0004G ||0004L |)2 for small 0004 this can be expanded as PZo ≈ Prdg (1 ± 2|0004G ||0004L |) PZo ≈ Prdg ± Prdg 2|0004G ||0004L | or in other words the approximate mismatch [3] uncertainty when making a power measurement where only the magnitudes of the source and load reflection coefficients are known is 200|0004G ||0004L |%. The mismatch uncertainty has a U -shaped distribution [4].
RF power measurement 333
15.3
Power sensors
There are a great variety of different techniques for measuring RF and microwave power. All the different sensor types have advantages and disadvantages. Several of the more common sensor types have been covered in earlier chapters and these will only be mentioned briefly along with a short introduction to some more unusual sensor types.
15.3.1 Thermocouples and other thermoelectric sensors •
Coaxial and waveguide sensors easily available on the market: − Coaxial: DC to 50 GHz − Waveguide: 8–110 GHz (limited supply outside these frequencies) • Power range: 1 µW to 100 mW (50 dB range) • Advantages (+) and disadvantages (−): + Good long-term stability + Reasonably linear + Generally lower VRC than thermistor mounts + Easily integrated into automatic systems − Often require a reference source − Only measure average power
15.3.2 Diode sensors • • •
Coaxial sensors easily available in range: 0.1 MHz to 50 GHz Power range: 1 nW to 100 mW (90 dB) Advantages (+) and disadvantages (−): + Good long-term stability + Reasonably linear at low levels + Generally lower VRC than thermistor mounts + Easily integrated into automatic systems + Fast response allowing envelope power to be tracked + High dynamic range − Require a reference source − Poor linearity at higher levels − Can be inaccurate for modulated and distorted signals
15.3.3 Thermistors and other bolometers •
Coaxial and Waveguide mounts available on the market: − Coaxial: 1 MHz to 18 GHz − Waveguide: 2.6–200 GHz • Operate with DC substitution (closed-loop operation) • Advantages (+) and Disadvantages (−): + Very good long-term stability + Fundamentally very linear
334 Microwave measurements − − − − − −
Power range: 10 µW to 10 mW (30 dB range) High VRC at high frequencies (especially waveguide) Older technology Slow response time Only measure average power Poor dynamic range
Fundamentally, if the requirement is for a fast, high dynamic range sensor then a diode sensor should be used. For slightly higher accuracy over a smaller power range then a thermocouple sensor should be used. Thermistor sensors are generally only used in situations where very high linearity and stability are needed, such as a calibration laboratory.
15.3.4 Calorimeters Calorimeters measure the heat produced by incident microwave radiation. They are typically constructed from a thermally insulating section of waveguide, a load and a temperature sensor such as a thermopile. They are in most cases the most accurate sensors available and so are used in national standards and some other calibration laboratories. Their main disadvantage is their extremely long time constant (often 20+ minutes) so they are not suitable for use in many measurement situations. 15.3.4.1 Twin load calorimeters Twin load calorimeters [5] consist of two identical loads at the end of thermally insulating RF line sections within a thermally insulating container (see Figure 15.3). The temperature difference between the two loads is measured with temperature sensors. RF power can be applied to one side of the calorimeter and DC power to the other. When the temperature difference between the two sides is zero the RF and DC powers can be considered equivalent. 15.3.4.2 Microcalorimeters Microcalorimeters [6] are used to calibrate thermistor type sensors. These sensors operate in a bridge circuit such that the power dissipated in the sensor should be constant whether or not RF power is applied. The microcalorimeter measures the small temperature change caused by the extra losses in the input line of the sensor in the RF case. A microcalorimeter consists of a thin-walled line section connected to the thermistor sensor being calibrated (see Figure 15.4). A thermopile measures the temperature difference between the thermistor and a dummy sensor or temperature reference. By measuring the temperature change due to the RF loss in the sensor and the input line, the efficiency of the sensor can be calculated. 15.3.4.3 Flow calorimeters Flow calorimeters [7] are suitable for higher power measurements than the other calorimeters mentioned so far. They contain a quartz tube carrying flowing water
RF power measurement 335 Copper blocks
50 Ω loads
Thin wall lines
Figure 15.3
A coaxial twin dry-load calorimeter
Figure 15.4
Waveguide calorimeters for WG27 and WG16
Resistance thermometer
336 Microwave measurements which is positioned at an angle across a waveguide. The power into the waveguide can be calculated by measuring the temperature rise of the water and the flow rate. The RF heating is compared to DC heating by means of heating wires within the quartz tube that provide an identical temperature distribution.
15.3.5 Force and field based sensors There are several unusual types of power sensor such as the torque vane [8] and electron beam sensors [9] that have existed previously but are not found in a commercially available form today. With improved fabrication techniques and component quality some of these designs may form the basis of future generations of power sensors. In the torque vane sensor a conductor vane is hung in a waveguide. In the presence of electromagnetic fields a torque will be produced on the vane and if this torque can be measured then the power level can be determined. A commercial version of this type of sensor has been produced in the past. The electron beam power sensor operates by measuring the field strength in a cavity of known geometry necessary to just stop a beam of electrons of known energy. From this the RF power can be calculated. Other novel power sensors include atomic fountain based power sensors, which have been the subject of recent research [10,11] and Hall Effect sensors [12] which measure the voltage across the faces of a piece of semiconductor in the presence of an RF magnetic field. 15.3.5.1 MEMS MEMS is an abbreviation of Micro Electro-Mechanical Systems and typically refers to a moving system fabricated on a silicon wafer with measurements made using electrical methods. MEMS interest has greatly increased over recent years as the cost of wafer production, a spin-off from the semiconductor industry, has decreased. MEMS-based power sensors offer the possibility of easily measuring the very small forces produced by the strength of electromagnetic field associated with a power level in the mW range or lower. Some recent MEMS power sensor designs [13,14] have been based on variations on the theme of capacitively measuring the deflection of a thin bridge caused by power passing along a coplanar waveguide structure beneath it.
15.3.6 Acoustic meter This type of quasi-optic sensor [15] is designed for use from mm wave up to optical frequencies. Pulse-modulated incident power is absorbed in a thin metal film supported by a mylar substrate within a closed cell. This generates a sound wave within the gas of the cell at the modulation frequency, which is picked up by a microphone. A DC current pulse of opposite phase is then applied until there is no microphone response, at which point the microwave and DC power can be said to be equal.
RF power measurement 337
0.965 mW
Ref
Standard power meter
0.000 mW
Ref
Generator Unknown power meter
Figure 15.5
15.4
A ‘simple’ power measurement made by exchanging power sensors
Power measurements and calibration
15.4.1 Direct power measurement In a direct power measurement such as the one shown in Figure 15.5 the calibration factor of the device under test (CFDUT ) in terms of the calibration factor of the standard sensor is given by CFDUT = CFstd
|1 − 0004Src 0004Std |2 PDUT |1 − 0004Src 0004DUT |2 PStd
(15.3)
where Px is the power measured by device x, 0004x is the reflection coefficient of device x and Src refers to the generator or source.
15.4.2 Uncertainty budgets Table 15.1 is an example uncertainty budget for a power measurement made by connecting a calibrated power sensor (such as a thermocouple) on to a badly matched source, where neither reflection coefficient is known. The numbers are for illustration only but are typical of real uncertainties in certain situations. There are several ways to improve this measurement and lower the uncertainties such as: (1) Measuring the complex voltage reflection coefficient (VRC) of the source and load and performing a full mismatch correction. (2) Evaluating the connector repeatability by doing several repeat connections using torque spanners.
338 Microwave measurements Table 15.1
Uncertainty budget for basic power measurement without mismatch correction
Source of uncertainty
Calibration factor Drift in calibration factor Reference source (including mismatch) Mismatch VRC magnitude of sensor: 0.03 VRC magnitude of source: 0.20 Power meter Repeatability
Divisor
Uncertainty contribution
Standard uncertainty
√2 3 √2 2
1.0 0.2 0.7 1.2
0.500 0.116 0.350 0.857
2 1
0.2 0.1
0.100 0.100
Combined standard uncertainty Expanded uncertainty (k = 2)
1.07 2.14
(3) Referencing the power sensor to a better characterised (with known output port match, for example) 50 MHz reference source than the one on the power meter.
15.5
Calibration and transfer standards
Calibration of a power sensor involves comparing it against another power sensor of known calibration factor. Rather than just connecting the two sensors in turn to a source this is generally done using a transfer standard. Usually this would take the form of a power splitter (or coupler) with a power sensor permanently attached to one arm of the splitter. The use of a transfer standard has many advantages: it allows the ratio of the instantaneous powers to be taken; the transfer standard can be measured against the standard, which may be a slow device, and then the device under test can be measured more rapidly against the transfer standard; the full S-parameters of the coupler (or splitter) do not need to be known; and the repeatability of the transfer standard can be evaluated over time.
15.5.1 Ratio measurements Many power meters have an internal reference source with an RF connector on the front panel for calibrating or checking the operation of the power sensor. These sources produce a known power level (generally 1 mW) at a single frequency (generally 50 MHz or DC). The sensor should be referenced to this known power level when it is first turned on and periodically after that. Often when calibrating this type of sensor a calibration of the response of the sensor at the calibration frequency compared to the reference frequency is required, such as the following
RF power measurement 339 definition: Cal Factor = Reference Cal Factor ×
Incident Power at 50 MHz Incident Power at Cal Freq
When calibrating this type of sensor on a splitter based transfer standard against a calibrated standard sensor the calibration factor of the DUT (CFDUT ) is given by CFDUT = CFStd
RStd50 RDUTRF MStdRF MDUT50 RStdRF RDUT50 MStd50 MDUTRF
where CFStd is the calibration factor of the standard sensor, RStd50 is the ratio of the power indicated on the standard sensor to the power indicated on the transfer standard at 50 MHz, MDUTRF is the mismatch factor for the DUT at the RF calibration frequency. MDUTRF = |1 − S0004DUT |2 where S, the equivalent output port match (here at port 2 of the splitter), is given by S = S22 −S21 S32 /S31 . The other definitions follow the same logic. Note the similarity of this equation to (5.3).
15.6
Power splitters
Couplers and splitters can both be used to make the power ratio measurements necessary to calibrate a power sensor (Figure 15.6) [11]. Two resistor power splitters (not to be confused with three resistor power dividers) are well-matched devices that are extremely useful for coaxial calibrations
1.000 mW
Ref
Reference power meter
Generator 1.005 mW
Figure 15.6
Calibration using a power splitter
Ref
340 Microwave measurements
Two resistor power splitter
50 Ω resistors
Figure 15.7
A two resistor splitter
(Figure 15.7 and Table 15.2). When used in a leveling loop the voltage at the centre of the T is held constant and a device on the other arm of the splitter sees an ideal source with a 50 characteristic impedance.
15.6.1 Typical power splitter properties • • • • • • •
Wide frequency range of operation 7 mm DC to 18 GHz 3.5 mm DC to 26.5 or 33 GHz 2.4 mm DC to 50 GHz Reasonably good output match Good long-term stability Limited power capability (6 dB loss: Max. input ≈ 0.5 W)
15.6.2 Measurement of splitter output match Knowledge of the splitter output port source match is necessary in order to perform a full mismatch correction: there are several ways to measure this. The easiest is probably to measure the S-parameters of a reasonably high value attenuator and attach this on to one arm of the splitter. The match of the attenuator and splitter together will be approximately that of the attenuator on its own. This method has the disadvantage of significantly reducing the output power which is often a particular problem at higher
RF power measurement 341 Table 15.2
Example uncertainty budget for measurement of the calibration factor of a power sensor wrt 50 MHz using a power splitter based transfer standard
Source of uncertainty Calibration factor Drift in calibration factor Ratio 1 Ratio 2 Ratio 3 Ratio 4 Drift in transfer standard Mismatch Std at 50 MHz Mismatch DUT at 50 MHz Mismatch Std at 18 GHz Mismatch DUT at 18 GHz Repeatability of standard Repeatability of DUT
Divisor
Uncertainty contribution
Standard uncertainty
√2 √3 √3 √3 √3 √3 3 1 1 1 1 1 1
0.60 0.20 0.10 0.10 0.10 0.10 0.20 0.04 0.08 0.15 0.20 0.10 0.10
0.300 0.116 0.058 0.058 0.058 0.058 0.116 0.029 0.057 0.150 0.200 0.100 0.100
Combined standard uncertainty Expanded uncertainty (k = 2)
0.50 1.00
frequencies where broadband, higher power sources are not so readily available. Another method is to measure all the S-parameters of the splitter with a load (or other known impedance) attached to the other ports in turn. The equivalent output port match can then be calculated from these values [16]. A third method, known as the ‘direct method’ [17,18], involves performing a one-port calibration on one arm of the splitter using a network analyser connected to the other two ports (Figure 15.8).
15.6.3 The direct method of measuring splitter output If for a setup similar to Figure 15.8, the uncalibrated S-parameter data (S11,raw and S21,raw ) from the ANA is extracted, for any item connected to the splitter port, and the ratio x taken of the two S-parameters x=
S11,raw S21,raw
then following the procedure below, the splitter output match can be calculated. Three devices of known VRC such as Short (0004SC ), Open (0004OC ) and Load (0004L ) can be connected to the splitter port in turn. The three ratios for the Load, Open and Short can be defined as being A, B and C, respectively, and the three one-port error terms defined as Directivity EDF , Source Match ESF and Reflection Tracking ERF .
342 Microwave measurements
VNA
L
ΓL
Figure 15.8
S
O
ΓSC
ΓOC
Measurement of splitter output match using the direct method
The equations relating all these can be written in matrix form as 1 A0004L 0004L EDF A 1 B0004OC 0004OC ESF = B 1 C0004SC 0004SC E C where E = ERF − EDF ESF . These can be solved by finding the inverse of the square matrix (or by any other matrix equation solving technique). Writing the solutions out in full gives ESF =
A(0004SC − 0004OC ) + B(0004L − 0004SC ) + C(0004OC − 0004L ) A0004L (0004SC − 0004OC ) + B0004OC (0004L − 0004SC ) + C0004SC (0004OC − 0004L )
EDF =
A(C − B)0004OC 0004SC + B(A − C)0004L − 0004SC + C(B − A)0004OC 0004L A0004L (0004SC − 0004OC ) + B0004OC (0004L − 0004SC ) + C0004SC (0004OC − 0004L )
E=
A(B0004OC − C0004SC ) + B(C0004SC − A0004L ) + C(A0004L − B0004OC ) A0004L (0004SC − 0004OC ) + B0004OC (0004L − 0004SC ) + C0004SC (0004OC − 0004L )
RF power measurement 343 Once ESF , ERF and EDF are calculated the values can be checked against a reference device of known VRC by performing a ‘normal’ one-port VRC measurement using (15.4). x − EDF ERF + ESF (x − EDF ) x − EDF = E + ESF x
S11 =
(15.4)
where x is, as above, the ratio of the two uncalibrated S-parameters for the known device. ESF , the splitter output match, has now been established.
15.7
Couplers and reflectometers
Calibration of waveguide sensors and higher power calibrations in coaxial line are often done using couplers. If the DUT and coupler S-parameters are already known then a calibration can occur in a manner similar to using a power splitter. If the coupler or DUT S-parameters are not known then two couplers and power sensors can be combined (Figure 15.9) to form a basic reflectometer that gives an indication of the forward and reverse powers and hence the DUT VRC. The directivity of the couplers will limit the accuracy of any calibrations made using this method. Calibrations at higher power levels than those at which calibrated standards exist can be performed using multiple, well-matched, high coupling factor couplers with power sensors on the sidearm and by varying the power level at each stage of the calibration process over the linear range of the sidearm power sensors.
15.7.1 Reflectometers If the transfer instrument is a Reflectometer such as a VNA, six-port or multistate reflectometer, the DUT reflection coefficient can be determined at the same
Prefl
Pinc
Pd
Standard sensor
Prefl
Figure 15.9
Unknown sensor
Calibration of a waveguide power sensor using two couplers
344 Microwave measurements Sliding short
Pref
Pinc Standard sensor
DUT
Impedance standards
Figure 15.10
Multistate reflectometer
time as taking the necessary power ratios to calibrate the device allowing mismatch corrections to be made. The multistate refiectometer [19] (Figure 15.10) consists of two couplers with power sensors to measure the forward and reverse powers and a sliding short circuit which alters the ‘state’ of the system. By measuring the power ratio between the forward and reverse coupler arms in several states for several known impedances the system properties (such as coupler directivity) can be found. For each state k the ratio of the powers on the forward and reverse arms of the couplers is given by dk 0004 + ek 2 Pref = Pinc ck 0004 + 1 where ck , dk and ek are state-dependent complex constants and 0004 is the reflection coefficient of any device attached to the output port. At NPL multistate reflectometers using three states and four known impedances are used for waveguide calibrations between 8.2 and 110 GHz.
15.8
Pulsed power
The topic of non-CW power measurements is extremely large and cannot be covered adequately in the space available here. The notes here present a brief introduction. In a CW signal, such as the one illustrated in Figure 15.11 the instantaneous power will cycle at twice the frequency of the voltage or current. The power reported by a sensor with much longer time constant than the RF frequency will remain constant at the average power. In a case such as the one shown in Figure 15.12 a slowly varying signal is then modulated onto a much higher RF frequency. Here, there are three obvious definitions of power: the instantaneous power, the average power and the envelope power
RF power measurement 345 1
0.5
V(t ) I(t ) PInstant
†
0
200
400
600
800
1000
1200
PAverage −0.5 −1
Figure 15.11
1.023×103
t
Voltage, current and instantaneous and average power
1
0.8
PInstant
†
0.6
PEnvelope
†
PAverage
0.4
PEP 0.2
3.425×10−11 0
200
400
600
t
Figure 15.12
800
1000
1200 1.023×103
Modulated RF – instantaneous, average and envelope power
averaged over each RF cycle. A slow-response power sensor will still measure the average power but a faster diode-based power sensor may be able to follow the envelope and provide details about the power–time template. A sensor with a very fast response, such as an oscilloscope, may be able to trace the RF frequency, and the envelope can then be extracted by various methods providing even greater details of the pulse shape.
346 Microwave measurements Peak envelope power Overshoot 4dB −6dB
Pulse average power
1dB −1dB Average power
−30dB Pulse width
Power off noise floor
−70dB Risetime
Figure 15.13
Falltime
GSM pulse specifications
Perhaps the simplest pulsed measurement involves measuring the average power of a repetitive pulsed signal and multiplying by the duty cycle to arrive at a ‘pulse’ power. However pulses are never exactly square, or of constant power and so this method tells us relatively little about the pulse. The GSM Pulse specification for envelope power shown in Figure 15.13 is typical of the usual pulsed measurements that are required – peak envelope power, pulse average power, average power and pulse risetime and falltime. The calibration factor of a diode power sensor capable of performing measurements on fast pulses will not, in general, be the same as its CW calibration factor. These sensors do not measure true RMS power and factors such as sensor impulse response time, recovery time or nonlinearity will lead to errors.
15.9
Conclusion
These notes have briefly covered the techniques and instruments needed to make a variety of common power measurements and power sensor calibrations. A more detailed guide to power measurements across a wide range of topics is the book by Alan Fantom [20] and this is recommended as a good starting point for those who wish to learn more about this area.
15.10 Acknowledgements The author would like to thank Geoff Orford and Alan Wallace who both previously worked in the Power Measurement area at NPL and RSRE and contributed greatly to previous versions of these notes and viewfoils.
RF power measurement 347
References 1 Ramo, S., Whinnery, J. F., and van Duzer, T.: Fields and Waves in Communication Electronics (Wiley, New York, 1965). 2 Kerns, D. M., and Beatty, R. W.: Basic theory of waveguide junctions and introductory microwave network analysis (Pergamon Press, London, 1967) 3 Warner, F. L.: Microwave Attenuation Measurements, (Peter Peregrinus, London, 1977) 4 ‘The expression of uncertainty and confidence measurements’, United Kingdom, Accreditation Service (UKAS) document M3003, London 1997 5 Fantom, A.: ‘Improved coaxial calorimetric RF power meter for use a primary standard’, Proc. Inst. Electr. Eng., 1979;126(9):849–54 6 Macpherson, A. C. and Kerns, D. M.: ‘A microwave microcalorimeter’, Review of Scientific Instruments, 1955; 26(1):27–33 7 Abbott, N. P., Reeves, C. J., and Orford, G. R.: ‘A new waveguide flow calorimeter for levels of 1–20 w’, IEEE Trans. Instrum. Meas. Inst. Electr. Eng., 1974; IM-23(4):414–20 8 Cullen, A. L. and Stephenson, L. M. A.: Torque operated wattmeter for 3 cm microwaves, Proc. Inst. Electr. Eng., 1952;99(4):112–20 9 Oldfield, L. C., and Ide, J. P.: A fundamental microwave power standard, IEEE Trans. Instrum. Meas., 1987;IM-36(2):443–9 10 Paulesse, D., Rowell, N., and Michaud, A.: Realization of an atomic microwave power standard, Digest of Conference on Precision Electromagnetic Measurements, Ottawa, Canada, 2002; pp. 194–5 11 Donley, E. A., Crowley, T. P., Heavens, T. P., and Riddle, B. F.: ‘A quantum-based microwave power measurement performed with a miniature atomic fountain’, Proceedings of the 2003 IEEE International Frequency Control Symposium, Tampabay, FL, 2003; pp. 135–7 12 Barlow, H., and Katoaka, S.: The Hall Effect and its application to power measurement at 10 G c/s, Proc. Inst. Electr. Eng., Part B, 1958;105:53–60 13 Fernandez, L. J., Visser, E., Sese, J., et al.: ‘Development of a capacitive MEMS RF power sensor without dissipative losses: towards a new philosophy of RF power sensing’, Digest of Conference on Precision Electromagnetic Measurements, London, UK, 2004; pp. 117–18 14 Alastalo, A.Kyynanainen, J., Sepa, H. et al.: ‘Wideband microwave power sensor based on MEMS technology’, Digest of Conference on Precision Electromagnetic Measurements, London, UK, 2004; pp. 115–16 15 NPL News, Spring 1990, no. 369, p. 12 16 Tippett, J. C., and Speciale, R. A.: ‘A rigorous technique for measuring the scattering matrix of a multiport device with a 2-port network analyser’, IEEE Transaction on Microwave Theory and Techniques, 1982;MTT-30: 661–6 17 Juroshek, J.: ‘A direct calibration method for measuring equivalent source mismatch’, Microwave Journal, 1997;40:106–18
348 Microwave measurements 18 Rodriguez, M.: ‘A semi-automated approach to the direct calibration method for measurement of equivalent source match’, ARMMS Conference, Bracknell, UK, April 1999, pp. 35–42. 19 Oldfield, L. C., Ide, J. P., and Griffin, E. J.: A multistate reflectometer, IEEE Trans. Instrum. Meas, 1985;IM-34(2):198–201 20 Fantom, A.: ‘Radio frequency and microwave power measurement’, Electrical Measurement Series no. 7’, (Peter Peregrinus, London, 1990) 21 Johnson, R. A.: Understanding microwave power splitters, Microwave Journal, Dec 1975, pp. 49–51, 56 22 Engen, G. F.: Power equation: a new concept in the description and evaluation of microwave systems, IEEE Transactions on Instrumentation and Measurement, 1971;IM-20(1):49–57
Chapter 16
Spectrum analyser measurements and applications Doug Skinner
Spectrum analyser is a measuring instrument, which is used to display many different kinds of signal. This chapter is an introduction to the spectrum analyser and covers the most important parts of the analyser performance that need to be understood. This overview of spectrum analysers is split into four parts. Part 1: Introduction. Describes the basics of signal analysis and compares the oscilloscope time-domain display with the spectrum analyser frequency-domain display and some basic spectrum analyser measurements are also described. Part 2: How the spectrum analyser works. Provides an explanation of how a basic spectrum analyser works. It includes a description of the importance and significance of the main operator controls and how they are used to ensure a clear understanding of the display and to reduce or prevent mistakes. Part 3: The important specification points of a spectrum analyser. Describes the important specification points that need to be known and understood in order to select the correct instrument for a particular measurement. Some sources of errors and measurement uncertainties are also covered in this section. Part 4: Spectrum analyser measurements. Discusses some of the common measurements that are made using a spectrum analyser and the measurements reviewed include harmonic and intermodulation measurements as well as the measurement of modulated and pulsed signals.
16.1
Part 1: Introduction
16.1.1 Signal analysis using a spectrum analyser Before making any measurements using a spectrum analyser the user should prepare the spectrum analyser for use by carrying out any pre-calibration procedure (Auto Cal)
350 Microwave measurements Amplitude
Frequency
Time
Figure 16.1
Three-dimensional graph
recommended by the manufacturer. Some spectrum analysers include a RESET button to return the analyser to the initial set of conditions if the user has problems in interpreting the display. The next step is to consider the type of input signal and power level that are to be applied to the spectrum analyser to avoid overloading or damaging the input circuitry. The final step is to interpret and understand the displayed results.
16.1.2 Measurement domains Suppose that there is a requirement to analyse a signal that consists of a sine wave with a second harmonic component. Consider the three-dimensional graph shown in Figure 16.1. It can be seen that the graph has three mutually perpendicular axes that are calibrated in terms of time, amplitude and frequency. The objective of the signal analysis is to display the components of such a signal and there is a choice to view the signal in terms of Amplitude against Time or as Amplitude against Frequency.
16.1.3 The oscilloscope display The display when viewed as an Amplitude against Frequency display is shown in Figure 16.2 and is recognisable as a typical oscilloscope display and it is known as a time-domain display. In this situation only a single combined waveform is shown on the display. This is the waveform in the Figure shown as a solid line, but there are in
Spectrum analyser measurements and applications 351 Combined waveform
Amplitude
Fundamental
Second harmonic
Time
Figure 16.2
Oscilloscope amplitude against time display
fact at least two sinusoids present as shown by the two thin lines. The oscilloscope time-domain display does not separate out the individual frequency components and its shape changes depending on the relative amplitudes and phase of the sinusoids present.
16.1.4 The spectrum analyser display The spectrum analyser display of Amplitude against Frequency is shown in Figure 16.3 and is known as a frequency-domain display. In this case, it reveals the two separate frequency components of the applied signal, the fundamental and the harmonic. The fundamental frequency is represented on the display by the first single vertical line. The shorter vertical line that can be clearly seen to the right of the fundamental represents the second harmonic. How the Amplitude against Frequency display is achieved using the spectrum analyser is explained later in this chapter.
16.1.5 Analysing an amplitude-modulated signal 16.1.5.1 Amplitude modulation – Oscilloscope The first analysis example is to look at the relatively simple amplitude-modulated signal as displayed on an oscilloscope. Figure 16.4 shows the familiar oscilloscope display of an amplitude-modulated signal. It can be seen that the high-frequency carrier has a low-frequency signal superimposed upon it. The modulation envelope can also be seen on the display. It is possible to measure the modulation frequency (f mod) and modulation depth from
Amplitude
352 Microwave measurements
Frequency
Figure 16.3
Spectrum analyser amplitude against frequency display % Modulation =
Emax − Emin Emax + Emin
× 100
Emin
Emax
Amplitude
Figure 16.4
1
Time
Fmod
The oscilloscope display
the display but it is difficult to obtain any further information over and above modulation depth and modulation frequency. Consequently, the oscilloscope is not widely used to analyse radio frequency (RF) and microwave signals because of the limitations described.
Spectrum analyser measurements and applications 353
Figure 16.5
The spectrum analyser display
16.1.5.2 Amplitude modulation – spectrum analyser Figure 16.5 shows an amplitude-modulated signal as displayed by a spectrum analyser. The carrier, upper and lower side frequencies and noise can all be clearly seen. Note that the analysis of the amplitude-modulated waveform clearly demonstrates the superior analytical powers of the spectrum analyser. Spectrum analyser display of Amplitude against Frequency is more useful because the harmonics, spurious signals, sidebands and noise can be observed. One further advantage of a spectrum analyser is its high sensitivity, which means that it can measure very low-level signals down to less than 0.1 µV because it is selective rather than broadband. It can also display low-level signals at the same time as high-level signals because logarithmic amplitude scales are used. An oscilloscope, which generally has a linear vertical scale, does not have this capability. Many other measurements can also be made on many different and complex signals using a spectrum analyser as will be described later in Part 4. It should be emphasised at this stage that the interpretation of some spectrum analyser displays of complex waveforms requires careful study.
354 Microwave measurements
16.2
Part 2: How the spectrum analyser works
16.2.1 Basic spectrum analyser block diagram A greatly simplified block diagram of a basic swept-tuned heterodyne spectrum analyser is shown in Figure 16.6. In practice, the implementation is considerably more complex as there are many more frequency conversion stages. The input signal is applied to the input mixer through an input attenuator, which adjusts the sensitivity and optimises the signal level at the mixer to prevent overload or distortion. An input low-pass filter is also included at this stage to avoid intermediate frequency (IF) feed-through and to reject the upper image frequency. The mixer converts the input signal to a fixed IF, at which point a range of Gaussian band-pass filters or digital filters are switched in to change the selectivity or resolution. To give a vertical scale, calibrated in dB, the signal at the IF stage is passed through a logarithmic amplifier. The signal is then applied to a detector and passes through selected video filters before being applied to the vertical scale of the display. The horizontal input of the spectrum analyser display (frequency) is achieved by using a variable amplitude ramp generator, or saw-tooth generator, which is also applied to a voltage-controlled oscillator that feeds the mixer. As the ramp voltage is increased, the receiver tunes to a progressively higher frequency and the trace on the display moves from left to right. Using this technique, an Amplitude against Frequency display is shown on the spectrum analyser.
16.2.2 Microwave spectrum analyser with harmonic mixer The basic block diagram of Figure 16.6 is generally only used for spectrum analysers covering up to around 4 GHz. For a 4 GHz instrument the first local oscillator would have to cover from approximately 5 to 9 GHz but the local oscillator for a 26.5 GHz spectrum analyser would have to cover approximately 30–56.5 GHz. This is a major engineering challenge especially as the oscillator needs to be at a high level and have good voltage frequency linearity, low-noise, low-level spurious signals and an output Mixer RF input
RF attenuator
Preselector
IF amplifier
IF attenuator
Resolution filters
Log amp
Detector Video filter
Local oscillator Reference oscillator Sweep generator
Figure 16.6
Block diagram of a basic spectrum analyser
Display
Spectrum analyser measurements and applications 355 level that is adequately independent of frequency. Furthermore, the design has to be implemented at an economical price. An alternative more practical approach, used in most microwave spectrum analysers, is to use a harmonic mixer. This concept is shown in Figure 16.7. The fundamental frequency of the local oscillator is used for the lower frequencies and higher harmonics are used to cover the higher frequencies. A separate harmonic multiplier is not actually used in practice; the mixer is designed to mix with harmonics of the local oscillator.
16.2.3 The problem of multiple responses The system described in Figure 16.7 will operate to high microwave frequencies but there is a major limitation. The type of analyser shown in the previous diagram has a fundamental flaw: one signal at the input generates multiple responses such that one signal has many other signals associated with it, as shown in Figure 16.8 which is obviously incorrect.
Mixer IF output
RF input
X1
X2
X3
X4
Local oscillator
Figure 16.7
Microwave spectrum analyser with harmonic mixer Fundamental
Figure 16.8
2nd Harmonic
3rd Harmonic
Multiple responses for a single input frequency
356 Microwave measurements RF input
Mixer IF output
YIG filter
X1 X1
X2 X2
X3 X3
X4 X4
Local oscillator
Figure 16.9
Microwave spectrum analyser with a tracking preselector
Not only does this one signal mix with each of the harmonics of the local oscillator to produce multiple responses but additional responses are also generated at the image frequencies. Some of the earlier microwave spectrum analysers used this technique but the limitations are so severe that it is very rarely, if ever, used today.
16.2.4 Microwave spectrum analyser with a tracking preselector The diagram in Figure 16.9 shows how adding a band-pass filter at the input of the spectrum analyser can refine the harmonic mixer technique. This is known as a tracking preselector and the microwave spectrum analyser uses a YIG (Yttrium Iron Garnet) swept band-pass filter for the tracking filter and is usually referred to as a preselector.
16.2.5 Effect of the preselector The effect of using a preselector is shown in Figure 16.10. The swept band-pass filter selects only the wanted signal so that all the unwanted signals are rejected to make the measurement valid. A quality instrument has a preselector with high out of band rejection and the ability to track closely the input tuned frequency. Certain earlier spectrum analysers required the preselector to be ‘peaked’ before a measurement was made to ensure that the preselector is tuned correctly but this is not necessary with the latest and more complex instruments.
16.2.6 Microwave spectrum analyser block diagram In practice, modern microwave spectrum analysers are usually a combination of a fundamental frequency analyser and a harmonic analyser. The fundamental frequency
Spectrum analyser measurements and applications 357
Figure 16.10
Effect of the preselector
‘Harmonic’ mode
Input
To 502.6 MHz IF
4.5–9 GHz 4.9 GHz
‘Fundamental’ mode 4.2 GHz 4.4 GHz
Figure 16.11
100 Hz to 4.2 GHz spectrum analyser
method of operation is used at the lower frequencies but at the higher frequencies the multiplication technique, with a preselector, is used. Figure 16.11 shows the architecture of a typical 100 Hz to 4.2 GHz spectrum analyser. In the fundamental mode the input signal is mixed with a local oscillator covering from 4.5 to 9 GHz. The IF is then downconverted to a 502.6 MHz signal by a fixed 4.4 GHz local oscillator. To cover the higher frequencies the change over switch operates to bring the swept harmonic mixer into play and the 4.5–9 GHz local oscillator is used to downconvert the signal to the IF of 502.6 MHz. Microwave spectrum analysers that use a harmonic mixer have a characteristic ‘stepped’ noise floor as illustrated in the display in Figure 16.12. The rise in the noise
358 Microwave measurements occurs at the frequency break points where the higher harmonics of the local oscillator are used. From Figure 16.12 it can be seen that the instrument is approximately 10 dB less sensitive at 22 GHz compared with the sensitivity at 2 GHz.
16.2.7 Spectrum analyser with tracking generator Spectrum analysers are made even more useful by the addition of a tracking generator. A tracking generator is a swept signal whose instantaneous frequency is always the same as the frequency to which the spectrum analyser is tuned. Many spectrum analysers incorporate tracking generators to increase the applications of the instrument to include wide dynamic range swept frequency response measurements. The use of
10 dB/ division
Start 2 GHz
Figure 16.12
Stop 22 GHz
Noise floor display Mixer
RF input
RF attenuator
IF amplifier
Preselector
IF attenuator
Resolution filters
Log amp
Detector Video filter
Local oscillator Reference oscillator
Sweep generator Display
Tracking generator output
Fixed oscillator Mixer Tracking generator
Figure 16.13
A spectrum analyser with tracking generator
Spectrum analyser measurements and applications 359 a tracking generator means that it is not always necessary to have an external signal source when making some measurements. Figure 16.13 shows how a tracking generator facility can be added to a spectrum analyser. The output signal synchronously tracks the input tuned frequency of the instrument with the advantage that the dynamic range is better than would be obtained if a broadband detector was used. A dynamic range of over 110 dB can be achieved with a spectrum analyser using a tracking generator.
16.3
Part 3: Spectrum analyser important specification points
Spectrum analysers are complex items of test equipment and they can easily be misused. At worst, a wrong result can be obtained; at best, the operator may not be getting the best performance from the instrument. The latest spectrum analysers have many automatic functions, but incorrect results are still possible. When using a spectrum analyser it is important that the operator understands the function of the basic controls of the instrument in order to be able to use it effectively and to avoid incorrect results. The spectrum analyser block diagram (Figure 16.14) is repeated here to show how the controls change the instrument functions. There are four main controls on a spectrum analyser and they are (1) (2) (3) (4)
RF Attenuator and IF gain, sweep speed, resolution bandwidth and video bandwidth.
The reason for highlighting the four controls listed above is that they are probably the most commonly misunderstood and abused. Incorrect settings of these controls can cause serious measurement errors, so it is important to realise their significance. The frequency and amplitude are also important controls, but they are more easily understood and less likely to cause problems. Mixer RF input
RF attenuator
Preselector
IF amplifier
IF attenuator
Resolution filters
Log amp
Detector Video filter
Local oscillator Reference oscillator Sweep generator
Figure 16.14
Spectrum analyser controls
Display
360 Microwave measurements Mixer To detector
RF input
Attenuator
Resolution filter
IF amplifier
Local oscillator
Figure 16.15
Input attenuator and IF gain controls
16.3.1 The input attenuator and IF gain controls The block diagram Figure 16.15 shows how the sensitivity of a spectrum analyser can be changed. To increase the sensitivity of the spectrum analyser the operator has two options, either the input attenuation can be reduced or the IF gain can be increased, but if the wrong option is chosen then the measurement may become invalid. It is essential to arrange the correct signal power input level to the mixer to ensure correct operation. If the input attenuation is reduced too much then the input mixer could be overloaded with the result that unwanted distortion products are generated within the spectrum analyser. If the IF gain is increased then the risk of overloading the input mixer is removed but the noise level could rise to an unacceptable level with the result that some signals of interest could be masked in the noise. A further problem that could arise is the introduction of distortion or intermodulation in the IF stages. Many spectrum analysers automatically select the optimum RF attenuation and IF gain settings once the reference level at the top of display has been selected. Under certain circumstances, however, it may be an advantage to override the automatic selection to select a mode of operation with either lower noise or lower intermodulation.
16.3.2 Sweep speed control The spectrum analyser sweep speed must be swept sufficiently slowly to allow the signal level in the narrow resolution filters to settle to a stable value. Figure 16.16 shows two different analyser responses to the same signal and the effects produced when sweeping too fast are clearly shown. First, the amplitude of the displayed signal is reduced because the filter does not have sufficient time to respond to the signal
Spectrum analyser measurements and applications 361
Correct sweep speed
Figure 16.16
Sweep speed too fast
Shows the effect of sweeping too fast
and second the maximum is moved to the right due to the delay in the response. This effect is sometimes referred to as ‘ringing’. The Sweep bandwidth factor is given by the following relationship: Sweep ∝
Span Resolution bandwidth2
(16.1)
We can see that for a given Span (total frequency scale across the screen) if the resolution bandwidth is changed then the sweep speed will change. For most spectrum analysers this is carried out automatically and modern instruments incorporate software control to ensure that the correct sweep speed is achieved. But under certain conditions, where high resolution is required, the sweep speed may need to be as slow as 100 seconds and then some form of digital storage is essential to ensure that a visible display is achieved. Manual adjustment of the sweep speed is sometimes provided on some instruments to override the automatic selection. Sweeping faster than the optimum value can be useful to carry out a rapid uncalibrated search for spurious signals or to study the effects of rapidly changing transient signals. However, the operator must be aware of the display errors that can be caused. Sweeping slower than the optimum sweep can be used, for example, when sweeping a filter with very steep skirts by using the Tracking Generator.
16.3.3 Resolution bandwidth Resolution filters are a very important part of the spectrum analyser operation and they need to be carefully used. Resolution bandwidth is the bandwidth of the IF filter that determines the selectivity of a spectrum analyser. It is basically the ability of the analyser to separate closely spaced signals. A wide resolution bandwidth is required for wide sweeps whilst a narrow filter is used for narrow sweeps. Figure 16.17 shows three displays of an amplitude-modulated signal, they illustrate why it is necessary to be able to change resolution bandwidth.
362 Microwave measurements
WideResolution resolution filter Wide Filter
Required Required Display display
Figure 16.17
Using a wide resolution bandwidth
The wide resolution bandwidth is effectively a plot of the response of the resolution filter of the spectrum analyser. As the resolution filter is swept across the frequency scale of the spectrum analyser, any signal that is within the pass-band of the filter will result in a response on the display. Figure 16.17 shows that if the signal that is being measured is a carrier with two side frequencies when the resolution bandwidth (shown dotted) is too wide it is not possible to display the signal correctly. We can see frequency response of the instrument’s filter is swept by the local oscillator and the side frequencies are not seen in this situation. The detail of the response on the display is clearly dependent upon the bandwidth of the resolution filter and speed that it is moved across the display. However, by using progressively narrower resolution filter bandwidths as shown in Figure 16.18, the display can resolve the side frequencies. However, the penalty for high resolution is that a slower sweep speed needs to be used. Most spectrum analysers have a number of resolution bandwidth filters. The wide resolution bandwidth filters are only normally used when the display needs to be updated rapidly.
16.3.4 Shape factor of the resolution filter Figure 16.19 shows two types of filter in use as resolution filters in spectrum analysers and they have defined filter shapes. 60 dB Bandwidth 3 dB Bandwidth The shape factor is defined as the ratio of the 60 dB bandwidth to the 3 dB bandwidth. The first type of filter is the Gaussian filter and it has a shape factor of 11:1 for high quality to 15:1 for a lower quality filter. The second type of resolution filter is a digital Shape Factor =
Spectrum analyser measurements and applications 363 (a)
Narrower resolution Resolutionbandwidth Bandwidth
(b)
Narrowest resolution bandwidth
Figure 16.18
(a) Using a narrower resolution and (b) the narrowest resolution
filter that has a shape factor of 5:1. The digital filter is particularly useful where a narrow resolution filter is needed, say from 1 Hz to 30 Hz. This minimum resolution bandwidth of a spectrum analyser is a key measure of the ability to measure low-level signals adjacent to high-level signals. Many spectrum analysers have a combination of Gaussian and digital filters included in their design. A measurement that illustrates the importance of minimum resolution bandwidth is the determination of low-level signal such as a 50 Hz side frequency (hum sidebands) close to a large signal. For example in Figure 16.20, the upper trace is achieved by using a 10 Hz resolution bandwidth and only one signal is discernible. The lower trace, which uses a 3 Hz resolution bandwidth, clearly shows the low-level signals. For example, if the sidebands are 70 dB down then a 10 Hz resolution bandwidth filter with a shape factor of 11:1 could not resolve the side frequencies because if the
364 Microwave measurements 3 dB
Digital filter
Gaussian filter
60 dB
Figure 16.19
Resolution bandwidth filter shape factor
10 Hz Filter filter 10Hz
3 Hz Filter filter 3Hz 3Hz Filter
100 Hz span (10 Hz/div)
Figure 16.20
Resolution bandwidth change
3 dB bandwidth is 10 Hz then the 60 dB bandwidth is 110 Hz. A signal 60 dB down and 55 Hz away could just be discerned but a signal 70 dB down and 50 Hz away would not be resolved. By using a 3 Hz filter with a shape factor of 11:1 a signal 16.5 Hz away can be resolved if it is less than 60 dB down; it follows that a signal 70 dB down and 50 Hz away can be easily measured. Digital filters are now common in spectrum analyser and they have a shape factor of 5:1 enabling close-in signals to be resolved and measured.
Spectrum analyser measurements and applications 365
Mixer RF input
To display IF amplifier Resolution filter
Local oscillator
Figure 16.21
Detector
Video bandwidth switch
Video bandwidths
16.3.5 Video bandwidth controls The previous section explained that spectrum analysers are often used to measure very low-level signals that may be almost indiscernible from the system noise. Using a narrower resolution bandwidth filter will reduce the average displayed value of the noise. However, to make the signals even easier to view it is often necessary to smooth out the random fluctuation of noise so that a coherent signal can be more clearly viewed. The traditional way to smooth the noise is to use a low-pass video filter after the detector as shown in Figure 16.21 In order to achieve the noise smoothing it is necessary to sweep more slowly because the time constant of the filter is reduced as the bandwidth of the filter is reduced. Modern instruments couple the video bandwidth controls to the sweep speed control so that the instrument automatically selects a slower sweep speed if the video bandwidth is reduced. Conversely, a lower frequency video bandwidth is automatically selected if the sweep speed is increased. A useful general rule is to set the video bandwidth to be one-tenth of the resolution bandwidth being used. 16.3.5.1 Video averaging An alternative method of noise averaging that has become increasingly popular on software-controlled instruments is to use multiple sweep video averaging. Successive sweeps are averaged so that the amplitudes of coherent signals are unchanged whilst the levels of varying noisy signals are averaged out. The effect of using video averaging is to see the noise level slowly fall. Any low-level coherent signals that have been obscured by noise may become visible. Clearly, it is most important that an operator is aware of the difference between the video bandwidth controls and the resolution bandwidth controls and not to confuse
366 Microwave measurements their different functions. Additional critical aspects of the performance of a spectrum analyser are noise, dynamic range, accuracy and local oscillator phase noise.
16.3.6 Measuring low-level signals – noise The problem when measuring low-level signals is that even a component such as passive resistor generates noise due to thermal effects. The noise voltage generated is given by the equation: V 2 = 4KTBR where K is the Boltzmann’s constant (1.374 × 10−23 J ◦ K−1 ), T is the temperature in K (absolute temperature), B is the bandwidth of the system (Hz) and R is the resistor value (generally 50 0003 for most measurements). Using the figures given above results in a value for V 2 of 8.927 × 10−10 V EMF and converting this to dBm gives a value of −174 dBm. If a spectrum analyser has a typical noise figure of 20 dB then with a 1 Hz resolution bandwidth, the lowest level signal that could be discerned would be 20 dB higher in amplitude than the noise of −174 dBm of a passive termination. This means that with a 1 Hz filter, a spectrum analyser with a 20 dB noise floor could theoretically measure −174 + 20 = −154 dBm. An analyser with the same noise Figure but with a minimum resolution bandwidth of 3 Hz could discern a signal at −149 dBm and with a 1 kHz resolution bandwidth could only measure down to −119 dBm, which is 30 dB worse (Figure 16.22). The use of a pre-amplifier at the input of a spectrum analyser can assist to measure lower amplitude signals.
16.3.7 Dynamic range A useful definition of the dynamic range is that it is the ratio of the largest to the smallest signal simultaneously present at the input of the spectrum analyser that Resolution bandwidth
Figure 16.22
Noise floor
10 kHz
−110 dBm
1 kHz
−120 dBm
100 Hz
−130 dBm
10 Hz
−140 dBm
3 Hz 1 Hz
−145 dBm −150 dBm
Shows how the noise floor drops as the resolution bandwidth is reduced
Spectrum analyser measurements and applications 367 permits the measurement of the smaller signal taking into account the uncertainty of the measurement. The dynamic range is usually quoted in dB. Note that uncertainty of measurement is included in the definition so we need to consider, how the internally generated distortion and noise affect the measurement that we make. For a constant local oscillator level the mixer output is linearly related to the input signal level and for all practical purposes this is true provided that the input signal is more than 20 dB below the local oscillator drive level. The input signal at the mixer determines the dynamic range. The level of signal we need for a particular measurement can be calculated using data from the manufacturer’s specification for the analyser and in some cases the manufacturer’s data sheets include graphs showing the information. 16.3.7.1 Intermodulation and distortion A spectrum analyser can introduce intermodulation and cause distortion on a measurement; certain measurements cannot be made if the instrument itself generates excessive distortion. The distortion is normally described by its order and is noted by its relationship to the signal frequency, therefore second harmonic distortion is known as second order and the third harmonic distortion is known as third-order. Let us consider the second-order distortion first. Suppose that the information from the manufacturer’s specification gives the following data that the second harmonic distortion is 75 dB down on the fundamental for a signal level of −40 dBm at the mixer input. We can plot the data on the graph in Figure 16.23. This means we can measure distortion down to 75 dB. The value can be plotted on a graph of Distortion (dBc) against the mixer input level. Now if the mixer level is changed to −50 dBm we know that distortion changes by 10 dB to −85 dBm. Now if 0 −10 −20
Distortion dBc
−30 − 40 −50 −60 −70 −80 −90 −100 −110 −60
Figure 16.23
−50
−40
−30
−20 −10 0 Mixer level dBm
Second-order distortion
10
20
30
368 Microwave measurements 0 −10 −20
Third-order slope = 2
Distortion dBc
−30 −40
Secondorder slope = 1
−50 −60 −70 −80 −90 −100 −110 −60
Figure 16.24
−50 −40 −30 −20 −10 0 Mixer level dBm
10
20
30
Third-order distortion added
the signal level at the mixer changes to −50 dBm then the internal distortion and the measurement range changes from −75 dBc to −85 dBc. From mathematical analysis of the mixer, it is known that for the second-order distortion the two points are on a line whose slope is 1 so we can draw a line on the graph giving the second-order performance for any level at the input to the mixer. Similarly, we can now construct a line for the third-order distortion. The manufacturer’s data sheet gives −85 dBc for a level of −30 dBm at the mixer input and this value is plotted on the graph in Figure 16.24. If the difference between the two values changes by 20 dB the internal distortion is changed to −105 dBc. Again from mathematical analysis of the mixer these two points are on a line of slope 2 giving the third-order performance for any level at the input to the mixer. 16.3.7.2 Noise There is a further effect on the dynamic range and that is the noise floor of the spectrum analyser. Remember that the definition of the dynamic range is the ratio of the largest to the smallest signal that can be measured on the display. So the noise level places a limit on the smaller signal. The dynamic range is relative to the noise and becomes the signal-to-noise ratio where the signal is the fundamental we require to measure. To plot the noise on a dynamic range chart we take the data from the manufacturer’s data sheet, which gives −110 dBm for a 10 kHz resolution bandwidth. If our signal level at the mixer is −40 dBm it is 70 dB above the average noise. Now for every dB we lose at the mixer input we lose 1 dB of signal-to-noise ratio so the noise curve is a straight line having a slope of −1 and this can be drawn on the graph as shown in Figure 16.25.
Spectrum analyser measurements and applications 369 0 −10 −20 −30
dBc
−40 −50 −60 −70 −80
No
ise
10
kH z
BW
A B
−90 −100 −110 −60 −50 −40 −30 −20 −10 0 Mixer level dbm
Figure 16.25
10
20
30
Dynamic range versus distortion and noise
Figure 16.25 shows two intercepts marked A and B. A is the second-order maximum dynamic range and B is the third-order maximum range. Therefore, the best dynamic range for the second-order distortion is therefore A = 72.5 dB and for the third-order distortion it is B = 81.7 dB. Practically, the intersection of the noise and distortion graph is not sharply defined because the noise adds to the continuous wave (CW) like distortion and reduces the dynamic range by a further 2 dB. The plot for other resolution bandwidths can be added to the graph as required and shows that by reducing the resolution bandwidth the dynamic range can be improved. The two points A and B in Figure 16.26 show the second and third dynamic range improvement by changing the resolution bandwidth from 10 kHz to 1 kHz. Unfortunately, there is no one to one change between the lowered noise floor and the improvement in the dynamic range. And for the second order the change is one-half of the change in the noise floor and for the third-order distortion two-thirds of the change in the noise floor. 16.3.7.3 Spectrum analyser local oscillator phase noise The final item affecting the dynamic range is the local oscillator phase noise on the spectrum analyser and this affects only the third-order distortion measurements. For example, if a two-tone third-order distortion measurement was being made on an amplifier and the test tones were separated by 10 kHz, the third-order distortion components are also separated by 10 kHz. Now, suppose we choose the resolution bandwidth of the spectrum analyser to be 1 kHz allowing for a 10 dB decrease in
370 Microwave measurements 0 −10 −20 −30
dBc
−40 −50 −60 −70
No ise 10 No kH ise zB 1k W Hz BW
Second-order Second order Dynamic dynamicrange range improvement improvement
−80
Third-order dynamicrange range Third order Dynamic improvement improvement
−90 −100 −110 −60
Figure 16.26
−50
−40
−30
−20 −10 0 Mixer level dbm
10
20
30
Reducing resolution bandwidth improves dynamic range
the noise curve then the maximum dynamic range is approximately 88 dB. But if the phase noise at a 10 kHz offset is only −80 dBc then this value becomes the limit of the dynamic range. 16.3.7.4 Selecting the optimum conditions Figure 16.27 combines the graphs given in the two previous illustrations. From this combined graph the optimum dynamic range can be determined. The signal-to-noise ratio improves as the input mixer level is increased. An example illustrates the use of the graph. To determine the optimum dynamic range available to measure third-order intermodulation products the ‘1 kHz bandwidth (BW)’ line is followed; at −34 dBm mixer level the signal-to-noise ratio is almost 90 dB. No further improvement is possible because as the mixer level is increased further the level of the third-order intermodulation products increases. At a mixer level of −30 dBm, the dynamic range is reduced to 80 dB. In addition to the three key aspects highlighted above, other points are also covered in this section, such as sideband noise, residual responses, residual FM and input overload, where experience shows that these areas are also frequently misunderstood. 16.3.7.5 Sideband noise Three specification points affect the ability of a spectrum analyser to measure lowlevel signals close to high-level signals. Two of the points have already been described; they are minimum resolution bandwidth and resolution filter shape factor. The third point is the sideband noise of the local oscillators in the instrument.
Spectrum analyser measurements and applications 371 −50
−60
dBc
−70 Phase noise @ 10 kHz offset
−80
−90 Dynamic range reduction due to phase noise
−100
−110 −60
Figure 16.27
−50
−40
−30
−20 −10 0 Mixer level dBm
10
20
30
Phase noise limit
Phase noise
Figure 16.28
Local oscillator noise sidebands
Figure 16.28 shows the sideband noise of the instrument’s local oscillator superimposed on the resolution bandwidth response. Measurement of low-level signals close to a carrier can be impaired if sideband noise is too high. When developing spectrum analysers designers endeavour to keep the local oscillator phase noise as low as possible. 16.3.7.6 Checking for internal distortion Some spectrum analysers have an ‘Intermodulation Identify’ key (Figure 16.29) to automate and simplify the self-test procedure. In the latest spectrum analysers the
372 Microwave measurements Intermodulation Identify button (may be soft key)
Mixer RF attenuator
Figure 16.29
IF amplifier
Intermodulation distortion identification button
intermodulation key may be a ‘soft key’ and is included as a part of the software functions that appear on the display. However, when the key is pressed additional input attenuation is introduced and the IF amplification is simultaneously increased by an equal amount. If signal levels seen on the display do not move then the measurement is valid. This is a useful, quick and effective way to check for a possible mixer overload situation. If this feature is not available then a useful way to check for any internal overload is to introduce temporarily additional RF attenuation. If a further 10 dB of attenuation is introduced, then all the signals on the screen should drop by 10 dB. If the level changes by a different amount then this indicates that the spectrum analyser is being overloaded and distortion is present.
16.3.8 Amplitude accuracy A good amplitude accuracy specification is essential for accurate and repeatable measurements, but there can be considerable measurement uncertainty if the input match is poor.
16.3.9 Effect of input VSWR The input match, generally expressed as VSWR, reflection coefficient or Return Loss, is a measure of the proportion of the signal incident at the input that is reflected back. Amplitude measurement uncertainty deteriorates; as the match becomes worse, the effect is aggravated more if the source match is poor. The graph of Figure 16.30 shows a convenient plot to give an estimate of the uncertainty limits for a variety of source and load values. The uncertainties rise considerably as the matches become worse. For example, Figure 16.30 shows the mismatch uncertainty for a source VSWR of 2.0:1 and the spectrum analyser input VSWR of 1.5:1 gives a mismatch uncertainty of 1.2 dB.
Spectrum analyser measurements and applications 373
1.5 2:1 1.5:1
Mismatch error limit dB
1.0
1.2:1
0.5 2:1
4:1
3:1
0 dB
Source VSWR −0.5
1.2:1
−1.0
1.5:1 2:1
−1.5 Instrument input VSWR
Figure 16.30
Input mismatch uncertainty
16.3.10 Sideband noise characteristics Figure 16.31 shows the typical sideband noise performance of a quality spectrum analyser. The Figure shows how the sideband noise can reduce close-in resolution as well as reducing dynamic range even for measurements 200 kHz away from the carrier.
16.3.11 Residual responses In an earlier section, the problem of spurious responses was highlighted. A spectrum analyser can display a signal on the screen although no signal is present at the input. Instrument designers endeavour to eliminate this undesirable phenomenon but these residual responses are known to be present in all instruments to a greater or lesser extent. Residual responses occur because within a spectrum analyser there are a number of local oscillator frequencies and their harmonics which can mix with each other to produce signals which can fall within the IF bandwidth and will appear as false signals. Active RF and microwave systems frequently generate non-harmonically related signals that need to be identified and measured. Tracking down and then reducing the level of unwanted spurious signals is a very common application of a spectrum analyser. Inexperienced spectrum analyser users can have problems with such a measurement if they are unaware of the limitations of the instrument. The problem of internally generated harmonically related distortion products has been described but a spectrum
374 Microwave measurements −30
10 Hz
100 Hz
1 kHz
10 kHz
100 kHz
1 MHz Resolution bandwidths
−40 −50
3 Hz
−60 −70 −80 −90 −100 −110 −120 −130 −140
10 Hz Noise dBc/1Hz
Figure 16.31
100 Hz
1 kHz 10 kHz 100 kHz Frequency offset from carrier
1 MHz
10 MHz
Sideband noise graph
analyser itself can have spurious responses. It is essential to ensure that a signal visible on the screen is not generated within the spectrum analyser. The internally spurious signals generated can either be caused by residual responses that are an inherent limitation of the design or caused inadvertently by the operator if the instrument is overloaded. Image responses and multiple responses are also encountered in microwave spectrum analysers if a preselector is not used. Residual responses (see Figure 16.32) can create significant measurement problems so it is important to purchase an instrument with a very good specification. Residual responses of a quality instrument are typically less than −120 dBm to −110 dBm. Some instruments can have inferior specifications or in some cases, the residual responses are not even quoted at all. To be absolutely certain that a signal is not being internally generated it may sometimes be necessary to replace the signal being analysed with a known pure signal and to investigate the difference.
16.3.12 Residual FM An important specification point is residual FM. If the local oscillator in the spectrum analyser has appreciable FM on it then close to carrier measurements cannot be made. Residual FM on a quality instrument will vary from around 1 Hz to 10 Hz depending on frequency range. Figure 16.33 shows how poor residual FM can invalidate close-in measurements.
Spectrum analyser measurements and applications 375
Figure 16.32
Residual responses
Poor quality
Figure 16.33
High quality
Residual FM
16.3.13 Uncertainty contributions A spectrum analyser is a very complex device with many elements, which can change with frequency, temperature and time. Each element contributes towards the inaccuracy or uncertainty of a measurement. Figure 16.34 shows a simplified block diagram of a typical instrument with uncertainty contributions added. These figures are taken from the specification of an instrument in present widespread use. For a given measurement, all the uncertainties may not necessary apply, but the accuracy of such an instrument is poor. The problem can be worse when it is realised that with many instruments it is necessary to adjust front panel presets to obtain such accuracy. This relies on the diligence and skill of the operator and is therefore not reliable. Some spectrum analysers use an automatic self-calibration process and at the touch of a button on the front panel or a soft key the instrument runs through a self-calibration
376 Microwave measurements Input mismatch ± 0.13 dB
RF attenuator RF input
± 0 to 0.8 dB
Mixer
IF amplifier
± 0.3 to 1.0 dB Resolution filters
± 0.1dB Detector
Log amp
Mixer and input filter flatness ± 0.1dB ± 0.2 to 0.8 dB Frequency response ± 0.4 to 2 dB
Display
Temperature drift 0.05 dB/deg C.
Internal calibrator
± 0.07 to 1.2 dB ± 0.25 to 0.4 dB
Figure 16.34
Uncertainty contributions
routine. A typical self-calibration routine includes setting up the amplitude and frequency of each of the resolution filters, measuring and correcting for the attenuation of each of the input attenuator steps. Instruments that have a built-in tracking generator can also correct for the frequency response of the system by sweeping through the entire frequency range whilst routing the amplitude levelled tracking generator into the input. The advantage of automatic self-calibration is that total level accuracy is improved dramatically and the specification is valid for all levels and frequencies and for any span or resolution bandwidth. For engineers who need to produce uncertainty budgets a useful approach is to list all the contributions to the uncertainty of measurement and then to include only those that affect a particular measurement in a final budget as shown in Figure 16.35.
16.3.14 Display detection mode Modern spectrum analysers use digital methods for acquiring and manipulating the data to display. The input data at the input of the spectrum analyser is placed in to segments sometimes called bins and the bins are digitally sampled for further processing and then displayed. The point in the bin where the data are sampled will clearly affect the displayed information. Spectrum analysers may have a number of selectable detector modes and the mode of detector chosen will determine how the input signal is displayed. Table 16.1 shows the advantages and disadvantages of the various detector modes.
16.4
Spectrum analyser applications
Spectrum analysers are used to make a very wide range of measurements. It is not possible to cover all the possible applications but the more common measurements are included in this section.
Figure 16.35
Table 16.1
✓
✓
✓
✓ ✓ ✓ ✓ ✓ ✓ ✓
Adjacent channel power ratio
Channel power ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
✓ ✓ ✓
Phase noise close to carrier
✓
3rd order intercept
3rd order inter modulation products
✓
Phase noise far from carrier
✓ ✓ ✓ ✓ ✓ ✓ ✓
Power versus time for TDMA signals
Absolute level Frequency response RF attenuation IF gain Linearity error Bandwidth switching Resolution Bandwidth Sampling Mismatch
Harmonic distortion
CW signal
Spectrum analyser measurements and applications 377
✓
✓ ✓ ✓
✓
✓
✓
Typical uncertainty contributions for some spectrum analyser measurements Detector modes
Detector mode
Method
Advantages
Disadvantages
Peak
Detects the highest point in the bin
Good for analysing sinusoidal waveforms
Over responds to noise
Sample
Detects the last point in the bin whatever the power
Good for noise measurement
Not good for CW signals with narrow bandwidths and will miss signals that do not appear at the same point in the bin
Negative peak
Detects the lowest power level in the bin
Good for AM/FM demodulation and can distinguish between random and impulse noise
Does not improve the analyser sensitivity although the noise floor will appear to fall
Rosenfell
Dynamically classifies the data as either noise or signal
Gives an improved display of random noise compared with peak detection and avoids the missed signal problem of sample detection
Only used in the high performance spectrum analysers
378 Microwave measurements
Figure 16.36
Harmonic distortion
16.4.1 Measurement of harmonic distortion A spectrum analyser can be used to measure the amplitudes of the fundamental and even very low-level harmonics. Sometimes, however, it is necessary to quote not only the level of the harmonic distortion products but also to give the total harmonic distortion. The total harmonic distortion as shown in Figure 16.36 can be calculated by measuring the amplitudes of all the harmonics and then take the square root of the sum of the squares.
16.4.2 Example of a tracking generator measurement The display shown in Figure 16.37 is a typical tracking generator measurement, the analysis of a 10.7 MHz band-pass filter over a wide dynamic range. The display shows two different traces simultaneously. The upper trace shows the overall response of the filter over a dynamic range in excess of 80 dB. The other trace shows the ripple on the pass-band of the filter displayed with a resolution of 0.5 dB per division.
16.4.3 Zero span The principal function of a spectrum analyser is to sweep through a selected part of the frequency spectrum. In certain circumstances, however, it may be necessary to analyse the characteristics of just one fixed portion of the spectrum. The zero span mode is used for such applications. In this mode, the local oscillator of the instrument is no longer swept; the oscillator is held at a fixed frequency so that the signal of interest can be studied. If sweeping ceases one would expect to merely see a dot or
Spectrum analyser measurements and applications 379 −34.7
Atten 00 dB 50 Ω TG-10.0 dBm
−36.32
−54.7
−36.82
−64.7
−37.32
−74.7
−37.82
−84.7
−38.32
−94.7
−38.82
−104.7
−39.32
−114.7
−39.82
−124.7
−40.32
−134.7 Ref 10.70000 MHz Inc 5.00 kHz
Figure 16.37
−35.82
−44.7
5.00 kHz/Div 200 ms /Div
−40.82 Res bw 300 Hz Vid bw 350 Hz
Measurement of a 10.7 MHz band-pass filter
line on the display, which moves up and down according to the change in amplitude of the signal to which the instrument is tuned. This would provide a certain amount of information, but much more information is obtained if a time base sweeps the spot horizontally in a manner similar to the technique used in oscilloscopes. By sweeping the spot horizontally the display will show amplitude versus time variations of the signal to which the instrument is tuned.
16.4.4 The use of zero span There are many applications of zero span mode but one of the most obvious is to demodulate an amplitude-modulated carrier as shown in Figure 16.38. Another common use is to measure response times, one example is the measurement of transmitter decay time at switch off; this can be a critical measurement since it may determine how quickly an adjacent sensitive receiver can be enabled. Synthesiser switching times and overshoots can also be evaluated using the zero span mode. The time base of modern sophisticated instruments is derived from the reference oscillator. This ensures the very best accuracy when timing measurements are made. Some instruments only have an inaccurate time base, so it is a wise precaution to check the specification of the instrument before making a measurement.
16.4.5 Meter Mode In addition to the zero span mode some instruments incorporate a ‘Meter Mode’. This is used for applications where a spectrum display needs to be retained whilst still monitoring the changing amplitude of a part of the spectrum. A typical application of ‘Meter Mode’ is shown in Figure 16.39. The amplitude of the FM carrier is continuously updated in real time whilst the rest of the display is saved. Any part of the display, selected by the movable marker, can be updated
380 Microwave measurements A Volts 5.00
AM Demodulation Atten 60 dB 50 Ω TG off
4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 Ref 2.010914 MHz Inc 0 Hz
Figure 16.38
Zero span res bw 30 kHz 200µs /div
AM demodulation
A dBm
FM 1kHz mod. freq 2.4 kHz deviation Atten 40 dB 50 Ω TG off
0.0 −10.0 −20.0 −30.0 −40.0 −50.0 −60.0 −70.0 −80.0 −90.0 −100.0
Figure 16.39
Meter−35.47dBm Ref 150.000000MHz Inc 500 Hz
150.000000 MHz 500 Hz/div
Res bw 100 Hz 200 ms/div Vid bw 1kHz
Meter Mode
and monitored. This method is very useful when measuring carrier deviation by the Bessel Disappearing Carrier Technique.
16.4.6 Intermodulation measurement Measuring the harmonic distortion caused by a device is not a very discriminating measurement. A more searching method is to use two or more test signals and to
Spectrum analyser measurements and applications 381 Signal generator F1 Device under test Spectrum analyzer Signal generator F2
Figure 16.40
Combiner
Two-tone test set up
measure the intermodulation products that are generated at the output of the device under test. By using more than one test signal the device receives signals that are closer to the more complex signals that are generally encountered in practical systems. Two separate signal generators and a combiner are needed as shown in Figure 16.40. There are also special signal sources developed that contain two or more sources in order to provide the best possible signals for this test. Another problem is that any non-linearity in the output amplifiers of the signal generators can produce intermodulation. Further problems can arise if the automatic level control (ALC) detector at the output of one signal generator also detects the signal from the other signal generator. It is for these two reasons that it is good practice to insert an attenuator between the signal generator output and the combiner. This may not be practical in some circumstances, because the signal level may be too low. For higher frequency measurements, an isolator is recommended to improve the measurement integrity.
16.4.7 Intermodulation analysis A typical spectrum analyser display of a two-tone intermodulation test is shown in Figure 16.41. Annotation has been added to explain the origin of the intermodulation products. Signal generator 1 has a fundamental frequency of F1 and signal generator 2 has a fundamental frequency of F2 . Non-linearity in the device under test will cause harmonic distortion products of frequency 2F1 , 2F2 , 3F1 , 3F2 , etc. to be generated. Spectrum analyser will record these harmonic distortion products but the significance of the intermodulation test is that the non-linearity causes the harmonic products to mix together to generate additional signals. Numerous intermodulation products can be generated but the two most commonly encountered ones are known as the third-order and fifth-order products. Third-order products have frequencies of 2F1 − F2 and 2F2 − F1 Fifth-order products have frequencies of 3F1 − 2F2 and 3F2 − 2F1
382 Microwave measurements F2
F1
2F2–F1
2F1–F2
3F2–2F1
3F1–2F2
Figure 16.41
Intermodulation display +30 Output level (dBm)
Intercept point
+20 +10 0
Fundamental
−10 −20 −30 −40
3rd order products
−50 −60 −70 −70
−60
−50
−40
−30
−20
−10
0
Input level (dBm)
Figure 16.42
Intermodulation intercept
Even order products such as F1 + F2 and F2 – F1 are also seen but are less significant since the intermodulation products are widely separated from the two frequencies (F1 and F2 ) and they can generally be readily rejected. High-performance spectrum analysers have an intermodulation distortion of typically −95 dBc or better with a signal level of −30 to −40 dBm at the input mixer to allow for the measurement of low levels of distortion.
16.4.8 Intermodulation intercept point The amplitudes of intermodulation products change according to the amplitudes of the test signals applied; therefore, it is necessary to specify the level of the test signals. It can be difficult to compare the performance of different devices if they were measured at different levels. The solution is to use the concept of an intermodulation intercept point. An intercept point is the theoretical point at which the amplitudes of the intermodulation products equal the amplitudes of the test signals, the illustration shows the concept. There are two lines on the graph in Figure 16.42.
Spectrum analyser measurements and applications 383 +25
+30
+20
+20
0
0
+15
+10
5
10
+10
0
10
20
+5
−10 10
15
30
0
−20
20
40
−5
−30
25
50
−10
−40
30
60
−20
−50
35
70
−30
−60
40
80
−40
−70 Signal level (dBm)
45
90
Intercept point (dBm)
Figure 16.43
2nd Order
3rd Order
Intermodulation products dB down
Nomograph to determine intercept
The fundamental line shows a linear relationship between the input and output signals, the line has been extrapolated beyond the output level of +5 dBm since at such levels the response becomes non-linear. Input and output signal levels have also been plotted for the third-order products and the line is extrapolated. The two lines meet at the intermodulation intercept point. The slope of the intermodulation product lines is equal to their order, that is, the second-order lines have a slope of 2:1, the third-order lines have a slope of 3:1. Practically, this means that if the level of the test signal is reduced by 10 dB then the third-order product will theoretically drop by 30 dB, provided that the device is operating in a linear mode.
16.4.9 Nomograph to determine intermodulation products using intercept point method The nomograph in Figure 16.43 gives a rapid but not very accurate means of determining the intercept point. A straight edge is used to join the two known values so that the unknown can be determined.
16.4.10 Amplitude modulation Figure 16.44 shows an idealised spectrum analyser display of an amplitude-modulated signal. The carrier frequency is Fc ; the frequency of the modulating signal is Fm . Three separate frequency components are seen The carrier frequency
Fc
Lower side frequency Fc − Fm Upper side frequency
Fc + F m
The modulation depth in per cent is given by the following formula: Per cent modulation = 2 ×
side frequency amplitude carrier amplitude
× 100 (measured on a linear scale)
384 Microwave measurements
Carrier frequency Fc Upper side frequency Fc + Fm
Lower side frequency Fc–Fm
Figure 16.44
Amplitude modulation measurement
The amplitude of the carrier always remains constant as the modulation depth changes but the sideband amplitudes will change in proportion to the modulation depth. The frequency separation between the carrier and either sideband changes as the modulation frequency changes. When the modulation depth is 100 per cent half of the power is in the sidebands and each sideband frequency amplitude will be 6 dB less than that of the carrier. For lower modulation depths, the sideband amplitude is proportionately less. To measure modulation depth it is thus necessary to measure the amplitude difference between the carrier and the sidebands.
16.4.11 AM spectrum with modulation distortion In practice, there will be harmonics of the modulation frequency also present at Fc ± nF m . Figure 16.45 shows distortion produced at Fc ± 2Fm .
16.4.12 Frequency modulation An FM spectrum theoretically has an infinite number of sidebands, which are symmetrical about the carrier and separated by the modulation frequency. The FM spectrum display shown in Figure 16.46 is thus considerably more complex than an AM spectrum display. Sideband and carrier amplitudes are determined by the unmodulated carrier amplitude and the modulation index (β) which is expressed as Modulation index, β =
Frequency deviation Modulation frequency
In practice, although there are an infinite number of sidebands the amplitudes of the higher frequency ones rapidly reduce to near zero and can be neglected.
Spectrum analyser measurements and applications 385
Additional spectrum caused by distortion Fc−2F
Fc−Fm
Fc
Figure 16.45
Modulation distortion
Figure 16.46
Frequency modulation spectrum
Fc+ Fm
Fc+ 2F
16.4.13 FM measurement using the Bessel zero method With frequency modulation the carrier amplitude is not constant; it varies according to the modulation index and will become zero at times. The sideband amplitudes also become zero at specific values of modulation index. Modulation indices at which the carrier or sidebands have zero amplitude can be calculated. Tables are available
386 Microwave measurements
Figure 16.47
Bessel null
IF filter response
Detected FM
Figure 16.48
FM demodulation
listing the zeros, or Bessel nulls as they are more commonly called. Bessel zeros (see Figure 16.47) are used for accurate calibration of signal generators and modulation meters.
16.4.14 FM demodulation If zero span mode is used on a spectrum analyser no information should be seen if frequency modulation is applied since zero span shows amplitude variation with time. However, if the spectrum analyser is de-tuned by a small amount then the demodulated signal will be seen. This occurs because the slope of the resolution filter acts as a slope detector as shown diagrammatically in Figure 16.48. Accurate measurements are not possible but this does provide a convenient method to view a demodulated signal. It should be noted that the technique might be invalid
Spectrum analyser measurements and applications 387 if significant spurious AM is present in addition to the FM. Some spectrum analysers can measure FM directly. The demodulated FM signal is displayed on a graticule that is vertically calibrated in FM deviation; the horizontal scale is calibrated in time as for the zero span. The illustration shows the technique used.
16.4.15 FM demodulation display Some spectrum analysers incorporate a function that demodulates the FM signal and displays deviation vertically against time horizontally. A typical FM demodulation screen display from a spectrum analyser is shown in Figure 16.49. The peak-to-peak FM deviation can be readily measured from the vertical scale.
16.4.16 Modulation asymmetry – combined AM and FM Simultaneous amplitude and frequency modulation is usually an undesired effect rather than a deliberate form of modulation. It usually results when amplitude modulation is being generated. What happens is that the carrier oscillator frequency is pulled by the modulating signal and hence introduces a small amount of FM together with the desired AM. The result is that AM together with narrowband FM is present at the same modulating frequency producing a combined spectrum. The AM spectrum consists of the carrier and two sidebands but the FM spectrum will consist of a carrier and an infinite number of sidebands but it must be remembered that the amplitude of the FM sidebands falls off very quickly outside of the peak deviation ±0005F. A dev FM 1.0 kHz mod. freq. 3 kHz deviation Atten 40 dB 50 Ω TG off 1kHz/div
Ref 150.000000 MHz Inc 0 Hz
Figure 16.49
FM demod Res bw 10 kHz 500 ps/div
Peak-to-peak FM deviation display
388 Microwave measurements
Figure 16.50
AM and FM asymmetry
For narrowband FM where 0005F is considerably less than the modulating frequency f , the higher-order sidebands fall off so rapidly that only the first sideband need be considered. The narrowband FM spectrum differs from AM in that one side band is 180◦ out of phase with respect to the other sideband. So the resulting spectrum when seen on the spectrum analyser as in Figure 16.50 will be a spectrum where one sideband is larger than the other and it clearly shows the presence of FM on AM. Where the difference in the amplitudes is less than 20 per cent the modulation depth can be calculated by taking the mean of the two-sideband amplitudes to represent the amplitudes of the sidebands due to the AM alone.
16.4.17 Spectrum of a square wave Pulsed RF waveforms are most commonly encountered in radar systems both at IF and at microwave frequencies. To understand the analysis of pulsed RF it is first necessary to study the spectrum of a square wave. Figure 16.51 shows the idealised oscilloscope display of a train of rectangular pulses of pulse repetition frequency, F, and pulse width, t. The corresponding spectrum analyser display in the illustration shows that the individual spectral lines are spaced by the pulse repetition frequency 1/t. The spectrum analyser display also shows that the amplitudes of the individual spectral lines rise and fall in a regular way; the pulse envelope of the spectral lines follows a curve of the form represented by the expression y = sin x/x. The first zero of the sin x/x envelope occurs at a frequency equal to 1/t. Subsequent zeros occur at multiples of 1/t. Each of the rising and falling patterns is referred to as a lobe. In theory, the lobes continue to infinity but in practice the amplitudes of the lobes soon become negligible as the frequency rises.
Spectrum analyser measurements and applications 389
Spectrum analyser
1/t
F
F = Pulse repetition frequency (PRF)=1/T t = Pulse width Oscilloscope T=1/F
t
Figure 16.51
Spectrum of a square wave
16.4.18 Pulse modulation Figure 16.52 shows a typical spectrum analyser display of a pulse-modulated carrier. The spectral line, which can be seen at the centre of the display, is the RF carrier. The individual spectral lines, which are symmetrical about the carrier, are separated by a frequency equal to 1/T as for the basic pulse train; refer back to Figure 16.45 for clarification. The sin x/x zeros again occur at multiples of 1/t. The display is only theoretically symmetrical about the carrier since in some practical radar systems, where there are imperfections, the display may be asymmetrical.
16.4.19 Varying the pulse modulation conditions Pulsed RF can be confusing since the spectrum analyser display depends on both the pulse repetition frequency and the period of the modulating signal. The illustration helps to clarify the situation by showing how the characteristics of a pulse-modulated spectrum change according to the changes in the pulse width and pulse repetition frequency. The upper portion of each of the four displays shows the oscilloscope representation of the modulating waveform; the lower portion of each of the four displays is the spectrum analyser representation of the pulsed RF signal. The Display 1 (top left) of Figure 16.53 is an arbitrary starting point. In Display 2 (top right) of Figure 16.53 the pulse width of the modulating signal is increased whilst the pulse repetition frequency is the same. Increasing the pulse width reduces the value of 1/t so the first zero is at a lower frequency; the lobes are thus narrower. In Display 3 (bottom left) of Figure 16.53 the pulse width is the same as for Display 1 but this time the pulse repetition frequency is lower. Spectral lines are spaced
390 Microwave measurements PRF
1/T
Spectrum analyser
f =1/t Oscilloscope
t
T
Figure 16.52
Pulse modulation
1
2
Pulse wider than 1 narrower lobes PRF and line density same
Narrow pulse wide lobes High PRF low line density
3
PRF lower than 1 higher line density Pulse width and lobes same
Figure 16.53
Varying pulse modulation
4
PRF and line density same as 3 Wider pulse narrower lobes
Spectrum analyser measurements and applications 391 Line mode BW < 0.3 × PRF
1. Line spacing constant in frequency 2. Displayed amplitude independent of resolution bandwidth 3. Line spacing independent of sweep time
Figure 16.54
Envelope display or pulse mode BW >1.7 × PRF
1. Pulse spacing independent of frequency span 2. Displayed amplitude changes with resolution bandwidth 3. Pulse spacing changes with sweep time
Line and pulse mode
according to 1/T so the line density is increased as the pulse repetition frequency is decreased. The Display 4 (bottom right) of Figure 16.53 again shows that a wider pulse causes narrower lobes.
16.4.20 ‘Line’ and ‘Pulse’ modes Pulsed RF spectrum analysis is complicated because the display changes according to the resolution bandwidth selected; if it is significantly higher than the pulse repetition frequency then individual spectral lines will not be resolved. Figure 16.54 shows the frequency response of the resolution filter superimposed over a train of pulses. On the left the resolution bandwidth is shown to be less than the pulse repetition frequency so individual spectral lines are resolved; this is known as ‘line mode’. On the right the resolution bandwidth is greater than the pulse repetition frequency so individual spectral lines are not resolved; this is known as ‘pulse mode’. In the pulse mode, the display seen is not a true frequency-domain display; it is a combination of a time and frequency display. The lines are displayed when a pulse occurs irrespective of the instantaneous tuned frequency of the instrument. The display is in fact a time-domain display of the spectrum envelope. One can rapidly determine that a pulse mode display is occurring by changing the scan time or sweep time; the pulse line spacing will change. The line spacing will not change when the span is changed, as one would expect for a normal spectrum analyser display. A further characteristic of a pulse display is that the displayed amplitude increases as the bandwidth increases. A ‘rule of thumb’ to apply for line mode is to use a resolution bandwidth of less than 0.3 × pulse repetition frequency. For pulse mode, the resolution bandwidth should be greater than 1.7×pulse repetition frequency.
392 Microwave measurements
LO out
IF in
Mixer
RF in (up to 300 GHz)
Figure 16.55
Extending the frequency range
16.4.21 Extending the range of microwave spectrum analysers Most RF spectrum analysers have ‘Local Oscillator Output’ and ‘IF Input’ connectors on the front panel to allow the frequency range to be extended higher with the use of external millimetric mixers. Although this can be useful for a ‘quick look see’ the measurements can be misleading due to poor amplitude accuracy and multiple responses. This feature shown in Figure 16.55 should be used with extreme caution!
16.4.22 EMC measurements The spectrum analyser can be used to make EMC measurements and in some cases additional types of detector are included such as Peak, Average, RMS and Quasi Peak detectors. The spectrum analyser is a very useful instrument to use as a diagnostic tool for EMC measurements. Figure 16.56 shows a plot from a spectrum analyser used for a conducted measurement measured in a semi-lined screened room. The test was made to comply with the European EMC Standards EN 55011 and EN55022 limits.
16.4.23 Overloading a spectrum analyser Applying AC or DC signals of greater than approximately 0.5 W (+27 dBm) can permanently damage the input of a spectrum analyser. The input attenuator and mixer can be destroyed resulting in costly repair and loss of use of the spectrum analyser.
Spectrum analyser measurements and applications 393
Figure 16.56
Spectrum analyser EMC display
Two techniques to protect against overload are incorporated in modern spectrum analysers. In VHF and UHF instruments, a coaxial relay is generally incorporated in the input. Protection to 50 W is possible on VHF instruments. Microwave instruments can be switched to AC input so that DC voltages up to 50 V can be safely applied.
16.5
Conclusion
The above paragraphs show how useful the spectrum analyser is in design and calibration and there are many more fields of measurements and applications where it can be used. The purpose of this chapter is to act as an introduction to the types and applications of spectrum analysers. Finally, remember what you see is not necessarily what you have got! There is a trend to develop multifunction RF and microwave instruments and they often include a spectrum analyser.
Further reading 1 Hewlett Packard: Spectrum Analyser Basics, Application note 150, Publication number 5952-0292, November 1989 2 Hewlett Packard: 8 Hints to Better Spectrum Analyser Measurements, Publication number 5965-6854-E, December 1996
394 Microwave measurements 3 Hewlett Packard: Amplitude and Frequency Modulation, Application note 150-1, Publication number 5954-9130, January 1989 4 Witte, R. A.: Spectrum and Network Measurements (Prentice Hall Inc., Englewood Cliffs, NJ, 1993) 5 Rauscher, C.: Fundamentals of Spectrum Analysis, 2nd edn (Rhode and Schwarz GMBH, Munich, 2002)
Chapter 17
Measurement of frequency stability and phase noise David Owen
An ideal frequency source generates only one output signal with no instability in its output frequency. In reality, however, all signal sources exhibit some uncertainty in their instantaneous output frequency. The uncertainty can be expressed in a number of different ways. The method of expressing the uncertainty is likely to depend upon the intended application as well as the performance of the signal source, and in many cases a source may be characterised in more than one way. High-accuracy frequency sources, such as crystal oscillators and rubidium or caesium frequency standards, are principally measured in terms of their long- and short-term frequency stability by directly measuring the source with a frequency counter. Aging rate is used to express the long-term change of the frequency of the source period of many hours (or more) over a while the short-term stability is a measure of the random fluctuation of the source over a period of the order of seconds. Provided a frequency counter with enough frequency resolution and a frequency standard with adequate performance are used as a reference, the measurement of stability presents no serious problems. Adjustable sources tend to have their frequency stability measured in other ways. For communication systems the most common method of expressing the frequency uncertainty is either as residual phase or frequency modulation or as phase noise. Residual modulation is typically measured by demodulating the carrier and filtering the base band signal through a band-pass filter and measuring the signal in terms of peak, average or RMS radians or Hertz deviation. Phase noise is the most generic method of expressing frequency instability. The carrier frequency instability is expressed by deriving the average carrier frequency and then measuring the power at various offsets from the carrier frequency in a defined bandwidth. The result is then expressed as a logarithmic ratio compared with the total carrier power. The power ratio is usually normalised to be the equivalent signal power
396 Microwave measurements present in a measurement bandwidth of 1 Hz. For some applications (e.g. specifying adjacent channel power on a transmitter) it can be expressed in other bandwidths (in the case of adjacent channel power the receiver bandwidth). The various ways of expressing frequency stability are all measurements of the same physical characteristics but are specified in terms of a critical characteristic of their application. The most useful general measurement, however, is the phase noise characteristics since other measurements can be derived from a phase noise plot. For communication systems the most important offset frequencies are those around 1 kHz, since this strongly influences the residual FM and therefore the ultimate signal–to-noise ratio, offsets between 10 and 25 kHz. At the higher frequency offsets phase noise affects transmitted adjacent channel power and adjacent channel selectivity measurements on narrow band receivers. Phase noise characteristics are important for digital as well as analogue communication systems. The 1 kHz phase noise characteristics of oscillators in transmitters using time-domain multiple access (TDMA) or time-domain duplex (TDD) techniques often determine the residual phase or frequency jitter within a single burst of the carrier frequency. As wider bandwidth systems are adopted phase noise at larger offsets will become increasingly specified, but in general the toughest target is likely to remain the 1 kHz offset performance. The sensitivity to the noise in the 1 kHz offset region on digital modulation systems arises because the signal is split into blocks of information, typically with a duration of 1–20 ms, for the purpose of encoding speech or adding error correction. The details of this are beyond the scope of this chapter. The blocks of information usually have within them a sequence of digital bits that are used to extrapolate the phase and frequency reference of the transmitted signal over the entire block. Having obtained this phase reference the digital data can be derived. This phase or frequency estimation process means that phase noise at low carrier frequency offsets is removed whereas noise at frequencies corresponding to the data block length can directly lead to an increase in measured modulation error. The longer the length of the data block used the more susceptible the system is to lower frequency noise. The measurement of phase noise is likely to continue to be an important activity in the design of communication systems.
17.1
Measuring phase noise
The performance of frequency sources varies considerably and consequently making measurements can be complex. Different methods can be used according to the expected performance and the controls available to set up a measurement (Figure 17.1). The phase noise performance of oscillators can vary greatly according to the type of oscillator and the complexity (and hence cost) of the design.
Measurement of frequency stability and phase noise 397 SSB Noise dBc/Hz −60 1 GHz VCO −100
100 MHz VCXO
−140 −180 10 Hz 100 Hz
1 kHz 10 kHz 100 kHz 1 MHz Offset frequency
Figure 17.1
Phase noise of a voltage controlled crystal oscillator compared to a typical 1 GHz VCO
A crystal oscillator can exhibit a phase noise of −170 dBc Hz−1 at a 20 kHz offset from a carrier of 100 MHz. A well-designed voltage controlled oscillator covering a frequency range of onequarter of an octave at 1 GHz will produce a phase noise of −115 dBc Hz−1 at a 20 kHz offset frequency. A typical microwave yttrium iron gasnet (YIG) oscillator could have a significantly worse performance and have the added complication of including large amounts of low-frequency uncertainty caused by disturbance of its magnetic tuning field from mains transformers, switch mode power supplies and display drive circuits. Measuring such widely divergent oscillators causes considerable measurement problems and it is not surprising that none of the techniques solves all the problems. Four basic measurement techniques are described based on spectrum analysers, delay line discriminators, quadrature technique and FM discriminators. All of these methods can be used to successfully measure the characteristics of a signal source and each has their advantages and disadvantages. The methods of all measurements rely on a similar basic principle (Figure 17.2). The signal to be measured is frequency converted to a baseband or IF and then passed through a device which extracts either phase or frequency information from the carrier. A frequency selective measuring device is then used to measure the noise as a function of offset frequency. A calibration system is used to scale the results into meaningful units.
17.2
Spectrum analysers
Since spectrum analysers measure the RF signal power in a specific bandwidth they can clearly be used to measure phase noise. Most modern analysers include software functions which will convert a measured signal level from its measured value (in the
398 Microwave measurements
Ref osc.
(except delay line discriminator)
Device to translate to phase/frequency
Frequency selective measuring device
Source under test Calibration system (software and hardware)
Figure 17.2
Principle of all phase noise measurements SSB noise dB/Hz 0 −20 Limited by filter bandwidth
−40 −60
Limited by LO noise
−80 −100 −120
Figure 17.3
10Hz
10kHz 10MHz Offset frequency
Limitations of phase noise measurements with a low/medium cost spectrum analyser
spectrum analyser filter bandwidth) to the equivalent noise signal in a 1 Hz bandwidth provided the noise can be treated as Gaussian. By measuring the total carrier power (on a wide filter setting) and then measuring the noise signal normalised to a 1 Hz bandwidth, a phase noise measurement can be derived. In practice, the performance of simple spectrum analyser measurements is very limited (Figure 17.3). Typical spectrum analyser noise performance is not adequate to measure noise at offset frequencies much beyond 1 kHz and the minimum filter resolution bandwidth of 3 or 10 Hz limits measurements to offset frequencies above 50 Hz. Those spectrum analysers which perform narrow band measurements using digital techniques can generally perform better close to carrier measurements than analogue versions and, with the right software, provide more reliable conversion of measurement results to phase noise.
Measurement of frequency stability and phase noise 399 The performance at larger offsets is limited by the performance of the synthesisers used to convert the input frequency signal to the spectrum analyser measuring frequency and the relatively poor noise figure of a spectrum analyser front end converter. The noise figure arises because the spectrum analyser usually has to be optimised to obtain the best linear operating range to its maintained intermodulation and spurious specification.
17.3
Use of preselecting filter with spectrum analysers
For some applications, the noise floor and synthesiser noise limitations of spectrum analysers can be partially overcome by the use of band-pass filters. A typical measurement will require the use of second reference RF or microwave source and a mixer to convert the signal to an intermediate frequency (IF). The signal from the mixer is then passed through a band-pass filter and amplifier before being measured by the spectrum analyser. Typically, the band-pass filter is a commercial inductor/capacitor, crystal or ceramic IF filter commonly used in radio receivers. Alternatively the filter can be a band stop filter to reject the IF, but such filters are not as commonly available (Figure 17.4). Some care needs to be taken in making measurements in this way. Suitable filters with narrow bandwidths are rarely designed for 50 0001 systems and often have severe changes of impedance with frequency. The mixer has to be buffered from this impedance variation to avoid errors due to reflected signals re-mixing. The filters can also exhibit non-linear behaviour at both low levels (particularly crystals) and high levels (as crystal or ceramic devices exceed their linear power ratings). These problems, combined with frequency response unflatness in the pass band, can make the measurement accuracy unreliable unless precautions are taken. It also has to be
Source under test
Mixer
Low pass filter
LNA
Reference source
Figure 17.4
Using a spectrum analyser with preselection
Xtal band pass filter
400 Microwave measurements remembered that both the phase and the amplitude components of noise are being measured. The technique is also restricted to measurements at offsets of typically greater than (typically) 10 kHz since it relies on the filter having to reject a significant proportion of the carrier signal at the IF. The improvement in performance using this method occurs because the signal from the local oscillators inside the spectrum analyser no longer mixes with the carrier frequency of the signal being measured because it is rejected by the band-pass or band stop filter. The spectrum analyser local oscillator noise no longer dominates the measurement and the ratio of the signal to be measured to the total power at the input of the spectrum analyser is much lower, which considerably lowers the dynamic range required of the spectrum analyser.
17.4
Delay line discriminator
A broadband FM discriminator can be constructed by taking the RF signal to be measured and splitting it into two paths (Figure 17.5). One path is fed directly into a mixer and the second path is passed through a delay line and the output is mixed with the non-delayed signal. The delay line includes a variable phase shifter or a mechanically adjustable transmission line so that the phase of the two signals applied to the mixer can be set for phase quadrature. The bandwidth of the discriminator is a classic sin x/x response with the first null at a frequency equivalent to the time delay between the two RF paths. The conversion sensitivity of the discriminator is dependent on the RF level applied, the conversion loss of the mixer and the time delay of the delay line. The longer the delay line the greater the sensitivity of the measurement but the more restricted is its measurement bandwidth. The great advantage of this technique is that it does not require the use of a second RF source to convert the frequency of the source to be measured to a fixed IF (or base band signal). This removes one potential source of error, that is, an additional source
Source under test
Splitter
Mixer
Delay line
Figure 17.5
Delay line discriminator
LNA
Measurement of frequency stability and phase noise 401 of noise. Also, since the method is based on the use of a frequency discriminator it is not too prone to being overloaded by low-frequency sources of phase noise (e.g. power supply related signals). It does have the practical disadvantage of not being easily automated. It needs to be calibrated which can be troublesome. The sensitivity of the system is dependent on the applied RF signal levels. The normal method of calibration is to adjust the time delay to find the peak positive and negative voltage that can be obtained from the mixer. From this the sensitivity can be deduced if it is assumed that the mixer is behaving in a linear fashion. At microwave frequencies the insertion loss of the delay line can result in the sensitivity of the measurement being limited. Commercial products are available based on the use of this measurement method.In general, this method is not capable of measuring high-performance oscillators over a significant bandwidth but is capable of measuring typical free running YIG and RF voltage–controlled oscillator (VCO) sources.
17.5
Quadrature technique
In the quadrature system, two oscillators at identical frequencies are used (Figure 17.6). Typically, one of the oscillators will be the source being tested and the other will be a reference source whose performance is known to be better than the source under test. The oscillator outputs are combined in a mixer and the resulting output signal is filtered and amplified by a low noise amplifier (LNA). A fast Fourier transform (FFT) analyser or a spectrum analyser typically measures the output from the mixer.
OSC 1
Mixer
OSC 2
Figure 17.6
Low pass filter
LNA
FFT analyser
or Spectrum analyser
Quadrature method shown with a feedback loop to maintain phase quadrature at the mixer
402 Microwave measurements In order to provide a valid measurement the phase of the two oscillators has to be set so that they are in phase quadrature at the mixer input. The mixer output will then be close to 0 V and the mixer will behave as a phase detector. Setting the sources to be in phase quadrature is not always very easy. If both frequency sources are synthesisers with good long-term stability, then there is usually not a great problem – the phase adjustment controls can be used to set the signals in quadrature. However, in the more typical applications where measurements are undertaken under less than ideal conditions, a feedback system has to be used to maintain phase quadrature. The feedback system forms a phase locked loop which drives one of the oscillators to correct for departures from quadrature. The use of phase locked loop to maintain phase quadrature does imply some knowledge of the tuning characteristics of one of the oscillators and the mixer drive levels since the bandwidth of the phase locked loop is affected by both of these parameters. In practice for many sources the availability of a low noise signal generator with a high-performance DC coupled FM capability, such as the IFR 2040 series, can considerably simplify the measurement system. If the peak phase excursion of the noise exceeds 0.1 radians, the mixer phase detector response becomes non-linear and degrades the measurement accuracy. Since the peak phase excursion is caused primarily by low-frequency noise then under these conditions, the phase locked loop bandwidth has to be widened in order to restrict the peak phase excursion. In order to carry out a measurement, the quadrature system has to be calibrated since the sensitivity of the measurement is dependent on the insertion loss and drive level used for the mixer. If the local oscillator (LO) input level required for the mixer is substantially greater than the RF port drive, a calibration assessment can be obtained by offsetting the frequency of one of the sources by a small amount. A low-frequency sine wave is produced at the output of the mixer whose amplitude can be measured to determine the sensitivity of the mixer. If both ports of the mixer are driven at a high level to give the maximum sensitivity then the waveform from the mixer will be more like a triangle waveform than a sinusoid and the mixer sensitivity should be more linear with errors in phase quadrature present. However, the slope of the triangle wave is more difficult to measure accurately than in the case where a sine wave is produced. A further complication in the calibration process can arise if the drive signals are not well matched to the source impedance. Whichever port of the mixer is driven hard, the mixer tends to convert the signal to a square wave and reflections can cause re-mixing and slope perturbations in the output. An alternative, and often more reliable method of calibration, is to use a signal generator as one of the sources and to set a known amount of phase or frequency modulation. Measuring the resulting output can provide the required calibration information. The phase modulation applied has to have a modulation index of less than 0.1 radians to avoid mixer overload, and a modulation frequency significantly in excess of the phase locked loop bandwidth used for setting up phase quadrature.
Measurement of frequency stability and phase noise 403 This in itself can be another source of error in the measurement since the phase locked loop is used to set up phase quadrature. The loop tends to remove low-frequency phase noise that is present on the source under test. The errors introduced by the phase-locked loop must either be set so that they are below the frequency offset of interest or they have to be corrected for by measuring the loop characteristics and then mathematically correcting the measurement result. There is a further practical problem that needs to be assessed. If there is a lack of isolation between the two RF sources then, as their frequencies are brought close together, there will be a tendency for them to become injection locked. If one of the oscillators is a VCO then this is certain to happen and will need to be characterised. Under these conditions it is advisable to ensure that the deliberate phase locked loop bandwidth exceeds the injection locked bandwidth. Even then the loop must be characterised if accurate measurements are to be made on the source (Figure 17.7). The phase locked loop response can be measured by injecting a calibration signal into the loop. The calibration signal can be swept signal (e.g. the tracking generator output of a spectrum analyser or the modulation oscillator of a signal generator) or a noise source (often available on an FFT analyser). Outside the loop bandwidth the analyser measures the amplitude of the calibration signal but inside the loop bandwidth the phase-locked loop (PLL) reduces the level of calibration signal measured. From the frequency response plotted on the analyser, a correction plot can be deduced and applied to correct the phase noise measurement results. Care needs to be taken when interpreting results that include high correction factors: the software may display the answers to a high degree of precision not reflected in the real accuracy of the numbers. Commercial systems are available from a number of vendors based on the use of the Quadrature Technique.
Calibration signal
OSC 1
Mixer
Low pass filter
+
LNA
or Spectrum analyser
OSC 2
Figure 17.7
FFT analyser
Method for calibrating the effects of phase locked loop
404 Microwave measurements
17.6
FM discriminator method
This method uses a mixer and a reference source to convert the signal to an IF where it is demodulated by an FM discriminator (Figure 17.8). In principle any FM discriminator, including a discriminator of the type found in a modulation analyser, can be used. However, the noise performance of the discriminator is likely to have a critical effect on the ability to make a phase noise measurement. A proprietary FM discriminator phase noise measuring system is used at IFR Ltd (now part of AeroFlex) to measure high-performance signal generators based on a high performance. A 1.5 MHz discriminator is shown in Figure 17.8. This system is used to aid the design of the oscillator systems deployed in the company’s signal generators. The discriminator is based on the use of a splitter, a band-pass filter and a mixer acting as a phase detector. The band-pass filter uses a coupled resonator design that ensures that at the centre frequency of operation, the phase shift through the filter is 90◦ so the inputs to the phase detector are in quadrature. In the practical implementation two band-pass filters are available, one allowing a measurement bandwidth of up to 20 kHz and the other allowing measurements to 100 kHz offset. In principle, the system behaves in a way similar to the delay line discriminator method but it does have some substantial advantages. In particular, since the discriminator operates at an IF, a limiter can be used to control the amplitude of the signal into the discriminator and hence the conversion gain of the discriminator is independent of RF input level. Operation at an IF also allows the FM discriminator to be implemented using a different type of phase detector operating at much higher signal levels. The design used in the IFR version uses two transformer coupled full wave rectifiers operating at very high signal levels to increase the signal-to-noise ratio. As with the Delay Line Discriminator, it is important to remember that FM noise is being measured rather than phase noise. Conversion between the two measurements
OSC 1
Limiter
LNA
FFT analyser
FM discriminator
Mixer
Low pass filter
300Hz to 3 kHz voltmeter
OSC 2
Figure 17.8
20kHz tuned voltmeter
Method of measurement using an FM discriminator
Measurement of frequency stability and phase noise 405 is relatively straightforward (by differentiation of the spectrum measurements) and some FFT analysers are available which can mathematically convert the measurement result automatically. Calibration of the system is very straightforward since the system sensitivity is independent of the input drive level to the frequency conversion mixer. Once a system has been constructed, the calibration factors are constants that can be allowed for by periodic (six monthly) calibration checks. Calibration is typically performed by making one of the sources a signal generator with calibrated amounts of FM or phase modulation. The system used at IFR Ltd includes a meter to measure the residual FM of a signal source in a 300 Hz to 3 kHz bandwidth (a common signal generator specification parameter) and a tuned voltmeter to measure phase noise at 20 kHz offset to give a fast measurement of these two signal generator parameters. The performance of an FM discriminator system is limited by the noise figure of the amplifiers and limiters which recover the signal from the output of the mixer and by the performance of the discriminator itself. In the case of the system described previously the discriminator consists largely of passive components, which exhibit very good noise characteristics, and very high signal levels can be used to maximise the Hz V−1 at the output of the discriminator. Performance tends to be controlled by the slope of the discriminator and it is for this reason that two band-pass filters are used to allow a compromise between sensitivity and measurement bandwidth. A high-performance FM discriminator is capable of measuring very low levels of phase noise. The above system is capable of measuring residual phase noise of −170 dBc Hz−1 at 20 kHz offset and residual FM of 0.003 Hz in a 300 Hz to 3 kHz bandwidth. The FM discriminator system also has some disadvantages. The need to have sources at different frequencies can be inconvenient. The mixing process can also generate intermodulation products that can give a false indication of there being spurious signals present. With a 1.5 MHz IF, however, this is unlikely to be a problem for carrier frequencies above 50 MHz. A less obvious problem is that if a source exhibits a flat noise profile from the offset frequency being measured to the image frequency (approximately 3 MHz offset for a 1.5 MHz IF) then the image frequency noise will be added to the noise at the required offset. Most signal sources, however, tend to exhibit better noise performance at the image frequency than at the closer offset frequencies. The substitution of a single-sideband (SSB) mixer for the double balanced mixer can eliminate this problem.
17.7
Measurement uncertainty issues
The measurement methods for measuring phase noise are often subject to large error bands. There are a number of basic problems that lead to difficulties. For this reason it is difficult to obtain truly traceable measurement results, and indeed improving the traceability of phase noise is a subject being actively pursued by the National Physics Laboratory and other standards organisations.
406 Microwave measurements Some of the issues are as follows: •
• •
• •
Removal of the carrier signal means the reference value has been removed and needs to be reinstated by the calibration system • inherent to quadrature and delay line methods (but important to its performance) • implies software correction (hard to prove under all conditions, hard to assign unique values, susceptible to changing levels, increases test time) Reliance on phase coherence at a mixer • more calibration and software problems for PLL effects • restricts the type of on device that can be tested The spectrum or FFT analysers are subject to significant errors • filter BW correction numbers • absolute level errors • inherent frequency response • absolute level errors • scale shape errors • detector response to noise like signals (noise is a power measurement) • display formatting algorithms (especially FFT analysers) • input attenuator accuracy and VSWR • reference level accuracy • IF switched gain errors • amplitude display non-linearities (not to be confused with display distortion) LO residual phase noise Injection locking defects
These errors make it difficult to assign a traceability figure to phase noise measurements. Often measurements of the same device will lead to differing answers, even when measured on the same system. It is not uncommon for instance to see ‘stitching’ errors in the results where the test system changes settings to measure noise at different offset frequencies.
17.8
Future method of measurements
There are, however, other techniques that may be developed in the future which could offer other solutions. A promising area is the use of direct Analogue to Digital conversion of IF from a mixer. Current levels of performance are limited by A to D linearity, quantisation error and aperture dither, the resulting noise tending to restrict the usefulness of this measurement technique to offset frequencies of a few kHz. However, improvements in converters are being steadily made.
17.9
Summary
From the above discussion it can be seen that no measurement scheme for phase noise can be said to offer a complete solution in all applications. Of the methods discussed
Measurement of frequency stability and phase noise 407 Table 17.1
Advantages and disadvantages of the various methods described
Method
Advantages
Disadvantages
Spectrum analyser
Simple to use Simple to get a result
Delay line discriminator
Requires no additional RF source Can measure drifting RF sources
Quadrature technique
Reference oscillator is at the same frequency Large dynamic range Measurements can be made at small and large offsets
FM discriminator
Large dynamic range Does not require frequent calibration Very accurate and hard to make errors Can measure drifting sources easily Tolerates LF noise
Poor dynamic range Cannot measure close to carrier noise Difficult to measure sources with frequency drift Requires frequent calibration Restricted dynamic range Restricted bandwidth Difficult to automate Requires direct manipulation of microwave sources Requires calibration of every measurement Requires the use of PLL and prior knowledge of the source Takes a long time to make accurate measurements Easy to make errors Requires a frequency offset source Limited frequency offset range Frequency conversion can make the results pessimistic due to image signals
the most reliable technique is the FM Discriminator Method, since it is the most ‘fail safe’ technique. The quadrature technique is the most widely used since it offers better overall capability (and the greatest number of commercial solutions) but requires much more care (and time) to undertake a measurement. The spectrum analyser based techniques are often the most convenient to undertake since the equipment is likely to be readily available in most laboratories. Table 17.1 shows the advantages and disadvantages of the various methods described in a summary.
Chapter 18
Measurement of the dielectric properties of materials at RF and microwave frequencies Bob Clarke
18.1
Introduction
In all RF and microwave (RF and MW) applications electromagnetic (EM) fields interact with materials, that is, with solids, liquids or gases. Viewed on a macroscopic scale, all materials will allow EM-fields to pass into them to some extent: even good conductors and superconductors. Therefore, in one sense, all materials may be said to be dielectrics: the word ‘dielectric’ is a contraction of ‘dia-electric’, which means that electric fields can (to some extent) pass through them. In designing RF and MW components for applications, therefore, we need to understand just how electric and magnetic fields propagate into and through materials. We also need to know how they behave (reflect, transmit, scatter, etc.) when they meet interfaces between different materials, for example, between air and an insulator or between a crystal and a metal. To achieve this understanding we need to be able to measure the dielectric and magnetic properties of the materials. The characterisation of the EM properties of materials is a very broad topic and we can only touch on the most general points in this overview. A wide variety of important functional or active materials are used in RF and MW applications. They include semiconductors, superconductors, chemically active media and non-linear media in general. Studies of such materials require special detailed consideration and they are generally regarded as specialist topics in their own right. We will not be considering such materials here, we will rather be concerned with materials that respond linearly to low-field strength electric fields and it is this subset of materials (which excludes semiconductors, superconductors and so on in their active functional roles) to which the term ‘dielectric’ is usually applied on a day-to-day basis. Good conductors such as metals are usually excluded from this class too, though virtually everything we will be saying about dielectrics at RF and MW frequencies applies to
410 Microwave measurements metals too – they can be regarded as dielectrics with very high conductivity. Even with this restricted definition ‘dielectrics’ nevertheless make up a very wide and important class of materials for RF and MW applications. They are variously used to transmit, absorb, reflect, focus, scatter or contain EM-fields and waves. Bear in mind also that in many applications – radar, RF and MW processing (e.g. in microwave ovens), also in biomedical studies and treatments – the materials that are being detected, studied or treated are themselves dielectrics, so we need to understand their EM properties too. At RF and MW frequencies, with wavelengths in the centimetre to millimetre range, we are normally dealing with macroscopic components – that is, to say that the linear scale of the components that we are concerned with is much greater than the molecular scale – this is true even in modern ‘micro’-devices such as RF MEMs (microelectromechanical devices). It is for this reason that we are normally concerned with parameters that characterise the materials on a macroscopic scale in our practical studies and uses of dielectrics. Of course, on a microscopic scale there are complex EM interactions between atoms, electrons, holes and molecules – and for full understanding of the theory of dielectrics we must also study dielectrics on this scale. However, in the practical realm of RF and MW activities we wish to deal with parameters that capture the macroscopic consequences of all of the microscopic phenomena in the material. The most important of these parameters are the complex permittivity, ε∗ , and the complex magnetic permeability, µ∗ . This chapter is mainly concerned with the characterisation of dielectric materials at RF and MW frequencies. There are a number of existing publications that deal with this topic in depth that are well worth consulting. The most recent is the Good Practice Guide from NPL [1] (on which this chapter is based), which deals with the topic comprehensively. The long-standing ‘bible’ of dielectric metrology is the book by von Hippel [2]. It has deservedly stood the test of time and remains one of the most useful treatises on RF and MW dielectric measurement ever written. It covers background theory in greater depth than Reference [1], though the measurement technology described in it is now rather dated. A number of reviews (e.g. [3] and [4]) and book with details on measurement (e.g. [5]), and conference proceedings (e.g. [6]) also provide a useful background to this discipline. However, before we take up the topic of measurement, we must turn first to the dielectric theory behind the parameters, ε∗ and µ∗ – the parameters that we wish to measure.
18.2
Dielectrics – basic parameters
Introductory theoretical treatments on dielectrics can be found in most standard textbooks on electromagnetism and in books on dielectrics (e.g. see [1,5,7–12]). The quantity with which we are most concerned here is the relative permittivity, ε ∗ . This can be converted to the absolute permittivity if we multiply it by the permittivity of free-space, ε0 = 8.8542 × 10−12 F m−1 . Note that absolute permittivities in the SI system have units of farads per metre, whereas relative permittivities are dimensionless quantities. In the practical world we are usually concerned with
Measurement of the dielectric properties of materials 411 relative permittivities. As it is a complex quantity, ε ∗ has two components: ε∗ = ε0005 − jε 00050005
(18.1)
√ where j = −1. If we assume that our dielectric material is placed between planeparallel electrodes to form a capacitor, as in Figure 18.1, ε 0005 , the real part of the permittivity, characterises the capacitative part of the admittance, Y , of the capacitor and ε 00050005 characterises the conductive or lossy part of the admittance. In all materials, ε0005 and ε00050005 depend on ambient parameters such as the temperature, relative humidity, as well as the frequency, so neither ε∗ nor ε 0005 should be given the name ‘dielectric constant’ – they are not constant (the only true dielectric constant is ε0 ). The properties of the capacitor in Figure 18.1 can be captured in simple equivalent circuits, such as those shown in Figure 18.2a and b, in which the resistive and conductive components R and G represent the dielectric loss of the specimen. It is usually better to use the parallel equivalent circuit of Figure 2b for dielectric materials because C and G are proportional to ε0005 and ε 00050005 , respectively. In some circumstances it is better or more conventional to quote the loss tangent, tan δ, to quantify the conductive or lossy part of the complex permittivity, rather than ε 00050005 : tan δ =
ε00050005 ε0005
(18.2)
Dielectric specimen
Electrodes
Figure 18.1
A dielectric specimen in a plane-parallel-electrode admittance cell
(a)
(b)
R
G
C C
Figure 18.2
Simple series (a) and parallel (b) equivalent circuits of the dielectric specimen in the admittance cell of Figure 18.1. R and G take account of the dielectric loss in the specimen. R is the equivalent series resistance and G is the equivalent parallel conductance of the dielectric
412 Microwave measurements For small losses it is often convenient instead to refer to the loss angle, δ, measured in radians, which is the arctangent of tan δ. As δ ≈ tan δ for small angles, they can be numerically equivalent for most practical measurements. The advantage of using loss angle is that one can use the convenient unit ‘microradian’ (µrad) to quantify small losses [similarly, ‘milliradian’ (mrad) can be used for medium losses]. As implied in Section 18.1, we may encounter many different types of dielectric material in our work and they will display a wide range of properties. ε0005 , for example, can vary from 1.0 for air, 2–3 for typical low to medium loss polymers, 5–100 for typical electroceramics, 80 for water, 5 to >1000 for biological tissues and up to >2000 for ferroelectrics. The loss tangent, tan δ, may be as low as 3 × 10−5 for crystals such as quartz and sapphire at room temperature (or as low as 10−7 at cryogenic temperatures). Typical low-loss polymers have tan δ in the range 10−4 − 10−3 , while absorbing materials like radiation absorbing materials (RAM) and bodily tissues can have tan δ > 0.1 or even >1. With such a wide range of dielectric properties and an equally wide range of physical properties (as dielectrics can be solids, liquids, powders, malleable, hard, etc.) it is not surprising that many different dielectric measurement techniques have been developed over the years. It is good practice in dielectric measurement, if we wish to reduce our measurement uncertainties to match the technique to the material. In this overview, for convenience, we refer to materials with tan δ less than 3 × 10−4 as low-loss, above 3 × 10−2 as ‘high-loss’ and those with tan δ in between these two values as ‘medium loss’. The magnetic parameter that corresponds to the dielectric parameter ε∗ is the complex relative magnetic permeability, µ∗ , which may be defined and treated by analogy with ε ∗ µ∗ = µ0005 − jµ00050005
(18.3)
In many materials for all practical purposes µ∗ ≈ (1.0 − j0.0) and we can refer to these as ‘non-magnetic materials’ or just simply as ‘Dielectrics’. If µ∗ differs significantly from (1.0 − j0.0) we have a magnetic material and we need to take account of its magnetic properties in our measurements. There is an important difference between dielectric and magnetic responses in most materials. The dielectric response to small signals is typically linear while the magnetic response can be non-linear even for small signals, so that µ∗ is a function of signal strength – one well-known manifestation of this non-linearity is magnetic hysteresis. At sufficiently high fieldstrengths all dielectric materials will also respond non-linearly to applied fields (e.g. see [2,13]). However, we will restrict our discussion here to the normal, low signal and linear regime. As we move up in frequency through to the millimetre-wave region of the spectrum and up through THz frequencies, it becomes more convenient to characterise dielectrics in terms of quasi-optical or optical parameters such as the complex refractive index: n∗ = n − jk [14]. This quantity is related to ε∗ and µ∗ by n∗ = n − jk =
0001 ε ∗ µ∗
(18.4)
Measurement of the dielectric properties of materials 413 For non-magnetic materials, 2
ε∗ = n∗ = (n − jk)2 ,
so ε0005 = n2 − k 2 and ε 00050005 = 2nk
(18.5)
Rather than using k to quantify the loss, it is more conventional in optical and quasioptical systems to employ the power absorption coefficient, αp , αp =
4π fk c
(18.6)
where f is the frequency and c is the speed of light and αp is the power absorption coefficient per unit length of signals transmitted through the medium. αp is conventionally measured in the units nepers per metre (Np m−1 ). As 1 Np = 8.69 dB, the power attenuation of a signal passing through the dielectric may also be expressed in decibels as 8.69 × αp dB m−1 . We can express the loss tangent of the material in terms of the (quasi-)optical parameters n and αp as follows: tan δ =
8π fncαp ((4π fn)2 − cαp )2
(18.7)
which for low-loss materials having αp << 4π fn/c reduces to tan δ ∼ = cαp /2π fn.
18.3
Basic dielectric measurement theory
As most dielectric measurements make use of cells to contain the dielectric, and as we can regard the cell as an RF and MW component, many dielectric measurement techniques, viewed at the instrumental level, are similar to other S-parameter measurement techniques that are covered in-depth in other chapters and also in textbooks on RF and MW measurements (e.g. [15–17]). A more comprehensive version of the treatment given here can be found in the Good Practice Guide [1]. Dielectric measurement methods and measurement cells largely fall into two broad classes: (1) Those in which the dielectric properties are measured as an impedance, Z, as in Figure 18.2a, or more commonly, as an admittance, Y , as in Figure 18.2b. These may collectively be called lumped-impedance methods and are generally used at low frequencies (LF) and in the RF region of the spectrum up to 1 GHz. (2) Those in which the dielectric is considered to be interacting with travelling and standing electromagnetic waves – these may collectively be called ‘Wave Methods’. Both lumped-impedance and wave techniques can be used in resonators. Resonators are measurement cells with resonating EM-fields inside them that are used to obtain high sensitivity for measuring the loss of low-loss dielectrics (see below).
414 Microwave measurements
18.3.1 Lumped-impedance methods In these methods we use an impedance/admittance analyser or bridge to perform the measurements on the cell. If we carry out a measurement in the cell of Figure 18.1, we usually measure the cell admittance Y = G + jB, where G is the equivalent parallel conductance and B is the equivalent parallel susceptance, both measured in units of siemens. The equivalent circuit for a lossy dielectric is shown in Figure 18.2b, where C is related to B by B = ω C, where ω = 2π f and f is the frequency in hertz. The cell shown in Figure 18.1 is commonly called an admittance cell because one determines ε∗ by measuring its admittance. In lumped-impedance analysis one therefore treats continuous dielectric media, and specimens thereof, in terms of lumped equivalentcircuits, that is, circuits containing discrete components: inductors, capacitors and resistors. This is perfectly acceptable as long as their physical dimensions are very small compared with the wavelength, λ, of the radiation. It is this requirement that limits the usefulness of lumped-impedance methods as one moves up through the spectrum.
18.3.2 Wave methods Measurements at MW frequencies usually differ from electrical measurements at lower frequencies because they are conceived of differently: they deal with waves rather than with impedances and admittances. Wave methods may be travellingwave or standing-wave (resonant) methods and they may employ a guided-wave or a free-field propagation medium. Coaxial, metal and dielectric waveguide, microstrip, co-planar waveguide and optical-fibre transmission lines are examples of guidedwave media while propagation between antennas in air uses a free-field medium. In guided-wave travelling-wave methods the properties of the measurement cell are measured in terms of Scattering Parameters or ‘S-parameters’ (e.g. see [16] and Figure 18.3). It is good practice in such measurements to ensure that as much of the measurement system as possible is matched to the transmission-line characteristic impedance, Z0 , because mismatches produce reflections and multiple reflections that can seriously reduce the accuracy of measurement. The reflection coefficient, , from an impedance Z that terminates a transmission-line of characteristic impedance Z0 [18] is given by =
Z − Z0 Z + Z0
(18.8)
so reflections are only absent if Z = Z0 . In fact, the propagation of EM waves through any uniform isotropic medium, or any uniform transmission-line containing such a medium, is governed by two parameters: the characteristic impedance, Z0 , and the complex propagation constant, γ , of the medium [10]. Both are functions of the complex permittivity, ε∗ , and permeability, µ∗ , of the medium. The propagation constant governs both the wavelength and attenuation of waves moving through the medium: 0001 γ = α + jβ = 2π f ε0 ε ∗ µ0 µ∗
Measurement of the dielectric properties of materials 415 or, because c= √
γ =
1 ε0 µ 0
2π f
√ √ ∗ ∗ ε µ 2π ε ∗ µ∗ = c λ0
(18.9)
where c is the speed of light in free-space and λ0 is the free-space wavelength, α is called the attenuation constant and β is the phase constant. For low-loss dielectrics in which it is assumed that α ≈ 0, β is sometimes itself called the propagation constant. In non-magnetic materials, µ∗ = (1.0 − j0.0) and γ =
2π √ ∗ 2π f √ ∗ ε = ε c λ0
In a low-loss dielectric α is small (α << β) and we find √ √ λ0 2π ε 0005 π ε 0005 tan δ π fn tan δ λ ≈ √ ,β ≈ and α ≈ or α ≈ λ0 λ0 c ε0005
(18.10)
(18.11)
so tan δ ≈ cα/π fn and referring back to (18.18), we find α = αp /2. This relationship actually follows more fundamentally from the definitions of α and αp . First is the exponential coefficient for decay of field-strength as the wave propagates through the medium, the second describes the decay of power, so the relationship α = αp /2 is valid even if α is not small. The measurement of propagation or transmission parameters, such as β, γ and λ, provides a means for deriving dielectric parameters. Many dielectric measurement methods are based on this principle. The same is true of the measurement of reflection parameters, , S11 , S22 , etc. Reflections at plane interfaces between two uniform media are governed by 0001 the intrinsic wave 0001impedances of the media, η1 and η2 , respectively, where η1 = µ∗1 /ε1∗ , and η2 = µ∗2 /ε2∗ , where µ∗1 , µ∗2 , ε1∗ and ε2∗ are the complex relative permeabilities and permittivities of the two media, respectively. By analogy with (18.8), the reflection coefficient in Medium 1 of a wave at normal incidence (i.e. at 0◦ angle of incidence) on Medium 2 is =
η2 − η1 η2 + η 1
(18.12)
Such reflections are dependent on the ratio of µ∗ and ε ∗ , whereas the transmission parameters defined in (18.9) are governed by the product of µ∗ and ε ∗ . In order to separate µ∗ and ε∗ we must normally, therefore, measure the specimen both in transmission and reflection (though other techniques are possible). This is readily achieved by measurements in transmission cells, such as the one shown in Figure 18.3, in which all four S-parameters are easily determined. If we are sure that we have a non-magnetic material, however, we have µ∗ = (1.0 − j0.0) and we can measure ε∗ either by transmission or by reflection methods. The choice should normally be made on the basis of which is the most accurate. For non-magnetic materials, the reflection
416 Microwave measurements Coaxial line: 50 Ω characteristic impedance S21
Forward travelling wave
S11
Port 1
Port 2
S22 S12 Dielectric specimen
Figure 18.3
Reverse travelling wave
Electromagnetic travelling waves in a coaxial measurement cell that contains a dielectric specimen. The cell is placed in a measurement system in which there are waves travelling in both directions, designated forward and reverse waves. The figure shows the reflection coefficients of the specimen, S11 and S22 , for the forward and reverse wave, respectively, and the corresponding transmission coefficients, S21 and S12 . The S-parameter subscripts refer to the measurement ports (that is the two ends) of the coaxial cell
from a dielectric interface between two media with permittivities ε1∗ and ε2∗ travelling at normal incidence from Medium 1 to 2 is 0001 ∗ 0001 ∗ ε − ε n∗ − n∗2 (18.13) = 0001 1∗ 0001 2∗ = 1∗ n1 + n∗2 ε1 + ε2 where n1 * and n2 * are the complex refractive indices of the two media. For freefield measurements in which the angle of incidence is not necessarily normal these equations may be generalised for any angle of incidence by using Fresnel’s Equations [10,19]. In the free-field it is also important to take account of whether the electric field polarisation of the incoming radiation is parallel to the dielectric surface or in a plane perpendicular to the surface. There are two sets of Fresnel’s equations – one each for the parallel and perpendicular cases.
18.3.3 Resonators, cavities and standing-wave methods Resonance methods are generally used for measuring the loss of low-loss dielectrics. The cell in such measurements is commonly referred to as a cavity or resonator. In such cells the real permittivity, ε0005 , is typically determined by measuring the change in resonant frequency when the specimen is inserted into the resonator or else it can be measured by changing the length (or some other key dimension) of the
Measurement of the dielectric properties of materials 417 RF source Inductance coil
Specimen
To high impedance detector Micrometer-driven electrode
Admittancecell
Figure 18.4
The basic principles of the Hartshorn and Ward method for low-loss specimens
resonator to return it to resonance at the same frequency. These contrasting methods are known, respectively, as the frequency-change and length-change methods for determining ε 0005 . It is possible to measure ε 0005 by the length-change method because the wavelength in the dielectric medium, λ, differs from that in free-space (18.11). The determination of dielectric loss, ε00050005 or tan δ, in such resonators usually proceeds via the measurement of Quality-Factor, otherwise known as Q-factor or Q [20], (see Section 18.7). Both lumped-impedance and wave techniques can be employed in resonators. In the former case an admittance cell can be resonated with an external inductor; (Section 18.9.2 and Figure 18.4). This RF ‘dielectric-test-set’ method was first used for measuring low-loss dielectrics in the 1930s. At higher frequencies where wave methods are more appropriate, the resonator is often modelled using standing-wave equations rather than a travelling-wave analysis. Note that wave resonance methods are also often referred to as ‘multi-pass techniques’ because a travelling-wave in the cell, in bouncing backwards and forwards between the two ends of the resonator, will pass through the dielectric specimen many times before it is absorbed. This concept helps to explain why resonant methods are more sensitive to low-losses than single (transmission) and double-pass (reflection) techniques.
18.3.4 The frequency coverage of measurement techniques It is worthwhile drawing attention to the frequency coverage of the various techniques used in different parts of the spectrum. At MW frequencies we generally need to adapt equipment dimensions to the radiation wavelength (this is almost a definition of what ‘microwave’ means in practice). We therefore tend to need many differently sized measurement cells in this region of the spectrum. In contrast, at LF and from THz frequencies upwards (above approximately 300 GHz), a single instrument/cell combination may measure over many decades of frequency. For example, a bridge/admittance cell combination can cover five decades of frequency at LF, while a single Fourier transform spectrometer [21] can cover five decades in the sub-millimetre to infrared regions of the spectrum. Note also that many resonance techniques operate at one spot-frequency only! We need to bear these limitations in mind when we set out to measure dielectrics – as explained at the end of Section 18.4, measurements at a few spot frequencies may suffice to characterise a low-loss material over a wide frequency band, but much more detailed frequency coverage is needed for high-loss materials.
418 Microwave measurements
18.4
Loss processes: conduction, dielectric relaxation, resonances
It is important, before we set out to measure our dielectric materials, that we know something about the physics of dielectric response behaviour. The most relevant physical processes here are those that give rise to power loss in bulk dielectrics. In the RF and MW region of the spectrum such power losses arise largely from four different physical processes – see [22–24] or [5] for details and [12] for an introduction. These four physical processes are associated with mechanisms for generating loss – that is, conversion of EM energy into other forms of energy – and so are commonly called ‘loss processes’. They are (1) Electrical Conduction, (2) Dielectric Relaxation, (3) Dielectric Resonance and (4) Loss from Non-Linear Processes. (1) Electrical Conduction in which charge carriers (electrons, ions or holes) in a material medium are relatively free to move physically through the medium under the influence of an electric field. The ease of conduction is quantified by the conductivity of the medium, σ , measured in siemens per metre (S m−1 ). In general, σ will depend on frequency, temperature, concentration of carriers, etc., though in many materials σ will change only slowly with frequency in the RF and MW range. In metals the effective conductivity depends on the physical properties of the metal surface (e.g. scratches, machining or grinding marks or debris) and so σ will depend on frequency because the skin-depth [18] is a function of frequency. (2) Dielectric Relaxation refers to the response of the electric dipoles in a material medium to the applied alternating EM-fields. Many different types of dipole can be present in dielectric media. Some materials have permanent molecular dipoles inside them and they are called polar materials. Their molecules are referred to as polar molecules. Materials in which the dipoles are induced only by the application of the electric field itself are called non-polar materials. Polar molecules typically exhibit a number of different relaxation processes. If they are in a liquid phase they can rotate bodily to try to align themselves with the field, giving rise to rotational polarisation. Otherwise portions of large molecules can move with respect to each other, giving rise to one or more distortional polarisation processes, each with its own relaxation behaviour. Any interfaces in a material that prevent or inhibit the passage of charge carriers will have dipolar layers set up across them when the electric field is applied and they give rise to interfacial polarisation, a phenomenon, essentially similar to the Maxwell–Wagner effect [5,22], which exhibits its own relaxation behaviour. The membranes in the cells of biological tissues typically exhibit this behaviour [25]. In a complex medium, many or all of these relaxation processes may be present, giving rise to very complex relaxation behaviour. Each process will have its own strength, which is a parameter that measures the extent to which it contributes to the total magnitude and behaviour of ε0005 and ε00050005 . All relaxations give rise to very slow changes in ε 0005 and ε00050005 with frequency. The behaviour shown in Figure 18.5 for water is typical.
Measurement of the dielectric properties of materials 419 80 70 ε′
Permittivity
60 50 40 30
ε″
20 10 0 108
Figure 18.5
fr 10
9
10
10 1011 Frequency (Hz)
1012
1013
A typical Debye Relaxation response, see (18.14). This plot is for deionised water. The diagram omits the effects of all other loss processes in the water, for example, conduction. The use of a logarithmic scale demonstrates just how slowly dielectric properties change with frequency when governed by a relaxation process
(3) Dielectric Resonance. Dielectric polarisation resonance should not be confused with dielectric relaxation. The physics of relaxations and resonances is completely different and the two should not be confused (see Figures 18.6 and 18.7). A resonance may appear either as a sharp or broad feature in the frequency domain, depending on its Q-factor (see Section 18.7), whereas relaxations always exhibit very broad spectral features. Furthermore, a resonance gives rise to a frequency dependence for ε 0005 in which ε0005 can either fall or rise with frequency, whereas in relaxation behaviour ε 0005 (or µ0005 ) can only fall with frequency. The physics of linear, homogeneous, non-composite solid and liquid dielectrics does not normally allow a resonance to occur at RF and MW frequencies. The molecules of such materials, because of their close proximity to one another, interact to such an extent that all potential resonances are damped effectively into non-existence. (This is not the case with gases in which spectral lines, that is, resonances in the EM response can readily be distinguished at MW frequencies). Therefore, it is a useful rule of thumb that for linear, homogeneous, non-composite solid and liquid dielectric materials any sharp features that we appear to measure in the spectrum of ε0005 and ε00050005 at RF and MW frequencies, and any apparent increases in ε0005 with frequency are invariably caused by non-intrinsic effects, usually imperfections in our measurement cells! There are, however, genuine dielectric resonances in the infrared region in the spectra of solids and liquids. These processes give rise to small but measurable effects at RF and MW, usually a slowly increasing
420 Microwave measurements
C1
C2 R
Figure 18.6
An equivalent circuit of a Debye Relaxation C
Figure 18.7
L
R
An equivalent circuit of a dielectric resonance
value of tan δ with frequency caused by the LF tail of the resonance – this is only visible in low-loss materials. Special notice should also be taken of RF and MW resonances that can occur in composite materials. Resonances can occur within the meso- or macroscopic particles and structures that make up such materials. This is particularly prominent if one component of the material is a high permittivity low-loss component, such as a sintered ceramic. Bear in mind that if√the free-space wavelength is λ0 , the wavelength in the material will be λ0 / ε 0005 . So, if ε 0005 for a particle is approximately 1000, resonances can occur in the millimetre-wave region of the spectrum even if the typical particle width, referred to as its structure-length, is as small as 0.1 mm. It is usually this phenomenon that limits the useful upper frequency of dielectric composites. (4) Loss from non-linear processes. It is well known that hysteresis in magnetic materials leads to loss [26]. Ferroelectrics [1,27] can exhibit much the same phenomenon in their electrical properties, leading to an independent source of electrical loss. The relative magnitude of these non-linear effects usually rises with the amplitude of the applied fields. Having listed the four likely sources of loss in dielectrics we should return to dielectric relaxation (2) because it is the most characteristic of dielectric loss processes in the RF and MW region of the spectrum.
Measurement of the dielectric properties of materials 421 Relaxation Models. The Debye Relaxation is our simplest relaxation model [5,13,22]. It corresponds to the equivalent circuit in Figure 18.6. Three real-number parameters (corresponding to the three lumped components in the equivalent circuit) are used to characterise the frequency response of the relaxation: (1) the ‘static’ permittivity, εs , is the value of ε0005 at very LFs; (2) the relaxation frequency, fr , giving the typical speed of the relaxation; and (3) the high-frequency permittivity limit, ε∞ , is the value of ε 0005 at high frequencies, well above fr . All three parameters are functions of temperature. The Single-Debye dielectric response is then described by the following equation: ε ∗ = ε∞ +
εs − ε∞ 1 + j f /fr
(18.14)
A typical response is shown in Figure 18.5. This behaviour is exactly analogous to the behaviour of the equivalent circuit shown in Figure 18.6 with fr = 1/2π RC1 Debye relaxations are exhibited by a number of liquids including water at RF and MW frequencies, but many other materials have more structured responses with frequency, for example, they exhibit Double-Debye or Multiple Debye responses [28,29], or else they relax even more slowly with frequency, as typified by the ColeCole [30], Cole-Davidson [31] or Havriliak–Negami relaxation formulae [32]. In most complex structured materials many different relaxation processes contribute to the dielectric response, which can therefore be quite difficult to describe in terms of any one simple model. In scientific studies, variable temperature measurements are always carried out because the features of relaxations (e.g. loss peaks) typically shift in frequency by different rates as temperature is varied, so temperature variation can be used to differentiate between the various processes. In all of these relaxation models the contribution from dielectric relaxations to the real permittivity, ε0005 , always falls with frequency (or else, in the limit, at very low and high frequencies, it may asymptotically be approximately constant; see Figure 18.5). Given (1) that free particle conductivity, σ , has no effect upon ε0005 ; (2) that intrinsic dielectric resonance does not occur in homogeneous non-composite dielectric solid and liquid materials in the RF and MW region; and (3) that dielectric behaviour in this region is normally dominated by relaxations, we can make the following general statement: In the RF and MW region of the spectrum ε 0005 always falls with frequency (or, in the limit, remains stationary) in homogeneous solids and liquids that exhibit a linear response to the applied fields.
Note though (as discussed above) that this statement does not necessarily apply to (1) gases, (2) composite materials with a structure-length close to the EM wavelength in any one of the components in the material and (3) non-linear materials. There are other important features of relaxations that we should know about. For example, the Kramers–Kronig relations [23,33] provide a formula which relates ε 0005 ( f ) to ε00050005 ( f ) over a broadband of frequencies. In 1971 Arnold Lynch derived and published [34] a simplified equation for relating changes in ε0005 with frequency to tan δ when the electrical response of the material is determined by dielectric relaxation behaviour. It is good practice to use such formulae to check our measurements; see
422 Microwave measurements also [1]. Another important practical rule of thumb follows from consideration of the Kramers–Kronig relations and from inspecting relaxation models such as the Debye relaxation of (18.14): In the RF and MW region of the spectrum for low-loss materials both ε 0005 and ε 00050005 change very slowly with frequency, so we do not need to measure them at all frequencies.
Thus, the fact that we normally use resonators to measure low-loss materials and that the resonators may be restricted to one frequency only is mitigated to some extent: we need to use only a few such resonators to cover a broad bandwidth. In fact, it is usually a waste of time and effort to measure low-loss materials at frequencies more closely spaced than once every octave (i.e. more closely than f , 2f , 4f , etc.). This statement does not apply to high-loss materials for which continuous frequency coverage is usually advisable.
18.5
International standard measurement methods for dielectrics
Internationally agreed standard methods of measurement allow us to share good practice and ensure the compatibility of measurements that are made in different laboratories. These methods are of particular importance when specifying a procedure for the determination of properties of a material for a well-defined end-use. That said, however, methods outlined in such standards often lag behind the state-of-the-art in metrology. This is inevitable because test houses and product-control laboratories cannot be expected to be as up-to-date or as well equipped as calibration laboratories or those that have the task of developing new measurement methods for new types of material. Standard methods can be read as a guide to the art of measurement and they clearly must be followed, where possible, in many commercially oriented measurements. But there are many areas of dielectric metrology where effective written standards do not exist or else where significant practical detail is lacking from them. In these circumstances one often has to fall back on the scientific literature for a more detailed account of the methods. Dielectric standards may be found in the American Society for Testing and Materials (ASTM) catalogs and in the International Electrotechnical Commission (IEC) and Comité Européen de Normalisation (CEN) systems. British Standards (BS) are nowadays subsumed into the IEC and CEN ranges. Note that CEN electrical standards are normally referred to as ‘CENELEC’ standards. A short overview of RF and MW dielectric standards is given in Reference [1].
18.6
Preliminary considerations for practical dielectric measurements
Please see the Good Practice Guide [1] for more details on the points that follow.
18.6.1 Do we need to measure our dielectric materials at all? Perhaps we can consult manufacturers’ data sheets or consult the scientific literature. Either option can be adequate for the early design stages of the system development
Measurement of the dielectric properties of materials 423 process, but for end-use applications it is usually advisable to measure (or have measured) the materials that are being used. There are a number of reasons for this. For example, the dielectric properties of all ceramics depend critically on how they are prepared and sintered, so there is no such thing as a ‘standard’ or ‘representative’ batch of sintered alumina. Likewise, a polymeric material like ‘PVC’ is far from being a uniquely defined substance – polyvinyl chloride is prepared in many different ways, having different amounts of plasticiser and other additives admixed with it. Both the additives and the processing of the polymer give rise to a whole range of different ‘PVC’ polymers with varying dielectric properties, so the uncritical adoption of data on ‘PVC’ from a database will not do. Usually, if we have a ‘one-off’ job, unless we already have a suitable measurement system available, it will be most cost-effective to ask a test house or calibration lab to perform measurements for us. If we have a long-term interest in measuring or testing dielectric materials we may well decide to set up a measurement system ourselves, but even in this case it may be more cost-effective to seek advice from an experienced laboratory first.
18.6.2 Matching the measurement method to the dielectric material Dielectric materials come in many different forms, physical phases, shapes and sizes. For example, high-loss solids (e.g. RAM), low-loss solids (e.g. quartz and other pure crystals, and ceramic dielectric resonator materials), hard or malleable solids, liquids with very different viscosities, toxic materials (e.g. many liquid organics and some solid inorganics like beryllia), magnetic solids, thin films, dielectric resonators, substrates, materials available only in small quantities (e.g. expensive crystals, trial samples of ceramic), materials available in copious quantities (e.g. radome materials, some substrates), composite materials, anisotropic materials, significantly inhomogeneous materials (e.g. many composites, foodstuffs, human tissues, etc.), moist materials and powders and so on. It is not too much of an exaggeration to say that each of these different physical classes of dielectric requires a different measurement technique for optimum measurement in the most accurate or the fastest way. Cost often forces us to carry out measurements on non-ideal equipment but it is good to bear in mind that we should ideally think of adapting the methods we use to the material rather than the other way around. Section 18.9 provides a short survey of methods and tells us which material types they are best used for. However, the following rule generally holds. 18.6.2.1 For low-loss materials It is invariably best to use a resonance method to obtain better sensitivity for loss. As noted above such methods may either be lumped-impedance methods (typically at RF) or standing wave methods (typically at MW frequencies and above). 18.6.2.2 For medium to high-loss materials It is usually better to use non-resonant methods. At RF, below approximately 1 GHz, the use of admittance bridges and admittance cells is effective. At MW frequencies, where it is appropriate to think in terms of travelling waves, the use of single-pass (transmission) or double-pass (reflection) techniques is usually more appropriate.
424 Microwave measurements 18.6.2.3 Cleanliness, specimen decomposition and contamination Dielectric specimens can be easily contaminated – the net result in many cases is that one measures a spuriously high-loss for the specimen. Especially in the case of low-loss materials, it is important to keep them clean and never touch them directly with the human hand – use clean tweezers or gloves instead – sweat from human fingers can enter the matrix of sintered materials and increase their loss considerably. In the case of hygroscopic liquids (e.g. organic liquids such as short-chain alcohols) it is important to store them in a well-sealed container as they will readily pick up moisture from the atmosphere. Some materials decompose in bright light (typically ultraviolet or sunlight), so store materials in the dark; other materials oxidise in the atmosphere so store them in sealed containers. 18.6.2.4 Specimen dimensions and preparation It is important to know that, with few exceptions, the uncertainty with which a specimen can be measured depends critically on one or more of its dimensions, typically either its thickness or diameter. Therefore one should use micrometers or optical techniques to measure critical specimen dimensions, and not less accurate methods, for example, callipers. For all but the most rudimentary or preliminary measurements, it is usually worthwhile ensuring that critical specimen dimensions are machined carefully to a uniform and known size. Grinding is often more accurate (though more expensive) than turning and low tool speeds are recommended for some polymers (to prevent melting the polymer). Cutting fluids must be avoided if they will contaminate the specimen. Specimen thickness, ts , should ideally be measured at a representative number of points across the area to be tested in order to check its uniformity. Remember that the thickness of hard specimens measured by micrometer may be too high, as it will only measure the high points, while for soft specimens it may measure too low if the specimen is compressed. Care should be taken to detect and correct for these effects in accurate measurements. For most techniques the actual specimen size, and not just its uniformity, will itself also have a major effect on the measurement accuracy. It is therefore good practice to model the measurement method numerically beforehand to determine the dimensions that the specimen should have to optimise measurement accuracy. Of course, in many cases we will not be able to choose the specimen dimensions ourselves and we will then have to do the best we can, but it is often worthwhile asking our specimen suppliers whether they can produce specimens of a more optimum size or shape. In some techniques specimen diameter is a critical parameter, for example, in the coaxial line method of Figure 18.3 and Section 18.9.6. It has been found that the use of air-gauging [35] is cost-effective and particularly convenient for the measurement of inner and outer diameters of both specimens and the coaxial cells in which they are contained. 18.6.2.5 Anisotropic and magnetic materials It is important to know whether the material one is measuring is an anisotropic or a magnetic material. Some measurement methods assume isotropy of the specimen’s dielectric properties or else they assume a non-magnetic material – if these conditions
Measurement of the dielectric properties of materials 425 do not hold they can lead to significant errors in the dielectric measurements. Some of the methods described in Section 18.9 can measure anisotropy or magnetic properties and it will sometimes be necessary to use such methods (perhaps in a preliminary study) if one does not know the EM properties of one’s materials at all. 18.6.2.6 Inhomogeneous, composite and structured materials As explained in Section 18.4, when discussing dielectric resonances it is always important to consider the structure-length of the inhomogeneities in the material (i.e. the typical linear dimension of the particles or components in the material) in relation to the wavelength inside the components of the material. If the structurelength and wavelength are comparable in size the component parts may resonate and the material may scatter radiation rather than reflect or transmit it. Except in (‘meta-’)materials which are specifically designed to do this – for example, photonic band gap (PBG) or frequency selective (FS) materials – this behaviour is usually undesirable, so that most composites will have an upper frequency limit of usefulness. But there is another reason for being aware of the structure-length in inhomogeneous dielectrics: one wants the specimen that one is measuring to be sufficiently large to be statistically representative of the material as a whole and this should influence one’s choice of method: for example, one would choose a large waveguide cell to measure foodstuffs rather than a small coaxial cell. The alternative may be to measure a large number of small specimens and take a statistical average, but this can be time consuming. Significantly, inhomogeneous materials can never be measured as accurately as homogeneous specimens and often the inhomogeneity will be the greatest source of uncertainty in the measurement. 18.6.2.7 Ferroelectrics and high-permittivity dielectrics, ε 0001 > 100 The RF and MW properties of ferroelectrics [11,12,27] are most easily measured by techniques that can measure thin film specimens, for example, the split-post resonator, see Section 18.9.4. Very high permittivity ferroelectric films may only be measurable if they are of sub-micron thickness, so special thickness measurement techniques must be used. Thicker specimens may be measured in admittance cells at RF frequencies if their permittivity is not excessively high (e.g. if ε0005 < 3000, depending on frequency and specimen size) by applying metal electrodes to both surfaces.
18.7
Some common themes in dielectric measurement
Section 18.9 presents a survey of a number of techniques used for RF and MW measurements upon dielectric materials. However, there are many practical features that these techniques have in common and we consider some of them together briefly here. The details are covered in much greater detail in the Good Practice Guide [1].
18.7.1 Electronic instrumentation: sources and detectors At MW frequencies it is common practice to use automatic network analysers (ANAs) connected to dielectric measurement cells as source/detector combinations. ANAs
426 Microwave measurements [15,16,36,37] are the ‘workhorses’ of microwave laboratories and are described in detail in other chapters. ANAs can be used both for measuring S-parameters of reflection/transmission cells (as in Figure 18.3) and for measuring frequency changes and Q-factors of resonance cells or cavities. Some ANA models have a synthesised time domain facility as one of their features [38]. This can be useful in a number of techniques for gating or de-embedding the S-parameters of a specimen from any mismatched components and imperfect transmission lines that lie between it and the ANA. ANAs can also be used at RF, but at lower frequencies, say below 100 MHz, and especially where the dielectric measurement cells are significantly mismatched to 50 0011, it is often better to use Impedance Analysers, ‘Materials Analysers’, Admittance or Impedance Bridges or Frequency Response Analysers (FRAs) [39,40] as they can be more accurate and sensitive. Some FRAs can work down to frequencies as low as a few microhertz (µ Hz) while others have an upper limit at about 100 MHz. FRA manufacturers provide accessories and cells that are specifically designed for dielectric measurements as a function of temperature, time, DC and AC voltage bias.
18.7.2 Measurement cells General advice: keep cells clean so that they do not contaminate specimens. It is important to be aware of the EM-field configuration in one’s cell in order to choose the optimum size and shape for specimens. Note, in particular, that electric fields usually pass through, that is, from face to face of, laminar specimens in ‘lumpedimpedance’ methods (see Sections 18.9.1 and 18.9.2) but, in contrast, they usually lie in the plane of the lamina in travelling- and standing-wave cells (see Sections 18.9.3, 18.9.4, 18.9.6, 18.9.9, 18.9.11 and 18.9.12). This fact can be important if the material to be characterised is anisotropic (i.e. if ε∗ is a function of electrical field direction). With the exceptions of (1) free-field measurements and (2) some resonance measurements, it is usually best to keep the measurement volume of cells as small as possible, consistent with their achieving the required resolution for ε 0005 and tan δ. Also keep connections as small and simple as possible to reduce impedance residuals and mismatches. If a cell is to be actively temperature controlled, small cell size may also be an advantage because power requirements can be lower and temperature-settling times faster. However, in some cases a contrary policy may be advantageous. Whenever a high resolution for a measured quantity such as capacitance is required, it can be an advantage to have a cell with a long thermal time-constant (a ‘massive’ cell), so that the constant temperature cycling of a temperature-control system does not compromise resolution. Cavities and resonators form a special class of measurement cells; see [8–10,41] for background theory. In general, we use resonators for measuring specimens of low-loss, and so we need to know how to reduce loss in the resonator itself and in its coupling mechanisms – this will increase the resonator Q-factor and increase its resolution for specimen loss. The benefits of resonators do not arise only in the measurement of dielectric loss – the increased resolution offered by resonator techniques also applies to real permittivity ε0005 : some of the most accurate methods for measuring ε 0005 at MW and millimetre-wave frequencies are resonator methods.
Measurement of the dielectric properties of materials 427 In resonators, we are also concerned with the measurement of Q-factor, which we consider next.
18.7.3 Q-factor and its measurement Q-factor is measured in resonance techniques to determine the loss of dielectric specimens. This is a topic that requires a book in its own right to cover – see the book by Kajfez [42] and the Good Practice Guide [1]. The term Q-factor is actually a contraction of ‘Quality Factor’ and its symbol is usually Q. It is defined in the frequency domain for resonating systems as follows: Q = 2π ×
Energy stored in the resonance Energy lost per cycle
(18.15)
In the resonators with which we are concerned here the ‘energy stored’ is the EM energy stored in the fields in the resonator, the ‘energy lost’ is the EM energy lost by whatever means from such storage and ‘per cycle’ refers to a cycle of the sinusoidal resonating EM signal at the frequency that is present in the resonator. For a typical resonator we can write 1 1 1 1 = + + + ··· (18.16a) Q Qspecimen Qresonator walls Qcoupling where Qspecimen accounts for the dielectric loss in the specimen – this is the parameter we are trying to measure, Qresonator walls accounts for the power lost in the metal walls of the resonator due to conduction losses, Qcoupling accounts for power lost through all coupling mechanisms into the resonators: note that power is lost both through output and input coupling ports. There are usually many other sources of loss in resonators, as illustrated in Figure 18.8. In a typical resonance measurement we must distinguish between the influence of the loss of the dielectric material on the Q-factor and the loss from all other causes. Our measurement technique must be designed either (1) to allow us to estimate these other sources of loss, or else (2) it must cancel them out, for example, by use of a substitution method. For our purposes (18.16a) can further be refined as follows [1]: 1 1 1 = Ff tan δ + + + ··· Ql Qresonator walls Qcoupling
(18.16b)
where tan δ is the loss tangent of the specimen and Ff is the ‘filling-factor’ of the specimen in the resonator defined as follows: Ff =
Average EM energy contained in the speciman(Ws ) Average EM energy contained in the whole resonator(Wr )
(18.17)
Ff can be seen to be another important factor which depends on the cavity and specimen dimensions and on the specimen positioning. We need to know the value of Ff in order to measure the dielectric properties of the specimen. The value of Ff can vary enormously from one technique to another. For example, Ff = 1 if the specimen completely fills the resonator but Ff can be less than 0.01 in perturbation techniques
428 Microwave measurements G F H D
B A
O
C E
H
F Input waveguide
Figure 18.8
G
Output waveguide
Power transfer and loss processes in a resonator. An open-resonator (see Section 18.9.11) is used as an example. The resonator has two small coupling apertures for input and output from waveguides (shown overscale for clarity). (A) Power coupled from the input into the resonant mode, (B) input power reflected by mismatch, (C) attenuation of input signal by the ‘cut-off’section of the input coupling aperture, (D) power coupled through the input aperture that does not enter the resonant mode, (E) power lost from the resonant mode via the input coupling aperture, (F) dissipation in the metal reflectors (conversion to heat), (G) diffraction at reflector edges, (H) scattering (diffraction) from the coupling apertures and (O) power transmitted to the output waveguide. Losses (E) to (O) load (i.e. reduce) the Q-factor of the resonant mode (After Clarke and Rosenberg [102].)
(see Section 18.9.10). Ff also affects the extent to which the resonant frequency, fr , is shifted when a specimen is placed in a resonator, and so it is also an important parameter in the measurement of real permittivity, ε0005 as well as loss. Computation of Ff requires an analytical model of the resonator, many of which can be found in the scientific literature. Q-factor is traditionally measured by the resonance-width technique, (Figure 18.9). With fully automatic detection systems such as ANAs it is often better to use curve-fitting techniques, which can take account of signal leakage in the detection system and can be more immune to noise. Signal leakage can give rise to apparently distorted resonances and so to significant measurement errors for Q-factor – the traditional technique is prone to these errors. If the ANA employed is a Vector ANA, that is, one that measures the S-parameters of the resonator as complex parameters, one should carry out a full complex-parameter fitting of the S-parameters to gain maximum benefit from the measurement technique [1,42]. One should always bear in mind that many resonators exhibit a number of resonances that may overlap in the frequency domain – they may in fact be completely degenerate (i.e. coincide in frequency). This is a condition that should be tested for and avoided or compensated for in any serious measurement.
Measurement of the dielectric properties of materials 429 Vc Vi
2
3 dB ∆f
fr (1 – 1/2Q)
Figure 18.9
18.8
fr
fr (1 + 1/2Q)
frequency
A typical resonator resonance curve, showing how the width of the curve, 0012 f , at the ‘half power’ or ‘3dB’ points can be used to measure the Q-factor by the resonance-width method: thus Q ≈ fr /0012 f , where fr is the resonant frequency. The vertical axis gives the square of the voltage excitation of the resonance, that is, it is proportional to the power in the resonance
Good practices in RF and MW dielectric measurements
It is not always possible to follow these practices in every measurement, but one can try to abide by their spirit. (1) Calibrate all significant equipment traceably to international standards. (2) Once the measurement system has been calibrated and prior to the measurements upon the specimens under test, check the calibration, either by a measurement upon a check specimen that has known dielectric properties or else by measuring a Traceable Dielectric Reference Material [29,43]. This can save considerable time and embarrassing problems if the calibration is faulty! (3) Measure a number of specimens of the same material but of different thickness (or length, diameter, and so on as appropriate for the technique) to check for systematic errors. However, when the aim of the measurements is to determine the differences in the intrinsic dielectric properties of a number of similar specimens, they should all have the same size and shape, so as to remove differences caused by systematic errors. (4) Whenever possible measure specimens across a broad frequency range to check for consistency of properties across that range. (5) All dielectric specimens should be individually identified. To prevent similar specimens from getting mixed up only one specimen at a time should be out of its container. Record the provenance of specimens. (6) Dielectric properties usually change rapidly with temperature. The temperature of dielectric measurements should always be recorded. In the case
430 Microwave measurements of ambient temperature measurements, an uncertainty of ±0.2 ◦ C or better should ideally be achieved, though this may not be possible at elevated temperatures. A relative humidity of less than 50 per cent is recommended for measurements, unless otherwise required by one’s experiment. In some cases, especially with low-loss specimens, it will be necessary to record relative humidity at the time of measurement and possibly also during the prior storage of the specimen. (7) Record all relevant information on measurements in a lab book or computer file. If doubts arise about a measurement at a later date, this may enable you to trace the cause of the problem. On the other hand, if there is nothing wrong with the measurement, the record will help you to demonstrate this fact at a later date and so provide confidence in the measurement. (8) It is good practice to generate a measurement uncertainty budget following the practices of ‘The Guide’ (GUM) [44] or of the UKAS document M3003 [45]. (9) Be Safety Conscious: always be aware that many materials are toxic or flammable. Follow COSHH guidelines [46] for handling and disposing of materials, especially liquids. Never accept a material for measurement unless you know what it is and how to handle it safely.
18.9
A survey of measurement methods
In this survey we attempt only to illustrate the wide range of methods that have been developed to meet the challenge of the wide range of material types discussed in Section 18.6. Some indication is given of the main purpose of the methods and the types of material they are best suited to, but the reader is referred to the Good Practice Guide [1] and the other references provided for more details.
18.9.1 Admittance methods in general and two- and three-terminal admittance cells If the admittance, Y , is measured between any two electrodes with and without a dielectric material of complex permittivity ε ∗ present, we have ε∗ =
(Y when the space around the electrodes is completely filled with the dielectric) (Y when it is completely filled by a vacuum) (18.18)
This equation forms the basis for a wide range of dielectric measurement techniques that are in use almost from DC up to 1 GHz – the higher the frequency the smaller is the cell that must be used. The most common methods are those based on adjustable parallel-plate electrode systems (see Figure 18.10). Liquid dielectrics will readily fill the full volume of a measurement cell, whereas solid specimens cannot do so and this gives rise to measurement errors for solids caused by electrode/specimen air-gaps and by fringing-fields. By immersing a solid specimen in a liquid of similar permittivity,
Measurement of the dielectric properties of materials 431 these disadvantages can be overcome. This principle is used in Liquid Immersion Techniques for solids – see the standards BS 7663:1993 and ASTM D1531-01 and the Guide [1]. A more common way of avoiding errors which arise with two electrodes is to use a guard electrode around the low voltage electrode – this ensures that the electric field lines through the specimen and between the measurement electrodes are parallel, which greatly simplifies the computation of the permittivity, as we have Y = jω
ε0 ε ∗ A d
(18.19)
where ω is the angular frequency = 2π f , A is the area of either of the two measurement electrodes and d is their separation, assuming that the dielectric completely fills the gap between the electrodes. Corrections to this formula can account for the small gap I in Figure 18.10, but they are usually very small. Such a cell is referred to as a three-terminal cell. Cells as shown in Figure 18.10 with only two electrodes are referred to as two-terminal cells. There are many ways of using such two- and three-terminal cells for dielectric measurements and the best for any given specimen must depend on its properties. In some cases it is better to leave a deliberate air-gap above the specimen and measure its (a)
Guard electrode
(b)
Figure 18.10
High voltage electrode
I
I
Low voltage electrode
Guard electrode
(c)
(a) A three-terminal admittance cell. ‘I ’ is a thin low-loss insulating ring (it is exaggerated in thickness for clarity in the diagram), which separates the low voltage measurement electrode from the annular guard electrode. (b) In a two-terminal cell the E-field lines fringe out around the edge of the electrodes, giving rise to a fringing-field that can pass partly through the specimen, thereby generating measurement errors. (c) In a three-terminal cell the field lines between the high and low voltage measurement electrodes are straight and the field is uniform so measurement errors caused by fringing-fields are removed
432 Microwave measurements dielectric properties by adjusting the gap d with and without the specimen to produce the same capacitance across the cell in both cases. For some materials (especially those of high permittivity) it is better to metallise the specimen. Please see [1] for details. These cells are usually used at LF and RF frequencies in conjunction with admittance or impedance analysers or FRAs, (see Section 18.7). They can be employed over many decades of frequency for dielectric measurements. Two-terminal admittance cells come into their own at higher RF where it is difficult to keep the guard ring in the three-terminal technique at ground potential. Traditionally their uncertainty of measurement has been much lower than that of three-terminal cells (often worse than ±5 per cent for ε0005 ) because of the presence of fringing fields around the electrodes, as in Figure 18.10, the effect of which was difficult to calculate. However with the advent of EM-field modelling packages such as finite difference time domain (FDTD) or finite integration (FI), modern software can correct for the fringing-field errors, if one so desires.
18.9.2 Resonant admittance cells and their derivatives Two-terminal techniques came into use many years ago when interest in measuring dielectrics in the 100 kHz to 100 MHz range first arose. A resonant two-terminal cell method was very widely used for many years from the 1930s onwards [47], and was named the Hartshorn and Ward (H & W) Technique, after the two NPL scientists who developed the method. It was used both for medium and low-loss specimens until the advent of sensitive impedance analysers in the 1970s, which were found to be more convenient and accurate for medium-loss specimens. However, the method may still be used to advantage for low-loss specimens. The principle of the method is to resonate a micrometer-driven admittance cell with an inductor, as shown in Figure 18.4. One commonly measures the permittivity by adjusting the gap between the electrodes with and without the specimen so as to resonate the system at the same frequency in both cases – this approach is often called an ‘equivalent-thickness method’. Loss is computed from the change of Q-factor. A given specimen can be measured at a range of frequencies by using a number of inductance coils. The H & W cell is the lowest frequency member of a family of resonance cells that can be employed all the way up through the spectrum into the microwave region (see Figure 18.11). They have in common the feature that the E-field passes directly through the specimen from bottom to top, as shown in the figure, so for cylindrical specimens, they are sensitive √ to ε ∗ in a direction parallel to the axis of the cylinder. In such a resonator fr ≈ 1/ LC so the resonant frequency of measurement cells in this family can be increased either by reducing L or by reducing C, or both. One can reduce L by abandoning the coil inductors of the H & W method (Figure 18.11a) and by effectively ‘wrapping’ the inductance L around the capacitor, as shown in Figure 18.11b. This configuration gives one a re-entrant cavity or hybrid cavity. Such cavities can be used conveniently in the frequency range 100 MHz to 1 GHz. To resonate at even higher frequencies one can effectively reduce C by using a thicker and narrower specimen. One ends up with the TM010 –mode (or TM020 –mode)
Measurement of the dielectric properties of materials 433
L
L E
E
(a)
Figure 18.11
L
C
E
C
C
(b)
(c)
A family of dielectric measurement resonators. (a) The principle of the Hartshorn and Ward method: the admittance cell is resonated with an inductor. (b) The re-entrant cavity is a coaxial cavity with a capacitance gap in its inner-conductor where the dielectric specimen is placed. The inductance L is that of the magnetic field in the region between the inner- and outer-conductors. (c) The TM010 -mode cavity can, in principle, be seen as a re-entrant cavity that has its innerconductor fully retracted so that only a cylindrical cavity remains. This reduces the capacitance, C, of the specimen, which in the TM010 cavity typically takes the form of a rod, as shown
cylindrical cavity shown in Figure 18.11c. Such cavities typically operate in the range 1–10 GHz. Re-entrant cavities should always be considered as an option for low-loss materials in the range 100 MHz to 1 GHz as other forms of cavity (see below) are physically large in this frequency range. Details of measurement methods are described in International Standard IEC 60377-2, ‘Part 2: Resonance Methods’ and in [48]. The TM010 –mode cavity (Figure 18.11c) is the next in our family of resonators (see also Figure 18.12a), typically used from 1 to 10 GHz. The last subscript ‘0’ in TM010 indicates that the strength of the E- and H-fields does not change as one moves from top to bottom along the axis of the cavity. The axial E-field is at a maximum on the axis of the cavity and falls away to zero amplitude on the cylindrical sidewall, as required by the electrical boundary conditions there. As in the re-entrant cavity, the magnetic or H-fields loop around the axis of the resonator and so the coupling arrangements are similar. Specimens normally take the form either of rods [49] or else tubes, which can be used for containing liquid dielectrics [50,51]. Specimens commonly reach from top to bottom of the cavity, but this is not necessary [5]. Traditionally [52,53] this method was used as a perturbation method; (see Section 18.9.11.) If perturbation computations are used, the diameter of the specimen must be small compared with that of the resonator. However, more recently, advantage has been taken of the relatively simple internal geometry of the TM010 -mode cavity to employ modal analysis to derive exact equations for the cavity [54]. With such an analysis the diameter of the specimen need not be restricted. Similar advantages
434 Microwave measurements (a)
(b) Electric field Zero surface current ring Thin dielectric rod specimen
Input Coupling loop
H
Output Magnetic field
Specimen H r
TM010 E Resonant frequency determined by diameter
Figure 18.12
r
(a) A TM010 -mode cavity resonator containing a dielectric rod specimen, which in this case is introduced though two small holes (not shown to scale) on the axis of the resonator. (b) A TM020 -mode cavity resonator, showing the position of the circle on the top of the resonator where there are no surface currents, this is the best place to make a break in the surface if a lid is needed (After [5].)
accrue if discretised FDTD or FI modelling packages are used for the modelling – such packages are available commercially. One disadvantage of the TM010 -mode cavity arises if its lid has to be removed to insert a specimen. Currents in the top of the cavity have to cross the gap between the lid and the rest of the cavity. Thus, whenever a lid is removed in order to introduce/remove the specimen, contact impedances can change, introducing measurement errors for tan δ. With the TM010 -mode it is impossible to find any points or lines in the walls or the top or bottom of the cavity where currents do not flow (except the two points on the axis of the cavity). Fortunately this problem can be avoided by using the TM020 mode rather than the TM010 -mode, as explained in Figure 18.12b. Both cavities are relatively easy to use, especially if employed with the perturbation method [5,53].
18.9.3 TE01 -mode cavities The TE01 -mode cavity [55,56] (see Figure 18.13), is used for measurements on laminar low-loss specimens, typically in the 8–40 GHz range. These resonators have a high resolution for low-losses and they are typically used for measuring cylindrical disc specimens that notionally have the same diameter as the resonator. The electric fields in the resonator are circularly or (‘azimuthally’) polarised with respect to the resonator (z-) axis, as in dielectric resonators (see Section 18.9.8). Tuning can be achieved easily, as shown in the figure, by changing the resonance length of the cavity with a micrometer-driven metal piston. Typically, the cylindrical dielectric specimen
Measurement of the dielectric properties of materials 435 Small coupling apertures to waveguide
Resonant frequency determined by length Piston for tuning
Helical waveguide
E Dielectric (disc) specimen Lagging or temperature control
Micrometer
Figure 18.13
A micrometer-tuned TE01 -mode cavity for dielectric measurements
sits on the piston during measurements. As the electric field must fall to zero on the outer wall of the resonator, the specimen itself need not be an exact fit to the diameter of the cavity. Typically the specimen can be up to 0.5 mm smaller in diameter in a 50 mm diameter cavity without having a significant effect on the measurement accuracy. The technique can be used across a range of temperatures [57]. One potential problem with the TE01 -mode in a circular cylinder is that it is always degenerated with (i.e. it always resonates at the same frequency as) the TM11 -mode, so a method must be found for filtering out the latter. One of the most effective methods was implemented at NPL in the 1970s [55,58], when the cylinder of the cavity was manufactured from helical waveguide to remove axial currents in the walls, which are necessary for the TM11 -mode to resonate. Coupling into the cavity is typically from waveguide via small coupling holes, as shown in Figure 18.13, delivering a high insertion loss of the cavity on resonance. As in many resonant techniques ε0005 can be measured by a length-change/equivalentthickness method. Q-factors may be as high as 60,000 at 10 GHz for the mode with nine half-wavelengths along the cavity in a 50 mm diameter cell. As in many standing wave techniques (e.g. also in open resonators, Section 18.9.11) specimens should ideally be an integral number of half guide-wavelengths thick, both because this renders the measurements insensitive to surface contamination on the specimen (both
436 Microwave measurements surfaces are at a field node) and because it can be shown that this is the condition that gives best uncertainties. Experience over many years with such a cavity operating at 10 GHz shows that resolutions for loss angles may be as low as 10µ rad, while uncertainties for ε 0005 < 5 can be as low as ±0.5 per cent for ‘ideal’ specimens (i.e. for flat homogeneous low-loss specimens that are an integral number of half-wavelengths thick).
18.9.4 Split-post dielectric resonators The split-post dielectric resonator (SPDR) (Figure 18.14) was developed by Krupka and his collaborators [59] and is one of the easiest and most convenient techniques to use for measuring microwave dielectric properties. It uses a fixed-geometry resonant measurement cell for characterising low- or medium-loss laminar specimens (such as substrates and thin films) in the frequency range 1–36 GHz. The main drawback with this technique is that each SPDR can only operate at a single fixed frequency, but it is practicable and cost-effective to measure the same specimen in several SPDRs operating at different frequencies. The SPDR uses two identical dielectric resonators of the usual cylindrical disc or ‘puck’ shape. They are placed coaxially along the resonator axis leaving a small laminar gap between them into which the specimen is placed for measurement. Once the SPDR is fully characterised, only three parameters need to be measured to determine the complex permittivity of the specimen: its thickness and the changes in resonant frequency, 0012 f , and in the Q-factor, 0012Q, obtained when it is placed in the resonator. Specimens are typically a millimetre or so in thickness, but the method is also suitable for thin films. The resolution for thin specimens can be improved by stacking a number of them in the gap. The two dielectric pucks resonate together in a coupled resonance in the TE01δ mode, and so a circularly polarised evanescent E-field exists in the gap region between z
Dielectric resonators
Support
C
C
Specimen under test
Figure 18.14
Metal enclosure
A Split-Post Dielectric Resonator (SPDR) cell for dielectric measurements. Transmission coupling is via both dielectric resonators, ‘C’ marks the coupling loops
Measurement of the dielectric properties of materials 437 them. The geometry of the system is such that simple analytical models cannot be used to relate ε ∗ to 0012 f and 0012Q, so numerical solutions must be employed. The geometry of the SPDR lends itself to modelling by mode-matching or Finite Difference (FD) techniques. The main limitation of the SPDR technique is that its resolution for very lowlosses is reduced by the Q-factors of the two dielectric resonators it employs, but it can typically be used to measure loss angles down to 100 µrad with reasonable accuracy. Typical uncertainties can be ±1 per cent for ε0005 up to 10 and ±5 per cent for tan δ. A conference paper [60] gives details of studies that show that measurements on reference specimens in SPDRs agree well with those carried out by other wellestablished methods.
18.9.5 Substrate methods, including ring resonators Substrate and printed-circuit manufacturers need to know the dielectric properties of their substrates. Special techniques have been developed to enable them to measure these properties with the facilities commonly at their disposal. Most notable among these are facilities for depositing metal resonant structures lithographically onto substrate surfaces. Such structures include ring [61,62], T-shaped [63] and strip-line [64] resonators, all of which may be used to measure dielectric properties at a number of harmonically related frequencies across a wide band. The main advantage of this approach is that it gives designers of integrated circuits precisely the information that they need: an effective value for permittivity, εe0005 , that is appropriate for their applications. This is not necessarily the absolutely ‘true’ value of ε0005 for the substrate material because, like all measurements, these measurements are subject to systematic errors. However, if one is using a strip-line technique to determine a parameter, εe0005 , subsequently to be used for designing similar strip-line circuits, some degree of beneficial compensation of errors must occur. Problems can arise here if one is interested in measuring loss. High-temperature processes used in manufacture can cause deposited metal to in-diffuse into a substrate, so measured properties may differ from those of pure bulk material. The loss tangent of low- and medium-loss substrate materials is generally not measurable by these techniques because radiative and conductivity losses (surface and bulk) in the deposited metal structure tend to dominate: in practice the measured Q-factors can be below 100 even for low-loss materials.
18.9.6 Coaxial and waveguide transmission lines This method makes use of annular specimens, which should fit closely between the inner- and outer-conductors of the coaxial conductors of precision coaxial airline, as shown in Figure 18.3. The air-line should ideally be fitted with precision connectors that allow for a well-matched coaxial connection to an ANA. The complex permittivity and permeability of specimens are computed from the S-parameters of the specimen, as measured by the ANA. Similar techniques apply with other types of uniform air-line – the use of rectangular waveguide for such measurements is very common.
438 Microwave measurements The first of such methods was the Roberts and Von Hippel method [65] – in which the specimen is placed hard up against a short-circuit and its reflection coefficient is measured. Such one-port techniques may still be recommended in many instances (e.g. for high-temperature measurements) but there are two advantages to be gained from measuring both reflection from and transmission through specimens in a matched transmission-line. (1) For purely dielectric specimens up to 10 mm in length, one often finds that reflection coefficient measurements tend to be more accurate at lower frequencies (<500 MHz), while transmission measurements tend to be more accurate at higher MW frequencies. The combination therefore allows broadband measurements to be performed on just one specimen from, say, 100 MHz to 18 GHz in a 7 mm diameter air-line, taking advantage of the best uncertainties from both methods. (2) As explained in Section 18.3, the measurement of both transmission and reflection coefficients allows one to determine the magnetic properties of the specimen as well as its dielectric properties. For magnetic materials, both transmission and reflection data are normally required, though reflection-only data can be used if the specimen is moved axially in the line. Inevitably, for solid specimens metrological problems arise from the presence of air-gaps between the specimen and the inner- and outer-conductors of the line. They dilute the apparent permittivity obtained from the measurement but, more seriously for accurate measurements, they also help to launch higher-order modes. Both effects give rise to significant measurement errors. Air-gap problems do not usually arise for liquid measurements, but a well-designed liquid cell is required instead. The liquid must be contained between solid dielectric windows, as shown in Figure 18.15, so a multi-layer theory based on cascaded two-ports is necessary for the S-parameter analysis of the specimen/cell combination. Liquid specimen
To ANA Port 1
To ANA Port 2
Windows
Figure 18.15
A coaxial line cell for measuring liquid dielectrics
These transmission-line methods are often the most cost-effective choice for (1) broadband measurements, (2) magnetic materials, (3) medium- to high-loss materials and (4) materials that are only available in small volumes. Uncertainties for ε 0005 can be as low as ±1 per cent for low-permittivity materials if a correction for air-gaps is made but it may be higher than ±5 per cent for high permittivity materials, so use of other methods is advisable if more accurate measurements are needed.
Measurement of the dielectric properties of materials 439 NIST Technical Note 1341 [66] provides an excellent guide to the theory of this method as does the NIST follow-up work by Baker-Jarvis and his colleagues [67,68]. The paper by Jenkins et al. [43] explains how uncertainties can be computed in these measurements. It is concerned with dielectric liquid measurements but with the exception of the uncertainties caused by air-gaps, the analysis can be extended to solids. The NIST Technical Note provides the formulae that correct for air-gaps, based on a simple capacitative model. There are two published standard methods for the transmission-line technique: ASTM D5568-01 and a UTE (Union Technique de L’Electricité) standard from France [69]. The paper by Vanzura et al. [68] illustrates just how dominant the resonances of higher-order modes can be at higher frequencies. It shows that it is not advisable to use this method at frequencies above these resonances. Most of the considerations discussed for coaxial transmission lines apply also to waveguide measurements. The main advantage of using a waveguide is that one does not have to machine axial holes through the specimen to tight tolerances to allow it to be fitted onto a coaxial inner-conductor. The absence of the inner-conductor also makes waveguide cells more suitable for temperature control. The main disadvantage of waveguide is that one is normally restricted in frequency coverage to a single waveguide band (less than an octave in frequency coverage). Please see [1] and [66] for more details of measurements in both types of line.
18.9.7 Coaxial probes, waveguide and other dielectric probes Coaxial probes [43,70–76] (see Figure 18.16) are extremely popular measurement tools. The principle of operation of the conventional flat-faced probe is illustrated in Figure 18.16. A TEM travelling-wave propagates in the coaxial line up to its end where it launches fringing EM-fields from the open end of the probe into the dielectric specimen. Their magnitude and geometry depends on the complex permittivity, ε∗ , of the dielectric, so the reflection coefficient of the TEM-wave from the end of the probe will depend on the value of ε∗ . One can relate the measured reflection coefficient, , to ε ∗ by using (1) a modal analysis of the fields in the coaxial line and (2) an analysis of the fields in the dielectric under test (DUT) that treats the probe as an antenna. Simpler analyses have been used, especially those based on capacitative models for the fringing-fields, but they have their limitations [70]: at sufficiently high frequencies the probe must be treated as an antenna as it actually radiates into the dielectric specimen so that | | < 1.0 even if the dielectric is lossless [43]. Flat-faced coaxial probes, such as the one shown in Figure 18.16, represent just one member of a whole family of reflectometric and non-invasive probe designs that can be used for dielectric measurements. Another flat-faced probe option is the open-ended waveguide probe [77–79]. This type of probe has the capacity to measure anisotropic materials [80]. Coaxial probes are widely used for characterising lossy solids like biological tissues because of their ability to perform measurements by contacting just one face of the specimen, rather than having to machine the specimen to fit into a measurement cell. This makes them very convenient to use. They are also ideal for measuring lossy liquids and are widely used for SAR liquid characterisation;
440 Microwave measurements Flange Coaxial line
Figure 18.16
Dielectric specimen
A coaxial probe, showing the fringing-fields that emerge from its ends. The field lines shown are those of the electric field, which is seen to fringe out into the dielectric specimen at the end of the probe
see British Standard BS EN 50361:2001, and IEEE Standard P1528 (D1.2). But with liquids one does not need to use a flat-faced probe and there are often advantages to be gained by using other geometries (see below). A single flat-faced coaxial probe can typically operate effectively over a frequency range of about 30:1 (e.g. 100 MHz to 3 GHz for a 15 mm diameter probe) whilst retaining a reasonable uncertainty performance of the order of ±4 per cent for ε 0005 for suitable materials. The actual frequency range depends on the diameter of the coaxial aperture of the probe and the permittivity of the dielectric specimen. The coaxial probe method has its limitations. Measurement uncertainties are usually of the order of ±3 per cent at best for ε0005 and ε 00050005 and a number of other techniques described in this survey can be more accurate (e.g. coaxial cells for liquids; Section 18.9.6). There are many types of measurement for which the probe would be the wrong choice. Thus, the assumption is commonly made in the theory that is used to relate ε ∗ to , that there are reflections of waves neither from the extremities of the specimen nor from permittivity steps or gradients within inhomogeneous specimens. In small, layered or low-loss specimens this is usually not the case. Furthermore coaxial probes are much better suited to measuring malleable materials (or liquids) that accommodate themselves to the shape of the probe than to hard specimens because they invariably leave uneven air-gaps between the specimen face and the probe face. The conventional theory assumes that there are no such air-gaps, and as the probe is particularly sensitive to the permittivity of the material closest to its face, even a small gap can give rise to a large error of measurement [81]. Layered structures and air-gaps can be modelled [73,74], however, see Figure 18.17, if the thickness of the layers is known, and the utility of the probe extended thereby. The measurement geometry of coaxial and waveguide probes, even for complex geometries similar to those shown in Figure 18.17, can be analytically calculable. An alternative approach that widens the range of probe designs and their range of application is to reduce one’s dependence on full calculability and to rely more on probe calibration with a set of known reference liquids to supply the accuracy that the theory lacks. Thus, one may prefer to use a probe without a flange (e.g. [75]) – it
Measurement of the dielectric properties of materials 441 (a)
(b)
Laminar dielectric specimen Conducting plane
Figure 18.17
etc.
ε1, t1 ε2, t2 ε3, t3
Use of a coaxial probe (a) for measuring a dielectric lamina backed by a metal conducting plane, (b) for measuring a multi-layered specimen. Each layer, i, has thickness ti and permittivity εi
is smaller and more convenient than a calculable probe with a (supposedly infinite) flange. One can regard probes having other non-calculable shapes as ‘black boxes’: whenever they have the property of being reasonably stable and of presenting one with a one-to-one and smoothly varying relationship between and ε∗ they can be effective. By measuring a suitably large number of reference liquids having known ε ∗ values, one can interpolate measured values of to calculate ε∗ for other dielectrics. Probes that are used in this way may be called non-calculable probes (e.g. [82]). Some of these probe designs can have much better field penetration into the specimen than coaxial probes [83,84]. Dielectric probes are normally used in conjunction with ANAs, so suitable calibration schemes must be developed for the ANA/probe combination. Typically for a coaxial probe one calibrates with (1) an open-circuit into air, (2) a short-circuit and (3) a measurement of a known reference liquid (e.g. [29]). Great care must be taken, particularly with the short-circuit, where one has to make a good electrical contact to the inner-conductor, and also with the reference liquid, which can easily change temperature by evaporation or absorb contaminants from the atmosphere, for example, water vapour. Both temperature change and contamination can easily lead to the dielectric properties of the liquid not being close to those assumed by the calibration software, and so they can result in significant calibration errors. Given such calibration difficulties it is always good practice to measure a second dielectric reference liquid immediately after a calibration to check calibration validity. It is not uncommon for calibrations to have to be repeated a number of times until a good calibration is obtained. This can be very time consuming. One approach that has been developed to overcome this problem is to use a least-squares calibration technique [1]. Least-squares calibration has another advantage as well: it enables some of the errors and uncertainties of the measurement to be estimated statistically. For liquid specimens it is often better to extend the outer-conductor of the probe to form a cell – see Figure 18.18 [43]. Extension of the inner-conductor as well, as in Figure 18.18b increases the capacitance of the cell and so makes it more sensitive at lower frequencies. The liquid can be poured in until its meniscus is sufficiently far away from the end of the inner-conductor for no change in reflection coefficient to be detected if more liquid is poured in.
442 Microwave measurements (a)
(b)
Semi-infinite circular waveguide section
Liquid specimen
Coaxial section
Measurement and calibration plane
Semi-infinite circular waveguide section
Liquid specimen Measurement and calibration plane
Bead Bead
Figure 18.18
Liquid Cells. (a) A modification of the coaxial probe shown in Figure 18.16 to allow easy measurement of liquids. (b) The Discontinuous Inner-Conductor Cell: a further modification that can be used to increase the measured capacitance of the dielectric liquid. For a given liquid, geometry (b) will be more sensitive at lower frequencies than (a). The inner-conductor extension is of any appropriate length. Both cells are fully calculable
Open-ended rectangular waveguide probes [77–79] are used less often than coaxial probes, partly because, like all waveguide-based systems, they are limited in frequency range and they may be physically quite large. However, the required probe size for a given frequency range can be reduced if the probe waveguide is itself filled with a ‘loading’ dielectric material. Reference [80] describes one such probe, based on a WG16 (normally 8.2–12.4 GHz) waveguide adaptor, which was loaded with glass dielectric (ε0005 ≈ 6) to allow it to operate in the range 3.5–5 GHz. Waveguide probes offer two potential advantages [80] over coaxial probes for specific applications. One is the fact that such probes are better matched for measuring lower permittivity than coaxial probes of similar size and at a similar frequency. The other perhaps more important advantage is that waveguide probes, being linearly polarised, can measure anisotropy in dielectrics [80].
18.9.8 Dielectric resonators Dielectric resonators (DRs) are widely used in electronics and telecommunications applications as high-Q components for narrow-band filters. The theory of their resonances is well developed [85]. The resonators typically take the form of ‘puck’-shaped cylinders of dielectric material. They can retain the EM-fields that are resonating inside them because the fields are totally internally reflected from the interior of the dielectric surfaces. A formal analysis of the fields reveals that there are also EM evanescent fields in the air (or other dielectric medium) that surrounds the resonator and that these fields decay exponentially in magnitude as one moves away from the resonator. It is the presence of these fields that allows one to couple RF and MW power into the DR, typically via coupling loops at the end of coaxial line feeds. However, these fields also interact with other objects in the vicinity of the resonator (e.g. its support or its container) and if these nearby objects are lossy the resonance
Measurement of the dielectric properties of materials 443 (a)
To micrometer drive
(b) Cavity lid
Flat copper plates
C
Dielectric resonator
Figure 18.19
C
C
Cavity Quartz support
Dielectric resonator
C
Quartz support
Dielectric resonator cells. (a) A Hakki-Coleman Cell, otherwise known as the Courtney Holder or the Parallel Plate Cell, and (b) a Cavity Cell. In both diagrams ‘C’ marks the coupling loops.
becomes loaded and the Q-factor falls, giving rise to errors if one is measuring the loss of the resonator. Figure 18.19 shows the coupling geometry for two configurations commonly used in dielectric metrology. Typical resonator sizes range from tens of centimetres on a side in 900 MHz cell-phone base-station applications, down to a centimetre on a side or less at around 10 GHz. The frequency depends on the size and the permittivity of the resonator. Dielectric measurements on ‘puck’-shaped specimens offer one of the most accurate and sensitive methods available to us for measuring the permittivity and loss of low-loss dielectric materials. They have a major advantage over other resonant techniques for characterising low-loss materials: the attainable filling-factors, Ff (see Section 18.7), in this technique are normally close to unity because most of the energy in the resonance is contained in the dielectric itself. Measurements are usually performed using the TE01δ -mode in which the E-field is azimuthally circularly polarised, but higher-order ‘whispering-gallery modes’ have also been used to obtain dielectric data at much higher frequencies [86,87]. When viewed on an ANA or spectrum analyser, one can see that DRs resonate in many different modes. One of the main preliminary steps to be undertaken before measurement, therefore, is to identify the TE01δ mode. TE01δ -mode resonators must be used in a container or cell, otherwise their Q-factors are loaded by radiative losses. The two types of cell most commonly employed in dielectric metrology are shown in Figure 18.19 and they are designed to prevent this. In the Courtney Holder or Hakki–Colemen Cell of Figure 18.19a the distance between the top and bottom plates must be less than λ/2 in air if this radiation loss is to be avoided. (NB. radiation loss is not so important for whispering-gallery modes). The Cavity Cell of Figure 18.19b prevents radiation escaping by completely enclosing the specimen with metal walls. These walls should be well separated, ideally by at least one specimen diameter, from the specimen to minimise losses from currents flowing in them. For the same reason, the specimen is normally placed on a small post or tube made from low-loss dielectric (e.g. quartz) to displace it away from the base of the cavity. Cells are often made
444 Microwave measurements from copper because its high conductivity reduces the metal losses in the walls. See Reference [1] for the relative advantages and disadvantages of the two types of cell in Figure 18.19. There may be two reasons why we may wish to perform DR dielectric measurements. First, we may wish to know the intrinsic dielectric properties of the DR specimen material: its real permittivity, ε 0005 , and loss tangent, tan δ, or we may ultimately wish to evaluate it as a dielectric resonator, for example, as a component of a filter in an electronic circuit. In the latter case we will want to measure its extrinsic parameters: its resonant frequency, Q-factor and its temperature coefficient of resonant frequency (TCRF). Similar measurement configurations can be used for either type of measurement, but extra analysis is required for intrinsic measurements. The TCRF is one of the most important factors in practical applications: one normally wishes it to be as close to zero as possible. Examples of the recent use of DRs for dielectric measurements can be found in the literature [88] and they demonstrate the versatility of the technique. Use of dielectric resonators for dielectric measurements is also described in some International Standards, for example, IEC 61338, Sections 18.1–18.3 and IEC 60377-2, Part 2.
18.9.9 Free-field methods Figure 18.20 shows three typical geometries employed for free-field measurements on dielectrics. These methods are best suited for materials that are intended for enduses in the free-field, as they are likely to be the only materials available in large enough cross sections to allow free-field methods to be effective. Typical materials are RAM – high-loss materials used for absorbing free-field waves – and Radome materials – typically low-loss materials used for protecting antennas from the elements (rain, wind, snow, etc.). Free-field methods may be categorised by three contrasting pairings of practical approaches to measurement: (1) Transmission or Reflection methods; (2) Intrinsic or Extrinsic methods. Intrinsic measurements determine the intrinsic dielectric and magnetic properties of the specimen, that is, ε∗ and µ∗ while Extrinsic measurements measure extrinsic parameters like reflectivity or scattering from materials and transmission through materials; (3) Focused (Quasi-Optical)-Beam or Unfocused-Beam Methods. Free microwave fields are typically launched as diverging beams from antennas, as in the unfocused measurement systems of Figure 18.20. The inevitable diffraction around the edges of antennas and specimens in these methods limits their accuracy. In focused-beam or quasi-optical methods, see Figure 18.21, lenses or concave mirrors are used to prevent the divergence of the beam. An attempt may also be made to ensure that it is fully calculable in its geometry. Such beams can be launched from corrugatedhorn antennas [89,90] as Gaussian Beams (GBs) [3,91,92]. They are potentially fully calculable all along their length, they decay exponentially to insignificant amplitudes as one moves away from their axis of propagation and they can be focused by concave mirrors or bloomed lenses [92]. Thus, diffraction problems may potentially be made negligible.
Measurement of the dielectric properties of materials 445 (a)
(b)
(c) Specimen
Input horn
Specimen
Figure 18.20
Output horn
Input horn
0001 Output horn
Horn
Free-field methods: (a) normal transmission through a specimen between two horn antennas, (b) normal reflection from a specimen and (c) measurement of transmission as a function of the angle of incidence, see text Waist of beam
Launch antenna
Gaussian beam
Receive antenna Lenses
Figure 18.21
A focused free-field measurement system. The specimen is placed at the waist of the beam. If corrugated-horn antennas are used, then the beam can be launched as a calculable Gaussian Beam
End-users of free-field materials such as RAM and radome laminates are often more interested in their extrinsic parameters, such as reflection or transmission coefficient, than the intrinsic parameters ε ∗ and µ∗ . Intrinsic measurements are required, however, for design and optimisation purposes. The actual measurement set-ups needed to implement these two approaches may be very similar, but extrinsic measurements ought ideally to be performed in a geometry that approximates to that of the end use of the material. For example, if the reflectivity of RAM at a 45◦ angle of incidence is required, then extrinsic measurements of reflectivity should be performed at this angle, whereas intrinsic measurements can be performed by any suitable method and the reflectivity at 45◦ incidence can subsequently be computed from Fresnel’s equations [10,19]. Free-field travelling-wave methods have much in common with guided travellingwave methods in that ε0005 is generally determined from the phase change of the transmission coefficient and dielectric loss from the attenuation of the beam on insertion of the specimen. The method of time domain gating [38] is particularly useful for improving the accuracy of free-field measurements (especially unfocused measurements) as it allows the wanted signals from the dielectric specimen to be separated from spurious reflections originating from elsewhere in the measurement system and from elsewhere in one’s laboratory!
446 Microwave measurements There are many approaches to unfocused free-field measurement, they range from the The Arch Method for RAM at arbitrary angles [93,94], to normal incidence methods [95,96], to Brewster angle methods [97] and to measurement of transmission as a function of the angle of incidence [98]. Focused or quasi-optical methods usually use travelling GB waves [91]. Complete measurement systems for laminar specimens are constructed either with lenses [99] or mirrors [94] for focusing – the latter generally give better performance.
18.9.10 The resonator perturbation technique High-Q cavity resonators are very sensitive measurement devices and this makes it possible to measure very small dielectric specimens inside them. If a sufficiently small specimen is inserted into a resonator and if no other changes are made to the measurement geometry, the resonant frequency fr and Q-factor, Q, of the resonator will both change by a small amount: 0012 fr and 0012Q, respectively. If both 0012 fr /fr and 0012Q/Q are small (typically less than 5 per cent) and the volume of the specimen is small compared with the volume of the resonator, first-order perturbation theory may be used to calculate the permittivity, ε0005 , and the loss tangent, tan δ, of the specimen. Such measurement techniques are referred to as Resonator (or Cavity) Perturbation Techniques [41]. One example of this approach is the application of perturbation theory to measurements in TM010 or TM020 -mode cavities when they are used with narrow rod specimens as described in Section 18.9.2. A number of advantages can accrue from using such a perturbation technique: (1) The measurement theory is much simpler: ε 0005 is usually proportional to 0012 fr and tan δ to 0012Q. (2) Even high-loss materials may be measured, if the specimens are sufficiently small, and if 0012Q/Q is also small. In fact, perturbation methods are normally the only resonator methods commonly used for measuring high-loss materials. (3) By placing small specimens in a cavity at points where the direction of the E- and/or H-fields are well defined, the anisotropy of permittivity, ε ∗ , and of permeability, µ∗ , can be measured. The perturbation method has been in use at least since the 1940s [52,53], but Waldron later extended and popularised it in the 1960s. His book [41] still provides one of the best guides to its application, both for permittivity and permeability measurement. There are a number of more recent applications described in the scientific literature, however, for example [100,101].
18.9.11 Open-resonators Open-resonators are millimetre-wave Fabry–Perot interferometers [102,103]. They provide one of the most accurate methods for low-loss dielectrics at millimetre-wave frequencies. Achievable uncertainties can be as low as ±0.2 per cent for ε 0005 below 3 and better than ±1 per cent for ε0005 ≈ 50. Uncertainties better than ±10 per cent for tan δ are also possible for specimens with loss angle above 200 µrad, while resolutions for loss down to 20 µrad or less are possible if the unloaded Q-factor of the resonator is greater than 150,000. A typical open-resonator configuration for dielectric measurement is shown in Figure 18.22. Typical sources of loss in an openresonator are shown in Figure 18.8, Section 18.7. An advantage of open resonators
Measurement of the dielectric properties of materials 447 Input
Output Waveguide coupling
Concave
mirror Coupling apertures
Beam diameter
Dielectric
Specimen
Plane mirror
Waist of beam Mirror position micrometer driven
Micrometer
Figure 18.22
An open-resonator geometry that can be used for characterising dielectrics at millimetre-wave frequencies
over most microwave cavities (e.g. TE01 , TM01n and TE01δ ) is that the resonant mode employed in these measurements is the fundamental transverse electromagnetic (TEM) mode which is linearly polarised – thus enabling specimen anisotropy to be measured [104]. The resonant mode used in the open-resonator is the fundamental TEM00n GB mode [91] and the high Q-factor resonance itself acts as a filter that ensures that this GB mode can be very pure. The cross-sectional shape and size of specimens for open-resonators is not important provided they are large enough to encompass the whole cross section of the GB at its waist, where it is narrowest. Specimens are flat laminas, their required minimum diameters depend on frequency. The following are typical: at 10 GHz typically 200 mm diameter, at 36 GHz 50 mm and at 72 GHz 35 mm diameter. The best practice is to compute the radius, w0 , of the GB at its waist and then use a specimen diameter of at least 5 × w0 . To achieve lower measurement uncertainties, specimens should be an integral number of half-wavelengths thick. Though they are potentially very accurate, open-resonator measurements are prone to many errors that have to be checked for and so measurements can be quite
448 Microwave measurements time consuming. Significant sources of error include mode coincidence, warped specimens and gaps between specimens and mirrors. Errors in estimated loss can also occur if the specimen is anisotropic but is not known to be so. The errors and how to avoid them are described in detail in the Good Practice Guide [1]. The use of open-resonators for dielectric measurements has been described in great detail in a number of reviews, scientific papers and books [102,103,105,106], and the reader is referred to these sources for full details of methods and measurement theory. The microwave open-resonator technique came into its own for low-loss millimetre-wave measurements in the 1970s and it has been continuously developed since then. Work at NPL in the early 1990s addressed the measurement of mediumloss specimens and investigated new techniques for measuring specimen loss [107], while studies down to cryogenic temperatures in Germany [108] have much improved the resolution for loss by increasing resonator Q-factor through better coupling methods.
18.9.12 Time domain techniques Time domain reflectometry (TDR) using pulse or step generators and sampling methods for detection, see Figure 18.23, was introduced in the second half of the twentieth Century [109] for dielectric measurements and is still widely used [110,111]. It is convenient to use for the purposes of scientific study, being a cost-effective broadband method which requires only small specimens, making temperature-control relatively easy. Solid specimens typically fit into a 7 mm coaxial line. The main limitation of the method is its absolute accuracy, which is not generally as good as that of reflectometry based on a calibrated ANA. The main reason for the continued popularity of TD methods using pulse/step generators is that they are cheaper than fully automated ANA measurements, and they are often more convenient to use. These days it is possible to employ synthesised time domain techniques [38] because it is a feature available in ANAs. In both ANAs and conventional TDR systems time domain gating or de-embedding can be used to improve the accuracy of dielectric measurements: for example, by removing the effects of unwanted reflections in a cell by gating them out in the time domain. Reflected signal Specimen Pulse generator
Sampling head Matched transmission line
Data processing Sampling oscilloscope
Figure 18.23
Block diagram of a typical time domain reflectometer
Measurement of the dielectric properties of materials 449
18.10 How should one choose the best measurement technique? Answers to this question are covered in some detail in the Good Practice Guide [1] in the light of the policy (Section 18.6) that one should ideally match the method to the material. A checklist taken from the Guide demonstrates just how many parameters and issues one has to take into account: • • • • • • • • • • • • • • •
The frequency range of interest. The dielectric loss (high, medium or low) and expected permittivity range. The type of material, for example, hard, malleable or soft solids, volatile or viscous liquids. Specimen machining imperfections and tolerances and their influence on uncertainty. Specimen shape and size and their influence on measurement uncertainty. Specimen anisotropy and homogeneity and their influence on measurement uncertainty. Inhomogeneity and the presence of surface layers on specimens. The possibility that the specimen may be made from a magnetic and anisotropic material. The required uncertainties. What level of uncertainty can be achieved by available methods? The specimen composition (e.g. does the specimen have a laminated structure). The availability of suitable methods for machining and grinding specimens. The presence of surface inclusions and pores, surface conditions in solid specimens. Toxicity, contamination and evaporation of liquid specimens. The cost of machining specimens and performing measurements: costeffectiveness. The time taken to perform the measurements – labour-intensiveness and the labour cost of measurements.
It is generally unlikely that one will have a completely free choice of method: more typically one will be asking questions like (1) how best can I press into service the facilities that I already have to perform the required measurement as accurately as possible? (2) Which techniques are best suited to checking consistency, rather than providing absolute accuracy. (3) Which techniques can be de-skilled? How proof are the various techniques against inexperience? (4) Which are most cost-effectively used in production control? All of these questions are addressed in the Guide [1].
18.11
Further information
The Good Practice Guide [1], scientific papers, textbooks and International Standards have all been discussed above but there are other sources of useful information such as manufacturers’ literature, including catalogues, manuals and application notes, as in Reference 24. National Measurement Institutes (NMIs) other than NPL produce
450 Microwave measurements detailed technical notes, reports and guides on measurement techniques, notably NIST in the USA. NPL runs an Electromagnetics Measurements Club. Other societies, clubs and associations including the ARMMS RF & Microwave Society (general microwave topics) and the Ampere Association (microwave processing) can also provide support. A number of learned societies also run active dielectrics groups, notably the Institute of Physics, or groups that cover dielectric-related topics, notably the Institution of Engineering and Technology in the UK. Further details of all of these organisations can be found on the Internet.
References 1 Clarke, R. N. (ed.): NPL good practice guide: a guide to the characterisation of dielectricmaterials at RF and microwave frequencies (Institute of Measurement and Control, NPL, 2003) 2 Von Hippel, A. R.: Dielectric Materials and Applications (Technology Press of MIT, Wiley, New York, 1954; new edition Artech House, Dedham, MA, 1995) 3 Birch, J. R., and Clarke, R. N.: ‘Dielectric and optical measurements from 30 to 1000 GHz’, The Radio and Electronic Engineer, 1982;52:565–84 4 Afsar, M. N., Birch, J. R., Clarke, R. N., and Chantry, G W. (eds.): ‘The measurement of the properties of materials’, Proceedings of the IEEE, 1986; 74:183–98 5 Anderson, J. C. (ed.): Dielectrics (Chapman and Hall, London, 1964) 6 Chamberlain, J., and Chantry, G. W. (eds.): ‘High frequency dielectric measurement’, Proceedings of the NPL Conference, Teddington, UK, 1972 (IPC Science and Technology Press, Guildford, 1973) 7 Grant, I. S., and Philips, W. R.: Electromagnetism, Manchester Physics Series (John Wiley, Chichester, 1996) 8 Ramo, S., Whinnery, J. R., and Van Duzer, T.: Fields and Waves in Communication Electronics, 3rd edn (John Wiley and Sons, New York, 1994) 9 Montgomery, C. G., Dicke, R. H., and Purcell, E. M.: Principles of Microwave Circuits (Peter Peregrinus, London, 1987) 10 Inan, U. S., and Inan, A. S.: Electromagnetic Waves (Prentice Hall, NJ, 2000) 11 Kittel, C.: Introduction to Solid State Physics (John Wiley and Sons, New York, 1996), Chapter 13 12 Neelakanta, P. S.: Handbook of Electromagnetic Materials (CRC Press, Boca Raton and New York, 1995) 13 Debye, P.: Polar molecules (Dover Publications Inc., New York, 1929) 14 Chamberlain, J.: ‘Sub-millimetre wave techniques’, Proceedings of the NPL Conference, Teddington, UK, 1972 (IPC Science and Technology Press, Guildford, 1973), pp. 104–116 15 Bailey, A. E. (ed.): Microwave Measurement (Peter Peregrinus Ltd (IEE), London, 1985 and later editions) 16 Somlo, P. I., and Hunter, J. D.: Microwave Impedance Measurements, IEE Electrical Measurement Series 2 (Peter Peregrinus Ltd (IEE), London, 1985)
Measurement of the dielectric properties of materials 451 17 Kibble, B.,Williams, J., and Henderson, L., et al. (eds).: A Guide to Measuring Resistance and Impedance Below 1 MHz (NPL and the Institute of Measurement and Control, London, 1999) 18 Moreno, T.: Microwave transmission design data (Dover, NY, 1948 (original print); 1958 reprint) 19 Lorrain, P., Corson, D. R., and Lorrain, F.: Electromagnetic Fields and Waves, 3rd edn (W H Freeman and Co., New York, 1988) 20 Kajfez, D.: Q Factor (Vector Fields, Oxford, MS, 1994) 21 Birch, J. R., and Parker, T. J.: ‘Dispersive fourier transform spectroscopy’, in Button, K. J. (ed.), Infrared and Millimetre Waves, vol. 2 (Academic Press, New York, 1979), pp. 137–271 22 Daniel, V. V.: Dielectric Relaxation (Academic Press, London, 1967) 23 Jonscher, A. K.: Dielectric Relaxation in Solids (Chelsea Dielectrics Press, London, 1983) 24 Williams, G., and Thomas, D. K.: Phenomenological and Molecular Theories of Dielectric and Electrical Relaxation of Materials (Novocontrol Application Note Dielectrics 3, Novocontrol GmbH, 1998) 25 Pethig, R.: Dielectric and Electronic Properties of Biological Tissues (John Wiley & Sons, Chichester and New York, 1979) 26 Chikazumi, S.: ‘Physics of ferromagnetism’ in Birman, J. et al. (eds), The International Series of Monographs on Physics, 2nd edn (Clarendon Press, Oxford, 1997) Crangle, J.: Solid state magnetism (Edward Arnold, London, 1991); Jiles, D. Introduction to Magnetism and Magnetic Materials (Chapman and Hall, London, 1991) 27 Burfoot, J. C.: Ferroelectrics: an introduction to the physical principles (Van Nostrand, London, 1967) 28 Garg, S. K., and Smyth, C. P.: ‘Microwave absorption and molecular structure in liquids LXII: the three dielectric dispersion regions of normal primary alcohols’, The Journal of Physical Chemistry, 1965;69:1294–301 29 Gregory, A. P., and Clarke, R. N.: Tables of complex permittivity of dielectric reference liquids at frequencies up to 5 GHz, NPL Report CETM 33, NPL, 2001 30 Cole, K. S., and Cole, R. H.: ‘Dispersion and absorption in dielectrics’, Journal of Chemical Physics, 1941;9:341–51 31 Davidson, D.W., and Cole, R. H.: ‘Dielectric relaxation in glycerol, propylene glycol, and n-propanol’, Journal of Chemical Physics, 1951;19:1484 32 Havriliak, S., and Negami, S.: ‘A complex plane analysis of α-dispersions in some polymer systems’, Journal of Polymer Science Part C, 1966;14:99 33 James, J. R., and Andrasic, G.: ‘Assessing the accuracy of wideband electrical data using Hilbert transforms’, IEE Proc. H, Microw. Antennas Propag., 1990;137:184–8 34 Lynch, A. C.: ‘Relationship between permittivity and loss tangent’, Proc. Inst. Electr. Eng., 1971;118:244–6 35 Ide, J. P.: Traceability for radio frequency coaxial line standards, NPL Report DES 114, July 1992
452 Microwave measurements 36 Engen, G.: Microwave Circuit Theory and Foundations of Microwave Metrology (Peter Peregrinus Ltd (IEE), London, 1982) Engen, G. F., and Hoer, C. A.: ‘Thru-Reflect-Line: an improved technique for calibrating the dual six-port automatic network analyser’, IEEE Transactions on Microwave Theory and Techniques, 1979;MTT-27:987–93 Hoer, C. A., and Engen, G. F.: ‘On-line accuracy assessment for the dual six-port ANA: extension to non-mating connectors’, IEEE Transactions on Instrumentation and Measurement, 1987; IM-36:524–9 37 Kerns, D. M. and Beatty, R. W.: Basic Theory of Waveguide Junctions and Introductory Microwave Network Analysis (Pergamon Press, London, 1967) 38 Ridler, N. M. (ed.): Time domain analysis using network analysers: some good practice tips, ANAMET Report 027, ANAMET Club, NPL, September 1999 39 Bartnikas, R.: ‘Alternating-current loss and permittivity’ in Electrical Properties of Solid Insulating Materials: measurement techniques, Engineering Dielectrics II B, ASTM STP926 (The American Society for Testing and Materials, Philadelphia, USA, 1987) 40 Schaumburg, G.: ‘New broad-band dielectric spectrometers’, Dielectrics Newsletter, (Novocontrol GmbH, Hundsangen, July 1994) 41 Waldron, R. A.: The Theory of Waveguides and Cavities (Maclaren & Sons Ltd, London, 1967) 42 Kajfez, D.: Q Factor (Vector Fields, Oxford, MS, 1994) 43 Jenkins, S., Hodgetts, T. E., Clarke, R. N., and Preece, A. W.: ‘Dielectric measurements on reference liquids using automatic network analysers and calculable geometries’, Measurement Science and Technology, 1990;1:691–702 44 Guide to the Expression of Uncertainty in Measurement, 1st edn (International Organisation for Standardisation (ISO), Geneva, Switzerland, ISBN 92-67-10188-9, 1993) 45 The Expression of Uncertainty and Confidence in Measurement, M3003 1st edn (UKAS, Feltham, Middx., 1997) 46 Control of Substances Hazardous to Health (COSHH), as specified by the UK government’s Health and Safety Executive (HSE). An introduction is given in HSE leaflet INDG136rev2, COSHH – A brief guide to the regulations’. Available at: www.coshh-essentials.org.uk. 47 Hartshorn, L., and Ward, W. H.: ‘The measurement of the permittivity and power factor of dielectrics at frequencies from 104 to 108 cycles per second’, Journal of the Inst. of Elec. Eng., 1936;79:597–609 48 Parry, J. V. L.: ‘The measurement of permittivity and power factor of dielectrics at frequencies from 300 to 600 Mc/s’, Proceedings of the IRE, 1951;98 (Part III):303–31 49 Verweel, J.: ‘On the determination of the microwave permeability and permittivity in cylindrical cavities’, Philips Research Reports, 1965;20:404–14 50 Mensingh, A., McLay, D. B., and Lim, K. O.: ‘A cavity perturbation technique for measuring complex permittivities of liquids at microwave frequencies’, Canadian Journal of Physics, 1974;52:2365–9
Measurement of the dielectric properties of materials 453 51 Risman, P. O., and Ohlsson, T.: ‘Theory for and experiments with a TM02n applicator’, Journal of Microwave Power, 1975;10:271–80 52 Collie, C. H., Ritson, D. M., and Hasted, J. B.: ‘Dielectric properties of water’, Transactions of the Faraday Society, 1946;42A:129–36 53 Horner, F., Taylor, T. A., Dunsmuir, R., Lamb, J., and Jackson, W.: ‘Resonance methods of dielectric measurement at centimetre wavelengths’, J. Inst. Electr. Eng., 1946;93 (Part III):53–68 54 Li, S., Akyel, C., and Bosisio, R. G.: ‘Precise calculations and measurement on the complex dielectric constant of lossy materials using TM010 perturbation techniques’, IEEE Transactions on Microwave Theory Techniques, 1981; MTT-29:1041–148 55 Cook, R. J.: ‘Microwave cavity methods’, in Anderson, J. C. (ed.), Dielectrics (Chapman and Hall, London, 1964), pp. 12–27 56 Stumper, U.: ‘A TE01n cavity resonator method to determine the complex permittivity of low loss liquids at millimetre wavelengths’, The Review of Scientific Instruments, 1973;44:165 57 Cook, R. J., and Rosenberg, C. B., ‘Dielectric loss measurements on low loss polymers as a function of temperature at 9 GHz’, Proceedings of the IEE Conference on Dielectric Materials, Measurements and Applications, IEE Conference Publication No.129, Cambridge, 1975 58 Rosenberg, C. B., Hermiz, N. A., and Cook, R. J.: ‘Cavity resonator measurements of the complex permittivity of low-loss liquids’, IEE Proc. H, Microw. Opt. Antennas, 1982;129:71–6 59 Krupka, J., Geyer, R. G., Baker-Jarvis, J., and Ceremuga, J.: ‘Measurements of the complex permittivity of microwave circuit board substrates using a split dielectric resonator and re-entrant cavity techniques’, Proceedings of the Conference on Dielectric Materials, Measurements and Applications, Bath, UK, (IEE, London, 1996) 60 Krupka, J., Clarke, R. N., Rochard, O. C., and Gregory, A. P.: ‘Split-Post Dielectric Resonator technique for precise measurements of laminar dielectric specimens – measurement uncertainties’,Proceedings of the XIII International Conference MIKON’2000, Wroclaw, Poland, 2000, pp. 305–308 61 Bernard, P. A., and Gautray, J. M.: ‘Measurement of dielectric constant using a microstrip ring resonator’, IEEE Transactions on Microwave Theory Techniques, 1991; MTT-39:592–5 62 Tonkin, B. A., and Hosking,M. W.: ‘Determination of material and circuit properties using superconducting and normal metal ring resonators’, Institute of Physics conference series, Proceedings of the 3rd European Conference on Applied Superconductivity, vol. 1: Small Scale and Electronic Applications, 1997; 158:291–294 63 Amey, D. I., and Horowitz, S. J.: ‘Microwave material characterisation’, ISHM ‘96 Proceedings, SPIE 1996, Part 2920, pp. 494–499 64 Tanaka, H., and Okada, F.: ‘Precise measurements of dissipation factor in microwave printed circuit boards’, IEEE Transactions on Instrumentation and Measurement, 1989;IM-38:509–14
454 Microwave measurements 65 Roberts, S., and Von Hippel, ‘A new method for measuring dielectric constant and loss in the range of centimetre waves’, Journal of Applied Physics, 1946; 17:610–16 66 Baker-Jarvis, J.: Transmission/Reflection and short-circuit line permittivity measurements (NIST Technical Note 1341, The National Institute of Standards and Technology, Boulder, CO, 1990) 67 Baker-Jarvis, J., Vanzura, E. J., and Kissick, W. A.: ‘Improved technique for determining complex permittivity with the Transmission/Reflection method’, IEEE Transactions on Microwave Theory Techniques, 1990;MTT-38: 1096–103 68 Vanzura, E. J., Baker-Jarvis, J. R., Grosvenor, J. H., and Janezic, M. D.: ‘Intercomparison of permittivity measurements using the Transmission/ Reflection Method in 7 mm coaxial lines’, IEEE Transactions on Microwave Theory Techniques, 1994;MTT-42:2063–70 69 UTE Standard 26-295, Mesure de la permittivité et de la permeabilité de materiaux homogenes et isotropes a pertes dans le domaine des micro-ondes – Methode de mesure en guide coaxial circulaire (UTE (Union Technique de l’Electricite et de la Communication), see C26-295, France, 1999) 70 Grant, J. P., Clarke, R. N., Symm, G. T., and Spyrou, N.: ‘A critical study of the open-ended coaxial line sensor technique for RF and microwave complex permittivity measurements’, Journal of Physics E: Scientific Instruments, 1989; 22:757–70 71 Jenkins, S., Warham, A. G. P., and Clarke, R. N.: ‘Use of an open-ended coaxial line sensor with a laminar or liquid dielectric backed by a conducting plane’, IEE Proc. H, Microw. Antennas Propag., 1992;139:1792 72 Jenkins, S., Hodgetts, T. E., Symm, G. T., Warham, A. G. P., Clarke, R. N., and Preece, A. W.: ‘Comparison of three numerical treatments for the open-ended coaxial line sensor’, Electronics Letters, 1990;24:234–5 73 Gregory, A. P., Clarke, R. N., Hodgetts, T. E., and Symm, G. T.: RF and microwave dielectric measurements upon layered materials using a reflectometric coaxial sensor, NPL Report DES 125, NPL, March 1993 74 Clarke, R. N., Gregory, A. P., Hodgetts, T. E., and Symm, G. T.: ‘Improvements in coaxial sensor dielectric measurement: relevance to aqueous dielectrics and biological tissue’, in Kraszewski, A. (ed.) Microwave Aquametry – papers from the IEEE 1993 MTTS Workshop on Microwave Moisture and Water Measurement (IEEE Press, Piscataway NJ, 1996) 75 Marsland, T. P., and Evans, S.: ‘Dielectric measurements with an open-ended probe’, IEE Proc. H, Microw. Antennas Propag., 1987;134:341–9 76 Evans, S. ‘The shielded open-circuit probe for dielectric material measurements’, Proceedings of the 8th International British Electromagnetic Measurements Conference, NPL, Teddington, UK, 1997, Paper 5-2 Marsland, T. P., and Evans, S. ‘Dielectric measurements with an open-ended coaxial probe’, IEE Proc. H, Microw. Antennas Propag., 1987;134:341–9 77 Gardiol, F. E.: ‘Open-ended Waveguide: Principles and Applications’, Advances in Electronics and Electron Physics, 63:139–65
Measurement of the dielectric properties of materials 455 78 Sphicopoulos, T., Teodoridis, V., and Gardiol, F.: ‘Simple nondestructive method for the measurement of material permittivity’, Journal of Microwave Power, 1985;20:165–72 79 Sibbald, C. L., Stuchly, S. S., and Costache, G. I.: ‘Numerical analysis of waveguide apertures radiating into lossy media’, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 1992;5:259–74 80 Clarke, R. N., Gregory, A. P., Hodgetts, T. E., Symm, G. T., and Brown, N.: ‘Microwave measurements upon anisotropic dielectrics-theory and practice’, Proceedings of the 7th international British Electromagnetic Measurements Conference (BEMC), NPL, Teddington, 1995, Paper 57 81 Arai, M., Binner, J. G. P., and Cross, T. E.: ‘Estimating errors due to sample surface roughness in microwave complex permittivity measurements obtained using a coaxial probe’, Electronics Letters, 1995;31:115–17 82 Stuchly, S. S., Gajda, G., Anderson, L., and Kraszewski, A.: ‘A new sensor for dielectric measurements’, IEEE Transactions on Instrumentation and Measurement, 1986;IM-35:138–41 83 Preece, A. W., Johnson, R. H., and Murfin, J.: ‘RF penetration from electrically small hyperthermia applicators’, Physics in Medicine and Biology, 1987; 32:1591–601 84 Johnson, R. H., Pothecary, N. M., Robinson, M. P., Preece, A. W., and Railton, C. J.: ‘Simple non-invasive measurement of complex permittivity’, Electronics Letters, 1993;29:1360–1 85 Kajfez, D., and Guillon, P. (eds), Dielectric Resonators (Vector Fields, Oxford MS, 1990) 86 Krupka, J., Derzakowski, K., Abramowicz, A., Tobar, M. E., and Geyer, R. G.: ‘Whispering-gallery modes for complex permittivity measurements of ultra-low loss dielectric materials’, IEEE Transactions on Microwave Theory Techniques, 1999;MTT-47:752–9 87 Krupka, J., Blondy, P., Cros, D., Guillon, P., and Geyer, R.: ‘Whisperinggallery modes in magnetized disk samples, and their applications for permeability tensor measurements of microwave ferrites at frequencies above 20 GHz’, IEEE Transactions on Microwave Theory Techniques, 1996;MTT-44: 1097–102 88 Krupka, J., Derzakowski, K., Riddle, B., and Baker-Jarvis, J.: ‘A dielectric resonator for measurements of complex permittivity of low loss dielectric materials as a function of temperature’, Measurement Science and Technology, 9:1751–6 Krupka, J., Derzakowski, K., Abramowicz, A., et al.: ‘Bounds on permittivity calculations using the TE01δ dielectric resonator’, Proceedings of the XIV International Conference MIKON, Gdansk, Poland, 2002 89 Clarricoats, P. J. B., and Olver, A. D.: Corrugated horns for microwave antennas, IEE Electromagnetic Waves Series 18 (Peter Peregrinus on behalf of the IEE, London, 1984) 90 Wylde, R. J.: ‘Millimetre-wave Gaussian beam modes optics and corrugated feed horns’, IEE Proc. H, Microw. opt. Antennas, 1984;131:258–62
456 Microwave measurements 91 Kogelnik, H., and Li, T.: ‘Laser beams and resonators’, Proceedings of the IEEE, 1966;54:1312–29 92 LeSurf, J.: Millimetre-wave Optics, Devices and Systems (Adam Hilger, Bristol, 1990) 93 Lederer, P. G.: ‘The fundamental principles of ram reflectivity measurement’, Symposium on the Measurement of Reflectivity of Microwave Absorbers (DRA now QinetiQ), Malvern, February 1993) 94 Qureshi, W. M. A., Hill, L. D., Scott M., and Lewis, R. A.: ‘Use of a Gaussian beam range and reflectivity arch for characterisation of radome panels for a naval application’, Proceedings of the International Conference on Antennas and Propagation (ICAP), University of Exeter (IEE, 2003) 95 Cook, R. J., and Rosenberg, C. B.: ‘Measurements of the complex refractive index of isotropic and anisotropic materials at 35 GHz using a free-space microwave bridge’, Journal of Physics D: Applied Physics, 1979;12:1643–52 96 Cook, R. J.: The propagation of plane waves through a lamella, NPL Report DES 52, August 1979 97 Campbell, C. K.: ‘Free space permittivity measurements on dielectric materials at millimetre wavelengths’, IEEE Transactions on Instrumentation and Measurement, 1978;IM-27:54–8 98 Shimabukuro, F. I., Lazar, S., Chernick, M. R., and Dyson, H. B.: ‘A quasioptical method for determining the complex permittivity of materials’, IEEE Transactions on Microwave Theory Techniques, 1984;MTT-32:659–65, 1504 99 Gagnon, N., Shaker, J., Berini, P., Roy, L., and Petosa, A.: ‘Material characterization using a quasi-optical measurement system’, IEEE Transactions on Instrumentation and Measurement, 2003;IM-52:333–6 100 Li, S., Akyel, C., and Bosisio, R. G.: ‘Precise calculations and measurement on the complex dielectric constant of lossy materials using TM010 perturbation techniques’, IEEE Transactions on Microwave Theory Techniques, 1981; MTT-29:1041–148 101 Parkash, A., and Mansingh, A.: ‘Measurement of dielectric parameters at microwave frequencies by cavity-perturbation technique’, IEEE Transactions on Microwave Theory Techniques, 1979;MTT-27:791–5 102 Clarke, R. N., and Rosenberg, C. B.: ‘Fabry-Perot and open-resonators at microwave and millimetre-wave frequencies, 2–300 GHz’, Journal of Physics E: Scientific Instruments, 1982;15:9–24 103 Vaughn, J. M.: The Fabry-Perot Interferometer – history, practice and applications, Adam Hilger series on optics and optoelectronics (Adam Hilger, Bristol, 1989) 104 Jones, R. G.: ‘The measurement of dielectric anisotropy using a microwave open-resonator’, Journal of Physics D: Applied Physics, 1976;9:819–27 105 Cullen, A. L., and Yu, P. K.: ‘The accurate measurement of permittivity by means of an open-resonator’, Proceedings of the Royal Society of London, Series A, 1971;325:493–509 106 Jones, R. G.: ‘Precise dielectric measurements at 35 GHz using a microwave open-resonator’, Proc. Inst. Electr. Eng., 1976;123:285–90
Measurement of the dielectric properties of materials 457 107 Lynch, A. C., and Clarke, R. N.: ‘Open-resonators: improvement of confidence in measurement of loss’, IEE Proc. A Sci. Meas. Technol., 1992;139:221–5 108 Heidinger, R., Schwab, R., Königer, F., and Parker, T. J. (ed.): ‘A fast sweepable broad-band system for dielectric measurements at 90-100 GHz’, Twenty-third International Conference on Infrared and Millimeter Waves, Colchester, UK, 1998, pp. 353–4 Heidinger, R., Dammertz, G., Meiera, A., and Thumm, M. K.: ‘CVD diamond windows studied with low- and high-power millimeter waves’, IEEE Transactions on Plasma Science, 2002;PS-30:800–7 Danilov, I., and Heidinger, R.: ‘New approach for open resonator analysis for dielectric measurements at mm-wavelengths’, Journal of the European Ceramic Society, 2003;23 (14):2623–6 109 van Germert, M. J. C.: ‘Evaluation of dielectric permittivity and conductivity by time domain spectroscopy. Mathematical analysis of Felner-Feldegg’s thin cell method’, Journal of Chemical Physics, 1974;60:3963–74 110 van Germert, M. J. C.: ‘Multiple reflection time domain spectroscopy ii. a lumped element approach leading to an analytical solution for the complex permittivity’, Journal of Chemical Physics, 1975;62:2720–6 111 Feldman,Y., Andrianov, A., Polygalov, E. et al.: ‘Time domain dielectric spectroscopy’, Review of Scientific Instruments, 1996;67:3208–15 112 Berberian, J. G., and King, E. ‘An overview of time domain spectroscopy’, Journal of Non-Crystalline Solids, 2002;305:10–18 113 Baker-Jarvis, J.: Transmission/Reflection and short-circuit line permittivity measurements (NIST Technical Note 1341, National Institute of Standards and Technology, Boulder, CO, 1990)
Chapter 19
Calibration of ELF to UHF wire antennas, primarily for EMC testing M. J. Alexander
19.1
Introduction
Wire antennas such as monopoles, biconical and log-periodic dipole array (LPDA) antennas are used for electromagnetic compatibility (EMC) testing, and typically, cover the frequency ranges 1 kHz to 30 MHz, 30–300 MHz and 200 MHz to 2 GHz, respectively. The primary parameter of interest is the maximum gain. EMC implies that the radiated emission from a product does not impair the performance of a ‘victim’ product, so that, for example, a radio and television set will operate satisfactorily when placed next to each other. It is useful to know the strength of the E-field that one product is ‘bathing’ the other product in. For this reason the antenna gain is given in terms of antenna factor (AF) which enables a direct conversion to E-field magnitude. Uncertainties for EMC-radiated emission measurements tend to be of several decibels; therefore, the AF data are generally not needed to uncertainties better than ±0.5 dB. The antenna return loss is usually measured during the calibration of AF so that the mismatch uncertainty of the receiver reading during an EMC test can be estimated. Above 30 MHz, EMC measurements are made with the antenna both vertically and horizontally polarised so the cross-polar discrimination of the antenna is required as a component of the uncertainty budget. EMC measurements below 1 GHz are made over conducting ground planes or in free-space environments, either outdoors or in an anechoic chamber, whose imperfections will be ‘seen’ according to the directivity of the antenna, so knowledge of the radiation pattern is necessary. Monopole- and dipolelike antennas, including biconicals, have an omni-directional pattern in the H-plane which means that they are equally sensitive to E-fields arising from reflections in every direction about the H-plane. Below about 200 MHz it is difficult to achieve good free-space conditions in a fully lined anechoic chamber so measurements are
460 Microwave measurements generally made over a ground plane. The reflection from a good quality ground plane can be accurately calculated and taken into account when deriving AF from the measured coupling between two or more antennas. However, the presence of a metal plane in proximity to the antenna can also alter the AF from its free-space value because the antenna will couple with its own image in the ground plane. Knowledge of this alteration can be used to correct the antenna output voltage, or more commonly, to estimate its uncertainty. An EMC measurement is made at a specified distance from the product under test, so in order for an LPDA antenna to remain at a fixed location, it is necessary to correct the receiver reading for the variation of the LPDA phase centre with frequency. This chapter covers the following topics: overview of traceability of E-field strength, measurement of free-space AFs, measurement of AFs over a ground plane, measurement of radiation pattern, cross-polar response, phase centre, balun imbalance and return loss.
19.2
Traceability of E-field strength
The units of E-field strength are volts per metre. The volt is traceable to the Josephson Junction and DC voltage can routinely be measured to an uncertainty of two parts in 107 . The metre is traceable to the wavelength of a helium–neon laser and is routinely measurable to an uncertainty of one part in 107 . To measure electric field, a sensor (e.g. an antenna) is placed in the field and a reading is obtained in volts, or more usually a power reading in watts, which can be converted into volts knowing the impedance characteristics of the transmission line. With the present state-of-the-art, field strength can be measured with wire antennas to an uncertainty of only about two parts in 102 , which is equivalent to 0.17 dB. Four methods, claimed to give traceability of field strength for the purpose of calibrating antennas or field probes, are all based on formulas that derive from Maxwell’s equations. A simplified treatment will be given here to show the principles. This is followed by a typical uncertainty budget for field strength in an EMC-radiated emission measurement. A big advantage of the methods described in Sections 19.2.2 and 19.2.3 is that the quantity measured is attenuation, which can be measured to an uncertainty of better than ±0.01 dB.
19.2.1 High feed impedance half wave dipole The first method is to place a half wave dipole in the field and measure the voltage at the feed point of the dipole. The open circuit voltage is related to the E-field and wavelength, λ, by the following formula: π E = Voc · (19.1) λ This can be realised in practice by placing a diode at the dipole feed point and measuring the rectified voltage [1]. It is necessary to calibrate the rectifying circuit by using an RF signal of known power level. The larger part of the uncertainty lies
Calibration of ELF to UHF wire antennas, primarily for EMC testing 461 in this calibration. Standards Laboratories can measure power in the VHF and UHF ranges to an uncertainty of around ±1.5 per cent. Reference [1] has a refinement on the above formula, which takes into account the diameter of the dipole. Advantages of this method are its simplicity in concept and the fact that the high feed impedance of the dipole makes it insensitive to coupling with its image in a ground plane. Disadvantages are the loss of frequency selectivity and therefore reception of all fields present, and the need for high field levels to generate sufficient voltage, which are not permitted by the broadcasting regulators in some countries. A further disadvantage is that the combined uncertainty is higher than for the methods described in Sections 19.2.2 and 19.2.3.
19.2.2 Three-antenna method The three-antenna method [2] uses the Friis formula to relate the insertion loss between two antennas to the product of their gains: 0001 0002 λ 2 PR = PT GT GR (19.2) 4πR where PR and PT are the powers received and transmitted, and GR and GT are the gains of the receive and transmit antennas. R is the separation distance between the antennas and λ is the wavelength, both in the same unit. Uncertainties of gain as low as ±0.04 dB can be obtained [3] using the threeantenna method if the antennas have relatively high gain, for example, 20 dB standard gain horn antennas. This is possible because the high-directivity horns will radiate only a small amount of power away from the main beam, so reflections from the surroundings will be low, combined with affordable low-reflectivity absorber. This is a popular method for measuring the gain of EMC horn antennas to 40 GHz. If the extrapolation method is used, the strength of the launched E-field can be calculated at any given distance from the antenna for a known RF power into the antenna. The insertion loss (ohmic) of the antenna must be known, and this together with power is the main component of uncertainty. By the principle of reciprocity an unknown incident E-field can be found by measuring the output power of the antenna. Realised gain, G, which includes mismatch into 50 0003, can be converted to AF, using the following equation: AF2 =
4π ZF Gλ2 Z0
(19.3)
where λ is the wavelength, ZF is free-space impedance (approximately 377 0003) and Z0 is the characteristic impedance of the antenna input transmission line, commonly 50 0003. The three-antenna method is also a very accurate method for measuring the AF of dipole antennas providing the ground plane is sufficiently large and flat. A straightforward formula [4] can be used for removing the ground reflected ray, provided the antennas are in each other’s far-field – for dipoles a separation of three wavelengths is sufficient for an uncertainty of better than ±0.15 dB to be achieved [5].
462 Microwave measurements It must be borne in mind that the measured AF applies for that height above a ground plane, that is, it includes the effects of coupling with its image; also the measurement uncertainties are generally greater for vertical polarisation because of reflections from structures such as the vertically dropping feed cable and the antenna mast. In addition to this, vertical polarisation is associated with greater sensitivity to site effects, such as edge diffraction (i.e. reflections from the edges of the ground plane).
19.2.3 Calculability of coupling between two resonant dipole antennas The third method involves comparing the measured and calculated insertion loss between two antennas [6]. This method is useful for dipole antennas that have uniform H-plane patterns and for which it is difficult to avoid reflections from the surroundings. By configuring the antennas over a large flat ground plane outdoors this ensures one electromagnetically well-defined source of reflection and an upper hemisphere with no reflections. Using method of moments code [7], it is possible to predict the measured insertion loss between two wire antennas above a ground plane to an uncertainty of less than ±0.3 dB, and hence AF to less than ±0.15 dB [8]. This includes the effect of mutual coupling of the antenna to its image in the ground plane, which for normal usage of EMC antennas can alter the gain by as much as 100 per cent.
19.2.4 Calculable field in a transverse electromagnetic (TEM) cell The fourth method of providing traceability for field strength is to deduce the field between the two conductors of a transmission line from the power input to the line. A TEM cell [9] is a coaxial line with an expanded cross section. Provided the characteristic impedance, Z0 , of the line is preserved with change in cross section, it is possible to achieve uncertainties better than 0.3 dB (3.5 per cent) in the E-field strength between the plates of the TEM cell [10]. A TEM cell is useful for the calibration of field probes at frequencies below 1 GHz. The field strength E (V m–1 ) is given from the power input to the cell P (Watt) and the plate separation b (metre) by the following formula: √ PZ0 (19.4) E= b For best accuracy the probe being tested should be electrically small to reduce coupling with the sidewalls, and it should occupy a relatively small volume within the cell so that the TEM wave is perturbed as little as possible.
19.2.5 Uncertainty budget for EMC-radiated E-field emission A statement of uncertainties implies traceability to national standards. In order for measurements to have a common meaning, and to support trade, within and across national boundaries, it is necessary that they are traceable to national standards. In turn, national standards laboratories take part in international intercomparisons to ensure that they are in step with the rest of the world [11]. Traceability of measurements in industry is assisted by the accreditation of test and calibration laboratories.
Calibration of ELF to UHF wire antennas, primarily for EMC testing 463 For this purpose Accreditation Bodies are set up whose job is twofold, first to ensure traceability of physical parameters and second to ensure that laboratories have a Quality System in place which ensures that the laboratory is able to deliver the traceability to the uncertainty which it claims it is capable of, and that this has been verified by appointed technical experts. The magnitude of uncertainty commonly used is the Standard Uncertainty multiplied by a coverage factor of k = 2, providing a level of confidence of approximately 95 per cent. An EMC radiated emission test often involves a product with power and data cables that make it difficult to get a reproducible result, giving rise to large uncertainties, of the order of ±10 dB. However the uncertainty contributions from the measuring site and equipment can be minimised, for example, uncertainties associated with the antenna can be quantified. Typical uncertainty components are listed in Table 19.1. Just because EMC uncertainties are very large compared with uncertainties for other physical parameters, such as voltage, does not mean that the evaluation of EMC uncertainties is pointless. Indeed the process of setting up an uncertainty budget highlights the largest components and directs the effort to reducing these. Table 19.1 shows a budget comprising the main components that could affect the E-field magnitude measured during emission testing using either a biconical antenna or a LPDA antenna. For AF the uncertainty is likely to be given in a certificate. If it is given to a confidence level of 95 per cent the probability distribution will be Gaussian (or Normal) with a k value of 2. If the specification of the instrument does not refer to a standard uncertainty one has to assume that the measurement could lie anywhere within the specified accuracy limits, and without further information about the distribution of repeated results this is assumed to correspond to a rectangular distribution. The method by which uncertainty components with different probability distributions are summed is given in the ISO Guide [12]. However this Guide is comprehensive and can be a challenge on first reading. It has been presented in a more amenable form [13] for the subject of EMC. The fourth component in Table 19.1 relates to antenna directivity, which is relative to a tuned dipole stipulated by CISPR 16-1-4:2004. Varying the height of the receive antenna over a ground plane means there are two ray paths between the equipment under test (EUT) and the antenna which diverge from the bore sight direction. For a biconical antenna the error is for vertical polarisation only, it being zero for horizontal polarisation because the H-plane directivity is uniform. The error is positive because it represents only loss of signal. The 12th component, site imperfections, relates to normalised site attenuation (NSA) performance. Simply put, this term indicates how close the test site is to an ideal environment. Since the site is only required to meet a criterion of NSA within ±4 dB of the theoretical value, strictly the value of this uncertainty component should be ±4 dB. However, it has been set to ±1 dB because this is the intention in Annex F of CISPR 16-1-4:2004 [14] and because good sites are likely to meet ±1 dB. The last components for ambient interference and cable layout have not been given values because these vary widely from site to site and operator to operator. These two components can increase by many decibels the expanded uncertainty of ±3.8 dB in Table 19.1. Further explanation of this table can be found in Reference [13] and CISPR 16-4-2.
464 Microwave measurements Table 19.1
Uncertainty budget for emission measurements on a 3 m open area test site
Component
Probability
Uncertainty dB
distribution
Biconical
LPDA
Antenna factor calibration Cable loss calibration Receiver specification Antenna directivity
Normal (k = 2) Normal (k = 2) Rectangular Rectangular
Antenna factor variation with height Antenna phase centre variation Antenna factor frequency interpolation Antenna balun imbalance Measurement distance error ±2 cm Height of antenna above ground plane (height error ±2 cm) Height of EUT above ground plane (height error ±2 cm) Site imperfections Mismatch System repeatability Ambient interference Reproducibility of EUT/cable layout Combined standard uncertainty uc (y)
Rectangular Rectangular Rectangular Rectangular Rectangular Rectangular
±1.0 ±0.5 ±1.5 +0.5 −0 ±2 0 ±0.25 ±1.0 ±0.1 ±0.1
Rectangular
±0.05
±1.0 ±0.5 ±1.5 +2 −0 ±0.5 ±2 ±0.25 ±0 ±0.3 +1.0 −0 ±0.05
Rectangular U-shaped Normal − − Normal
±1.0 ±1.1 ±0.5 Large Poor +1.92 −1.90 ±3.8 −
±1.0 ±0.5 ±0.5 Large Poor +2.1 −1.8 +4.2 −3.6
Expanded uncertainty U
19.3
Normal (k = 2) −
Antenna factors
Ideally AF should be independent of the antenna surroundings. However, the standard method for EMC testing is to measure emission over a ground plane at a distance of 10 m from the product under test. Signal nulls are caused by destructive interference of the direct and ground-reflected ray paths between the antenna and the product. To avoid measuring in nulls the antenna is height scanned between 1 and 4 m and the maximum signal is recorded. Height scanning brings into play the effects of the radiation pattern and mutual coupling of the antenna with its image, resulting in errors of around ±2 dB (refer to Table 19.1). A widely used method for calibrating antennas is the American National Standard Institute (ANSI) procedure [15] which mimics the EMC radiated test method in that it uses the same geometry, including height scanning, to perform the three-antenna method. The product is replaced by a transmitting antenna at a fixed height of 1 or 2 m. This method will give low uncertainties for EMC testing in cases where the product
Calibration of ELF to UHF wire antennas, primarily for EMC testing 465
Figure 19.1
The 60 × 30 m ground plane at the National Physical Laboratory, Teddington, UK, whose surface is flat to within ±15 mm over 95 per cent of its area
behaves like that antenna, radiating at that fixed height, but more likely the product will radiate anywhere from the floor, via its cabling, to the top of the unit which may be more than 1 m from the ground. The height of the radiating source on the EUT varies with frequency and it is not practical to predict the height of maxima, as we do for a single antenna source during an ANSI calibration, and therefore the correct choice of receiving AF becomes an issue. A compromise would be to use an average of the receiving AF measured with the transmitting antenna at a range of heights. A study performed at NPL [17], in which the AF of a biconical antenna was both computed and measured (Figure 19.1) at a range of heights showed that the AF averaged over different heights was within ±0.5 dB of the free-space AF (AFFS ), and that the AF measured by the ANSI method on a 10 m site was also within ±0.5 dB of AFFS . There are techniques in which it is possible to measure AFFS more efficiently and more accurately than by height scanning, and in view of the good comparisons cited, AFFS is a sound basis from which to quantify antenna-related uncertainties of measurement. Furthermore AFFS is a basic property of an antenna, with no built-in mutual coupling effects. Alternative methods of performing radiated emission tests in free-space conditions are being developed, such as the fully anechoic room, in which AFFS will give the lowest uncertainties. CISPR, a sub-committee of the IEC (International Electrotechnical Commission) is defining acceptable methods of calibration of antennas that are used for EMC testing, and the methods will be described in a future issue of CISPR 16-1-5.
466 Microwave measurements
19.3.1 Measurement of free-space AFs Free-space conditions are defined as the illumination of an antenna in free-space by a plane wave, which implies that the antenna is in the far-field of the source. Antennas are often used in non-free-space conditions with the antenna above a ground plane or close to absorber lined walls and illuminated by a non-uniform field. It can be difficult to unravel these effects in order to quantify uncertainties but the best starting point is the free-space AF. Absorbing material can be very effective above 200 MHz and a relatively small amount can be used to set up free-space conditions for the calibration of LPDA antennas. With ingenuity one can set up affordable methods for measuring AFFS of dipole-like antennas below 200 MHz. These methods are outlined below. Uncertainties of ±0.5 dB can be routinely achieved for dipole, biconical and LPDA AFs [16,17].
19.3.2 The calculable dipole antenna This method gives the lowest uncertainty obtainable for AF. The calculable dipole antenna is used by National Laboratories as a primary standard antenna. The antenna comprises two thin dipole elements fed in anti-phase by a 3 dB hybrid coupler. The verification of AF of the calculable dipole is given in References [6] and [8]. The AF is calculable either for free-space conditions or with the antenna mounted above a ground plane. The dipole antenna can be used as an accurate broadband dipole using numerical methods such as NEC [7]. As mentioned in Section 19.2.3 the uncertainty in the AF, above a ground plane or in free-space is better than ±0.15 dB. The calculable dipole is especially useful in providing traceability for tuned dipole and broadband antennas, and also evaluating the quality of EMC test sites.
19.3.3 Calibration of biconical antennas in the frequency range 20–300 MHz In this frequency range, dipole-like antennas of length less than 1.5 m are fairly omnidirectional and it is not so practicable to measure free-space AF by conventional methods. This is because the antennas have to be several wavelengths away from conducting surfaces, including the ground. This implies heights of greater than 10 m if the antennas are horizontally polarised – the problem with vertical polarisation is that it is difficult to reduce reflections from the input cable to an acceptable level, also the mast is a vertical structure and will be a source of reflection. At frequencies above 300 MHz the usual solution is to line a large room with pyramidal RF absorbing material (RAM). This is not practicable at 30 MHz. Ferrite tiles of about 6 mm thickness are used to line EMC chambers but their return loss is typically less than 15 dB, whereas reflections must be less than –25 dB to measure gain to uncertainties of less than ±0.5 dB. It is possible to simulate free-space conditions without using absorber. One method is to mount the antenna vertically polarised at 2 m height above a ground plane. At this height mutual coupling to the ground image is negligible at the resonant
Calibration of ELF to UHF wire antennas, primarily for EMC testing 467 frequency (where it is most sensitive) of the biconical antenna, around 70 MHz, and below resonance the high self-impedance makes the antenna insensitive to its ground image. A sufficiently plane wave to illuminate the antenna can be set up by placing a source antenna close to the ground at a distance of around 20 m. The standard antenna method is used with the broadband calculable dipole antenna as the standard. The cable must be extended horizontally behind the antenna several metres before dropping vertically in order to reduce the effect of reflections.
19.3.4 Calibration of LPDA antennas in the frequency range 200 MHz to 5 GHz The traditional way to calibrate LPDA antennas is by the ANSI method at a distance of 10 m across a ground plane. A typical antenna for this frequency range is 0.65 m long. If the separation of the antennas is measured from their centres, the uncertainty in AF at the top and bottom frequencies is 0.3 dB due to the movement of the LPDA phase centre. Also in the UK, when limited to using the allowed transmit power, there is relatively high interference from TV transmissions. A more elegant method is to calibrate the antennas at fixed heights above RAM. If the phase centre is known at each frequency the separation can be reduced, overcoming ambient signals and reducing the amount of RAM required. Phase centre can be found in a variety of ways. The methods used at NPL are (1) from the mechanical dimensions of LPDA elements, (2) from measurement of signal phase as the antenna is rotated in free-space and (3) using NEC modelling. The results agree well and phase centre is typically known to better than ±1 cm. NPL uses a mid-antenna separation of 2.5 m which allows an uncertainty in AF of ±0.5 dB to be achieved. The same method is used for conical log spiral antennas to an uncertainty of ±1 dB.
19.3.5 Calibration of hybrid antennas A conical-hybrid antenna is a physical combination of a biconical antenna and a log antenna into one antenna with a typical frequency range of 26 MHz to 2 GHz. At NPL these are calibrated to uncertainties of less than ±0.7 dB using the two methods described in Sections 19.3.3 and 19.3.4. The AF data are ‘sewn’ together within the frequency overlap. One reason that the uncertainty is higher than ±0.5 dB is that the phase centre at frequencies in the region between the ‘biconical element’ and the longest log-periodic element is only estimated by linear interpolation. Another reason is that hybrid antennas can be very large and day-to-day alignment on the mast is not so precise as for the smaller LPDA.
19.3.6 Calibration of rod antennas Rod antennas are conventionally calibrated by replacing the monopole element with a capacitor of approximately 12 pF. This can give AF to within ±1 dB below about 15 MHz but it does not work so well above this frequency. This method might be
468 Microwave measurements suited to antenna manufacturers because they can design a power splitter jig for their own model of antenna, but it is a big overhead for a calibration laboratory to develop the right jig for all types of rod antenna. Because this method is essentially a substitution of the real element there are some important aspects in the construction of the calibration jig, which may lead to incorrect AF values if wrongly done ([17], Section 9.10). NPL’s principal method involves placing the rod antenna with its base on a large (60 × 30 m) ground plane and illuminating it with a source 20 m away. The standard antenna method is used. The standard is a calculable rod antenna whose AFs are calculated using NEC. Because of the difficulty with getting enough radiated signal below 10 MHz, calibrations below this frequency are done in a MEB1750 GTEM cell. The validity of using the GTEM cell was demonstrated by comparison with results obtained on the NPL ground plane. For this test a very large strip line, 2.5 m high, was built on the ground plane and the reception by a standard antenna was compared with that from the antenna under test (AUT).
19.3.7 Calibration of loop antennas Loop antennas can be calibrated in a TEM cell to uncertainties of less than ±1 dB, typically over the frequency range 20 Hz to 30 MHz. The power output of the cell is measured and used to calculate the field strength between the plates, in which the loop is immersed. The validity of using the TEM cell was demonstrated by building a standard loop whose current was measured and the generated field could therefore be calculated; the AUT was placed on a common axis in a nearby parallel plane to the transmitting loop. The magnetic AF may then be calculated by the AUT response in the known field.
19.3.8 Other antenna characteristics There are undesirable characteristics of antennas that can cause a great deal of trouble to practicing engineers. A Measurement Good Practice Guide [17] identifies the main problems and gives guidance on how to deal with them and more generally gives tips on calibrating antennas. This section deals with baluns, cross polar discrimination and breakdown of RF connection in antenna elements. 19.3.8.1 Balun imbalance In the early stages of establishing a calibration service NPL discovered that some models of popularly used biconical antennas had severe balun imbalance. All one had to do was to invert the vertically polarised antenna and get a change in received signal of ±5 dB. The cause was imbalance of the balun which set up common mode currents on the cable, which radiated and interfered with the antenna. The effect is related to the size of current and the proximity of the vertically hanging cable to the vertically polarised antenna elements. Since the 1970s engineers have noticed problems with the reproducibility of readings for certain models of antenna. A substantial literature including this topic has been spawned, giving advice on the orientation of the antenna, the layout of
Calibration of ELF to UHF wire antennas, primarily for EMC testing 469 cables and the use of ferrites to suppress braid currents. Balun imbalance has been the cause of many man-days of wasted effort at many test sites, particularly with site validation. Putting ferrite toroids on the cable close to the antenna input can make some improvement, but alternative proprietary models of antenna that do not have this problem are readily available. The majority of dipole-like antennas pass the test in CISPR 16-1-4 with a balance of better than ±0.5 dB. Text has been included in clause 4.4.2 of CISPR 16-1-4, which describes the measurement of balun imbalance and imposes a limit on the magnitude of the imbalance allowed. 19.3.8.2 Cross-polar performance The following text has been included in clause 4.4.3 of CISPR 16-1-4: When an antenna is placed in a plane-polarised electromagnetic field, the terminal voltage when the antenna and field are cross-polarised shall be at least 20 dB below the terminal voltage when they are co-polarised. It is intended that this test apply to LPDA antennas for which the two halves of each dipole are in echelon. The majority of testing with such antennas is above 200 MHz, but the requirement applies below 200 MHz. This test is not intended for in-line dipole and biconical antennas because a cross-polar rejection greater than 20 dB is intrinsic to their symmetrical design. Such antennas, and horn antennas, must have a cross-polar rejection greater than 20 dB; a type test by the manufacturer should confirm this.
19.3.8.3 Mechanical construction of antennas Some models of antenna have given poor repeatability of measured signal because of mechanical defects. The most common one is breakdown of RF contact between the elements on a log antenna and the transmission line they are screwed to. This can be caused by a build-up of metal oxide in the joint or simply a loose joint. 19.3.8.4 Return loss It is assumed that the calibration of an antenna includes the measurement of return loss, with the antenna mounted in free-space conditions. This enables the operator to calculate the mismatch uncertainties of the emission result.
19.4
Electro-optic sensors and traceability of fields in TEM cells
There are two fundamental methods that are used to provide traceability for E-field strength. One is to use a calculable dipole to measure (or set up) the field, and the other is to generate the field in a TEM waveguide from a known input power. An electro-optic field sensor is an ideal device to make an intercomparison between the two methods because of its small size, high sensitivity. It is also non-intrusive to the field because of minimal use of metal parts and the use of an optical fibre to feed it. The field in a TEM cell is calculable at frequencies below the resonant frequency of the first higher-order mode. The uncertainties of the field at the centre of the cell arise from measurements of the insertion loss from the input to the centre of the cell,
470 Microwave measurements the input power, the impedance of the (loaded) cell at the centre compared with the design impedance, and the effect on the field of placing the field sensor or other object at the centre of the cell. The onset of resonance dictates the maximum frequency of the cell, which is inversely proportional to the size of the cell. A cell that operates up to 1 GHz is small (of the order of 0.1 m). Such a cell has been developed at Physikalisch-Technischen Bundesanstalt (PTB) as a standard to calibrate small field probes [10] which in turn provide traceability for larger antennas. NPL investigated the calibration of a TEM cell by using a transfer standard to trace the field strength to the calculable dipole [18]. The calculable dipole has a length of half a wavelength and by definition cannot fit between the plates of a cell. Also the current design is fed by a coaxial cable and this would cause uncertainties when inserting the dipole into the cell. The electro-optic transfer standard is a short dipole embedded in a lithium niobate crystal fed by optical fibres. An agreement of less than ±0.3 dB has been demonstrated between the field measured by a calculable dipole antenna and the field in a TEM cell. This should enable commercial field probes to be calibrated in TEM cells with uncertainties of less than ±0.5 dB.
Acknowledgements Acknowledgements are due to the National Measurement System Policy Unit of the DTI for funding this work through several Electrical Programmes, and to staff of the RF & Microwave Group who contributed to the developments.
References 1 Camell, D. G., Larsen, E. B., and Ansen, W. J.: ‘NBS calibration procedures for horizontal dipole antennas’, International Symposium on Electromagnetic Compatibility, Seattle, 1988, pp. 390–394 2 IEEE Standard Test Procedures for Antennas, ANSI/IEEE Std 149-1979 3 Gentle, D. G., Beardmore, A., Achkar, J., Park, J., MacReynolds, K. and de Vreede, J.P.M.: CCEM Key Comparison RF-K3.F, Measurement Techniques and Results of an Intercomparison of Horn Antenna Gain in IEC-R 320 at 26.5, 33.0 and 40.0 GHz, NPL Report CETM 46, Sep 2003. Search for ‘RF-K3.F’ at http://kcdb.bipm.org/ appendixB/KCDB_ApB_search.asp [Accessed 2007] 4 Smith, A. A.: ‘Standard-site method for determining antenna factors’, IEEE Transactions on Electromagnetic Compatibility, 1982;24:316–22 5 Morioka, T., and Komiyama, K.: ‘Measurement of antenna characteristics above different conducting planes’, IEEE Transactions on Instrumentation and Measurement, 2001;50 (2):393–6 6 Alexander, M. J., and Salter, M. J.: ‘Low measurement uncertainties in the frequency range 30 MHz to 1 GHz using a calculable standard dipole antenna and national reference ground plane’, IEE Prococeedings-Science, Measurement and Technology, 1996;143 (4):221–8
Calibration of ELF to UHF wire antennas, primarily for EMC testing 471 7 Logan, J. C., and Burke, A. J.: Numerical Electromagnetic Code (Naval Oceans Systems Centre, CA, USA, 1981) 8 Alexander, M. J., Salter, M. J., Loader, B. G., and Knight, D. A.: ‘Broadband calculable dipole reference antennas’, IEEE Transactions on Electromagnetic Compatibility, 2002;44 (1):45–58 9 Crawford, M. L.: ‘Generation of standard EM fields using TEM transmission cells’, IEEE Transactions on Electromagnetic Compatibility, 1974;16 (4): 189–95 10 Münter, K., Pape, R., and Glimm, J.: ‘Portable E-field strength meter system and its traceable calibration up to 1 GHz using a µGTEM cell’, Conference of Precision Electromagnetic Measurements, Braunschweig, 1996, pp. 443–444 11 Alexander, M.: ‘International comparison CCEM.RF-K7.b.F of antenna factors in the frequency range 30 MHz to 1 GHz’, Metrologia, 2002;39:309–17 12 Guide to the Expression of Uncertainty in Measurement. International Organisation for Standardisation, Geneva, Switzerland, 1993 13 The Treatment of Uncertainty in EMC Measurements, LAB34, UKAS, April 2002 (update on NIS81 May 1994) 14 CISPR publication 16. Specification for Radio Disturbance and Immunity Measuring Apparatus and Methods, Part 1-4:2004 Apparatus, Part 160-2-3:2004 Methods, Central office of the IEC, 3 rue de Varembé, Geneva, Switzerland 15 ANSI C63.5:2004. Calibration of antennas used for radiated emissions measurements in electromagnetic interference (EMI) control 16 Alexander, M. J.: ‘The measurement and use of free-space antenna factors in EMC applications’, Proceedings of 13th International Symposium on Electromagnetic Compatibility, Zurich, 1999, paper F6 17 Alexander, M.J., Salter, M.J., Gentle, D.G., Knight, D.A., Loader, B.G., Holland, K.P.: Measurement Good Practice Guide No. 73: Calibration and use of Antennas Focusing on EMC applications, Dec 2004. www.npl.co.uk/publications 18 Loh, T.H., Loader, B., Alexander, M.: ‘Comparison of electric field strentgh at VHF frequencies generated by dipoles and TEM cells’, 18th International Zuric symposium on EMC, Sep 2007
Index
AFs (antenna factors) 464–9 about AFs 459, 464–5 ANSI procedure 464 and Balun imbalance 468–9 biconical antenna measurements 466–7 calculable dipole antenna method 466 CISPR acceptable calibration methods 465 and cross-polar performance 469 free-space measurement 466 hybrid antenna calibration 467 loop antennas calibration 568 LPDA antenna calibration 467 National Physical Laboratory (UK) ground plane 465 and return loss 469 rod antenna calibration 467 see also E-field strength traceability; EMC (electromagnetic compatibility) measurement/testing air lines (precision air-dielectric coaxial transmission lines) 188–93 about air lines 188–9 characteristic impedance 190–1 conductor imperfections 192–3 fully supported air lines 190 partially supported air lines 189–90 phase change 191–2 RF impedance 194–8 lossless lines 194–5 lossy lines 195–8 propagation constant 197 skin depth issues 192–3 standards 190–2 unsupported air lines 189
amplitude modulation measurement, with spectrum analysers 383–4 antenna factors: see AFs (antenna factors) attenuation measurement about attenuation measurement 91 basic principles 91–3 calibration standards 116 definition of attenuation 91–2 detector linearity 112–14 measurement uncertainty budget 114 insertion loss 91–3 mismatch error/uncertainty 92–3, 110–12 two-resistor power splitter 111–12 repeatability 115–16 RF leakage 112–13 stability and drift 115 system noise 115 system resolution 115 attenuation measurement systems AF substitution method 104–5 automatic network analyser 108–10 vector network analyser 108–9 IF substitution method 105–7 piston attenuator 105–6 inductive voltage divider 98–104 attenuation 98 automated system 99–100 commercial attenuation calibrator 102–3 construction 98 dual channel system 101 error 99 gauge block system 100 IFR 2309 FFT signal analyser 103–4
474 Index attenuation measurement systems (Cont.) power ratio method 94–7 power sensor linearity problem 94–5 range switching/resolution problem 95–7 signal generator amplitude drift problem 94 zero carry over problem 95 RF substitution method 107–8 rotary vane attenuator 107–8 voltage ratio method 97–8 attenuation measurement worked example, 30db attenuation 116–19 contributions to uncertainty, Type A random uncertainty 117 detector linearity 117 leakage 117 power meter resolution 117 uncertainty spreadsheet 118 automatic network analysers (ANAs) 108–10, 425–6 see also calibration of automatic network analysers; network analysers; one-port devices/error models; scalar network analysers; TRL calibration; two-port error model for measurement; vector network analysers (VNAs); verification of automatic network analysers avalanche diode noise sources 163–4 balanced device characterisation 305–28 about balanced device characterisation 305–7, 309–10 about balanced and unbalanced systems 305–6 conversion parameters 310 de-embedding 326–8 differential structure issues 306–9 differential through connection example 321–6 Far End Crosstalk (FEXT) measurements 320 ideal devices 307–8 mixed-mode-S-parameter-matrix 318–19 modal decomposition method 312–18 Near End Crosstalk (NEXT) measurements 320 real devices 307–10 SAW-filter measurement example 326–7 self parameters 310
single-ended to balanced device characterisation 319–20 typical measurements 320–1 using network analysis 310 using physical transformers 310–11 virtual ideal transformers 311 Balun imbalance 468–9 Bessel zero method/Bessel nulls 385–6 biconical wire atennas, with EMC testing 459, 467 bolometers 333–4 and microbolometers 249 Boltzmann’s constant 159 calibration of automatic network analysers 263–89 about calibration 263 see also network analysers; one-port devices/error models; scalar network analysers; TRL calibration; two-port error model for measurement; vector network analysers (VNAs) calorimeters 334–6 cascaded receivers, noise 169 cascade matrix, S-parameter matrix 27–8 Cavity cell 443 Central Limit Theorem 46, 50–1 characterisation: see balanced device characterisation characteristic impedance measurement 35–6 non-TEM waveguides 33–5 one-port devices 21–2 real and imaginary parts 32–3 and S-parameter measurements 30–6 transmission lines, with losses 30–3 transmission lines, no losses 4 coaxial air lines historical perspective 181 see also air lines (precision air-dielectric coaxial transmission lines) coaxial connectors 59–90 about coaxial connectors 59–60, 66 airline handling 61 bead resonances 188 buffer adapters 65 cleaning 63–4 normal procedure 64 static sensitive devices 64 connector recession 65–6 connector savers 65
Index 475 dial gauges and test pieces 87–8 calibrating 87 gauge calibration blocks 88 measurement resolution 87–8 push on/screw on types 87 electrical characteristics 187–8 frequency ranges of common types 66–7, 188 future developments 200 gauging connectors 62–3 higher-order mode resonances 188 historical perspective 180–1 insertion loss repeatability for connector pairs 85 life expectancy 65 line sizes 60 repeatability issues 61–2 specifications 62 torque wrench setting values 86 ‘Traceability to National Standards’ 59 coaxial connector types 1.0 mm (Agilent W) connector 82–5 1.85 mm (V™ ) connector 81–2 2.4 mm (Type Q) connector 80–1 2.92 mm K connector 79–81 3.5 mm connector 77–9 7/16 connector 73–6, 201 7 mm precision connector 68–71 connection procedure 68–70 disconnection procedure 71 14 mm precision connector 66–8 compatibility possibilities 185–6 electrical discontinuities from 186 GPCs (general precision connectors) 60, 185 line diameters summary 186 LPCs (laboratory precision connectors) 60, 185 mechanical characteristics 185–7 N 7 mm connectors (rugged) 71–4 dimensions chart 74 gauging type N connectors 73 precision/non precision 183–5 sexed connectors 183 sexless (hermaphroditic) connectors 60, 182–3 SMA connectors 76–8 dimensions chart 78 coaxial lines structures and properties 148–50 applications 149–50
dispersion characteristics 149 complex refractive index 412 complex relative magnetic permeability 412 connectors: see air lines (precision air-dielectric coaxial transmission lines); coaxial connectors conversion parameters 310 coplanar waveguides (CPW) probes 231–2 structures and properties 153–4 couplers, power measurement 343 coupling factor 209–10 Courtney Holder cell 443 Debye relaxation 419, 420, 421–2 decibels 330 delay line discriminators, for phase noise measurement 400–1 Dicke (switching) radiometer 164, 166 dielectric rod probe 249–50 dielectrics, basic concepts about dielectrics 409–10 absolute permittivity 410 basic parameters 410–13 complex refractive index 412 complex relative magnetic permeability 412 equivalent circuits 411 loss tangent 412 magnetic hysteresis 412 microradian 412 permittivity of free space 410 power absorption coefficient 413 radiation absorbing materials (RAM) 412 relative permittivity 410 dielectrics, basic measurement theory 413–17 about dielectric measurement 413 dielectric-test-set method 417 frequency-change methods 417 frequency coverage of the methods 417 length-change methods 417 lumped-impedance methods 414 admittance cells 414 cell admittance 414 lumped equivalent circuits 414 multi-pass techniques 417 Q-factor (Quality Factor) 417 resonance methods 416 cavities 416 wave methods 414–16 attenuation constant 415
476 Index dielectrics, basic measurement theory (Cont.) Fresnel’s equations 416 guided wave media 414 phase constant 415 propagation/transmission parameters 415 Scattering Parameters 414 standing-wave methods 414 travelling-wave methods 414, 416 dielectrics, loss processes 418–22 dielectric relaxation 418–22 Debye relaxation 419, 420, 421–2 interfacial polarisation 418 Kramers-Kronig relations 421–2 Maxwell-Wagner effect 418 polar/non-polar materials 418 relaxation frequency 421 rotational polarisation 418 dielectric resonance 419–20 electrical conduction/conductivity 418 non-linear processes 420 dielectrics, measurement methods about choosing a method 449 admittance methods 430–2 Hartshorn and Ward (H & W) technique 432–3 liquid dielectrics 430–1 perturbation method 433–4 resonant admittance cells 432–4 three-terminal cells 431–2 TM010 -mode cavity 434 two-terminal cells 432 Cavity cell 443 coaxial probes 439–41 coaxial transmission lines 437–9 Courtney Holder cell 443 dielectric probes 441 dielectric resonators (DRs) 442–4 free field methods 444–6 Hakki-Colemen cell 443 open-ended rectangular waveguide probes 442 open resonators 446–8 resonator perturbation technique 446 ring resonators 437 Roberts and Von Hippel method 438 split-post dielectric resonators (SPDR) 436–7 substrate methods 437 TE01 -mode cavities 434–6
time domain techniques 448 waveguide probes 440–1 dielectrics, measurement practicalities 422–30 about the need to measure 422–3 anistropic materials 424–5 automatic network analysers (ANAs) 425–6 cleanliness aspects 424 dimensions and preparation 424 ferroelectrics 425 frequency response analysers (FRAs) 426 good practices 429–30 high-permittivity dielectrics 425 hygroscopic materials 424 inhomogeneous materials 425 international standard measurement methods 422 low-loss materials 423 magnetic materials 424–5 matching method to material 423 measurement cells 426–7 medium/high-loss materials 423 Q-factor (Quality Factor) measurement 427–9 dielectric waveguide 154–5 diode power sensors 333 dispersion, waveguides 148 dispersion effect, transmission lines with losses 9–10 DMMs (digital multimeters) 122, 124–5 digitising DMMs 124–5 DVMs (digital voltmeters) 97–8 effective directivity 274, 277, 293–6 E-field strength traceability 460–4 about E-field strength 460 with electro-optic sensors 469–70 high feed impedance half wave dipole 460–1 TEM cell, calculable field 462 three-antenna method 461–2 two resonant dipole antennas, coupling calculability 462 uncertainty budget 462–4 see also AFs (antenna factors); EMC (electromagnetic compatibility) measurement/testing electrical conduction/conductivity 418 electrical sampling scanning-force microscopy 254
Index 477 electric-field probing 251–4 electron beam probing 251 electro-optic sampling 252–4 electro-optic sensors, and E-field strength traceability 469–70 EMC (electromagnetic compatibility) measurement/testing 459–70 about EMC testing 459–60 with spectrum analysers 392, 392–3 see also AFs (antenna factors); E-field strength traceability ENR (excess noise ratio) 160, 163 equivalent circuit modelling (ECM) 226–8 error term verification for two port measurements 293–300 effective directivity 293–6 effective source match 296–9 offset load/airline method 295–6 sliding load method 294–5 time domain gating 297–8 effective isolation 299 effective linearity 300 effective load match 299 time domain and de-embedding 300 transmission and reflection tracking 299–300 Far End Crosstalk (FEXT) measurements 320 fast sampling DMMs 124–5 FFTs (fast Fourier transforms) 401 finline transmission line 154 flicker noise 159 FM discriminators 404–5 free space permeability 10–11 frequency modulation analysis, with spectrum analysers 384–5 frequency response analysers (FRAs) 426 frequency spectrum 122 frequency stability/phase noise: see phase noise/frequency stability measurement Fresnel’s equations 416 gas discharge tubes 163 Gaussian distributions 46–7 probability density function 158 generalised scattering parameters 22–4 generator measurement tracking, with spectrum analysers 378–9 GPCs (general precision connectors) 160, 185
group velocity, waveguides 16 GSM pulse specification 346 GUM (Guide to the Expression of Uncertainty in Measurement) 43–52 see also uncertainty and confidence in measurements Gunn diodes 246 Hakki-Colemen cell 443 harmonic content, with voltage measurement 137–8 harmonic distortion measurement, with spectrum analysers 378 Hartshorn and Ward (H & W) technique 432–3 HEMT technology 248 hermaphroditic (non-sexed) connectors 60 see also coaxial connectors high feed impedance half wave dipole 460–1 impedance and admittance parameters 24–7 inductive voltage divider: see attenuation measurement systems insertion loss 91–3 interfacial polarisation 418 intermodulation measurement/analysis, with spectrum analysers 380–2 intrinsic impedance 11 inverse Fourier transform (IFT) 221 Josephson Junction 460 Kramers-Kronig relations 421–2 Kuhn’s rules, signal flow graphs 37 Lorentz reciprocity relation 37–8 losslessness, scattering parameters 39–40 loss tangent 412 LPCs (laboratory precision connectors) 160, 185 LPDA (log-period dipole array) antennas, with EMC testing 459–60, 467 magnetic-field probing 250–1 magnetic hysteresis 412 Maxwell’s equations 11 Maxwell-Wagner effect 418
478 Index measurement verification 301–4 about measurement verification 301 customised verification example 301–2 manufacturer supplied verification example 302–4 MEMS (Micro Electro-Mechanical Systems) 336 microbolometers 249 microradian 412 microstrip transmission lines, structures and properties 151–2 dispersion 152 microwave frequency spectrum 122 microwave network analysers: see network analysers microwave voltage measurement: see voltage measurement mismatched loads, one-port devices 20 mismatch error 92–3 mixed-mode-S-parameter-matrix 318–19 MMIC (monolithic microwave integrated circuit) (or RFIC) 217–55 about S-parameter measurement 217–18, 254–5 bolometers/microbolometers 249 cryogenic measurements 247–8 HEMT technology 248 dielectric rod probe 249–50 electric-field probing 251–4 electrical sampling scanning-force microscopy 254 electron beam probing 251 electro-optic sampling 252–4 opto-electronic sampling 252 photo-emissive sampling 252 electromagnetic field probing 249–50 magnetic-field probing 250–1 thermal measurements 246–7 Cascade Microtech Summit Evue system 247 Cascade Microtech Summit S300-863 system 246 Gunn diodes 246 MMIC/RFIC probe station measurements 230–45 about probe station measurements 230–1 advantages of probe station measurements 231 DC biasing 240–1 layout considerations 241–3
low-cost multiple DC biasing technique 243 measurement errors 240 passive microwave probe design 231–6 ACP probe (Cascade Microtech) 233–5 Picoprobe™ (GGB) 232 tapered coplanar waveguide (CPW) probes 231–2 waveguide input infinity probe 231–5 probe calibration 236–40 about probe calibration 236–8 automated probes 239–40 LRM technique 238–9 Short Open Load Reflect routine 240 SOLT technique 238 stability checking 240 TRL technique 238–9 upper-millimetre-wave measurements 243–5 MMIC/RFIC test fixture measurements 218–30 about test fixture measurements 218–20 calibration kits 219 calibration methods summary 219–20 one-tier calibration 229–30 text fixture design guidelines 230 two-tier calibration 220–8 banded VNA 221 broadband VNA 221 equivalent circuit modelling (ECM) 226–8 in-fixture calibration 225–6 synthetic-pulse TD reflectometry 221 T-D reflectometry (TDR) 221–5 time domain gating 221–5 VNA reference planes 220 modal decomposition method for characterisation 312–18 monopole wire antennas, with EMC testing 459 Near End Crosstalk (NEXT) measurements 320 network analysers 108–9, 207–16 about network analysers 207–8 block diagrams 208, 214–16 built-in signal source 209 coupling factor 209–10
Index 479 diode detectors 211–12 directional bridge 210–11 directional coupler 209–10 dynamic range 214 reference plane 208 sampler systems 213–14 signal separation hardware 209–11 tuned receivers 212–14 see also automatic network analysers (ANAs); scalar network analysers; vector network analysers network analysis characterisation 310 noise 157–64 about noise 157–8 available noise power 160 effective noise power 160 ENR (excess noise ratio) 160, 163 equivalent input noise temperature 161 flicker noise 159 Gaussian distribution probability density function 158 noise factor/figure 161–2 noise performance of receivers 161 noise temperature 162 quantum noise temperature 159 and sensitivity 157 shot noise 159 thermal noise 158–9 noise measurement 164–76 accuracy of measurement 166–71 automated measurement 174–6 noise figure meters/analysers 175 on-wafer measurements 175–6 cascaded receivers 169 correlated noise 173 Dicke (switching) radiometer 164, 166 mismatch effects/factor 171–4 noise resistance 173 passive two-ports 169–71 radiometer sensitivity 166 receivers and amplifiers 172–4 total power radiometer 164–6 uncertainties (type A and B) 167–9 noise sources 162–4 about thermal noise 162 avalanche diodes 163–4 gas discharge tubes 163 temperature-limited diodes 163 Nomographs, with spectrum analysers 383 n-port devices, scattering parameters 24–7
Omni-Spectra SMA connector/wedge-shaped board socket 228 one-port devices/error models 19–22, 273–6 characteristic impedance 21–2 effective directivity 274, 277 frequency response (tracking) error 275 mismatched loads 20 open circuit termination model 276, 278 ‘perfect load’ termination model 276 phasor notation 21 power 21–2 reflection coefficient 20–1, 273–5 short circuit termination model 276, 278 see also transmission lines opto-electronic sampling 252 oscillator phase noise performances 396–7 see also phase noise/frequency stability measurement oscilloscopes for voltage measurement 127–9 analogue 128–9 calibrator calibration 138–40 digital 128–9 sampling 129 switched input impedance 129–30 permeability of a medium 10–11 permittivity 11, 410–11 absolute permittivity 410 permittivity of free space 11, 410 relative permittivity 11, 410 phase constant/wave number 11 phase locked loops 402–3 phase noise/frequency stability measurement 395–407 about phase noise 395–6, 406–7 delay line discriminator technique 400–1 FM discriminator method 404–5 future possible methods 406 measurement uncertainty issues 405–6 oscillator phase noise performances 396–7 quadrature technique 401–3 fast Fourier transforms (FFTs) 401 phase locked loops 402–3 spectrum analyser techniques 397–9 improvement with band-pass filters 399–400 limitations 398 summary of methods 406–7 phase velocity/phase constant, lossless transmission lines 5–6
480 Index phase velocity, waveguides 15 phasor notation 21 photo-emissive sampling 252 Picoprobe™ (GGB) 232 Planck’s constant 159 plane/transverse electromagnetic (TEM) waves 10–12 polar/non-polar materials 418 power flow, sinusoidal waves, lossless transmission lines 6–7 power measurement: see RF power measurement power sensors 333–6 acoustic meters 336 calorimeters 334–6 diode sensors 333 flow calorimeters 334–6 force and field based sensors 336 MEMS (Micro Electro-Mechanical Systems) 336 microcalorimeters 334 thermistors/bolometers 333–4 thermocouples/thermoelectric sensors 333 twin load calorimeters 334 power splitters 339–43 direct method for splitter output 341–3 output match measurement 340–1 splitter properties 340 two resistor splitters 339–40 probe station measurements: see MMIC/RFIC probe station measurements pulsed modulation display/analysis 389–91 pulsed power 344–6 Q-factor (Quality Factor) measurement 417, 427–9, 443 quantum noise temperature 159 radiation absorbing materials (RAM) 412 radio frequency integrated circuit (RFIC): see MMIC radiometers: see noise measurement reciprocity 37–8 rectangular metallic waveguides: see waveguides, rectangular metallic reference plane 208 reflection coefficient lossless transmission lines 5 one-port devices 20–1
reflectometers, power measurement 343–4 return loss, lossless transmission lines 7 RF frequency spectrum 122 RFIC (radio frequency integrated circuit): see MMIC RF impedance air lines 195–8 lossless lines 194–5 lossy lines 195–8 historical perspective 181–2 terminations 198–200 mismatched terminations 199–200 near-matched terminations 199 open-circuits 198–9 short-circuits 198 RF millivoltmeters 125–6 RF power measurement 329–46 basic theory 329–32 calibration factor 332 calibration/transfer standards 338–9 couplers 343–4 direct power measurement 337 effective efficiency 332 GSM pulse specification 346 incident, reflected and delivered power 330–1 mismatch uncertainty 332 pulsed power 344–6 ratio measurements 338–9 reflectometers 343–4 substitution techniques 330 uncertainty budgets 337–8 see also power sensors; power splitters RF voltage measurement: see voltage measurement ridged waveguides 150–1 ring resonators 437 Roberts and Von Hippel method 438 rotational polarisation 418 sampling RF voltmeters 126–7 scalar network analysers 263–6 applied power level problem 269 calibration reflection measurements 267–8 transmission measurements 267 fully integrated analysers 265–6 limited dynamic range problem 269 see also network analysers; vector network analysers (VNAs)
Index 481 scattering parameters: see S-parameters (scattering parameters) self parameters 310 shot noise 159 signal flow graphs, scattering parameters 36–7 Kuhn’s rules 37 skin effect 2 slot guides, structure and properties 152–3 SMA printed circuit board socket 228 S-parameters (scattering parameters) about S-parameters 19 generalised S-parameters 22–4 impedance and admittance parameters 24–7 losslessness 39–40 measurements with MMIC/RFIC 217–18 wave methods 414 n-port devices 24–7 reciprocity 37–8 self parameters 310 signal flow graphs 36–7 two-port networks 22–4 two-port transforms 40 see also one-port devices S-parameter matrix (scattering matrix) about S-parameters 23–4 cascade matrix 27–8 de-embedding 29–30 mixed-mode-S-parameter-matrix 318 network parameter examples 26–7 renormalisation 28–9 see also characteristic impedance S-parameters equations, two-port error model 283–4 spectrum analysers, applications 376–93 amplitude modulation measurement 383–4 EMC measurements 392–3 FM demodulation 386–7 frequency modulation analysis 384–5 with Bessel zero method 385–6 generator measurement tracking 378–9 harmonic distortion measurement 378 intermodulation intercept point 382–3 intermodulation measurement/analysis 380–2 meter mode 379–80 modulation AM/FM asymmetry 387–8 nomograph usage 383 overload dangers 392–3
phase noise/frequency stability measurement 397–9 pulsed modulation display/analysis 389–91 square wave spectrum 388–9 zero span mode 378–80 spectrum analysers, facilities and use 349–59 amplitude modulation analysis 351–3 basic usage 349–50 block diagram/description 354, 356–8 harmonic mixer concept 354–5 multiple responses problem 355–6 tracking generator 358–9 tracking preselectors 356 measurement domains 350 and network analysers 207–8 oscilloscope amplitude/time display 350–2 for amplitude modulation 351–2 pre-calibration (Auto Cal) 349–50 spectrum analyser amplitude/frequency display 351 for amplitude modulation 353 spectrum analysers, specification points 359–76 about the main controls 359 amplitude accuracy 372 display detection mode 376–7 dynamic range 366–72 intermodulation and distortion 367–8 internal distortion checking 371–2 local oscillator phase noise 369–70 noise 368–9 sideband noise 370–1 input attenuator/IF gain 360 input VSWR effect 372–3 noise/low-level signals 366 residual FM 374–5 residual responses 373–4 resolution bandwidth 361–2 shape factor 362–4 sideband noise characteristics 373, 374 sweep speed/span 360–1 uncertainty contributions 375–7 video averaging 365–6 video bandwidths 365 split-post dielectric resonators (SPDR) 436–7 square wave spectrum analysis 388–9 standing waves from sinusoidal waves, lossless transmission lines 7–8 switching (Dicke) radiometer 164, 166 synthetic-pulse TD reflectometry 221
482 Index tapered coplanar waveguide (CPW) probes 231–2 TDD (time-domain duplex) techniques 396 TDMA (time-domain multiple access) techniques 396 T-D reflectometry (TDR) 221–5 error sources 223–5 Telegraphist’s equations transmission lines, lossless 3–4, 9 transmission lines with losses 9 TEM: see transverse electromagnetic (TEM) cell/waves temperature-limited diodes 163 test fixture measurements: see MMIC/RFIC test fixture measurements thermal noise 158–9 thermal voltage converters (TVCs) 122–3 thermistors/bolometers 333–4 thermocouples/thermoelectric sensors 333 three-antenna method for E-field strength 461–2 time domain and de-embedding 300 time domain gating 221–5, 297–8 transmission lines, lossless waveguides: see one-port devices; waveguides, lossless transmission lines, structures and properties 147–55 about transmission lines 147–8 coaxial lines 148–50 coplanar waveguides 153–4 dielectric waveguide 154–5 finline 154 higher mode operation 148 microstrip 151–2 rectangular waveguides 150 ridged waveguides 150–1 slot guides 152–3 waveguide dispersion 148 transmission lines, two-conductor lossless basic principles 1–4 characteristic impedance 4 equivalent circuit 1–2 phase velocity/phase constant 5–6 power flow, sinusoidal waves 6–7 reflection coefficient 5 return loss 7 skin effect 2 standing waves from sinusoidal waves 7–8 Telegraphist’s equations 3–4
Voltage Standing Wave Ratio (VSWR) 7–8 wave equations 3–4 transmission lines, two-conductor with losses basic principles 8–9 dispersion effect 9–10 equivalent circuit 8 pulses, effect on 9–10 sinusoidal waves, general solution 10 Telegraphist’s equations 9 transverse electromagnetic (TEM) cell/waves 10–12, 19, 307 calculable field 462 transverse electromagnetic (TEM) waveguides, and E-field traceability 469–70 TRL calibration 284–9 basic principles 284–6 calibration procedure 287–9 four receiver operation 286–7 isolation 286 source match/load match 286 two-port error model for measurement 279–84 error sources 279–80 leakage/isolation 281–2 S-parameters equations 283–4 ‘through’ measurement 283 transmission coefficient 280 two-port networks, generalised scattering parameters 22–4 two-port transforms, scattering parameters 40 UHF measurement uncertainty 461 uncertainty analysis, voltage measurement 136–7 uncertainty budgets, RF power measurement 337–8 uncertainty and confidence in measurements 43–57 Central Limit Theorem 46, 50–1 combined standard uncertainty 50–1 coverage factor 51–2 expanded uncertainty 51 expectation value 45 flagpole example 48–51 GUM Type A and Type B evaluations 44 imperfect matching 45 normal distributions 46, 49, 51–2 normal/Gaussian probability distributions 47
Index 483 probability distributions 45–6 and standard uncertainties 49 purpose of measurement 44 quantity (Q) in uncertainty evaluation 43 sensitivity coefficients 48, 50 standard uncertainty 44 temperature uncertainty 48 uncertainty budget 56 U-shaped distributions 47 voltage reflection coefficients (VRCs) 53 uncertainty sources in RF and microwaves 52–7 calibration of coaxial power example 54–7 uncertainty budget 56 directivity 54 RF connector repeatability 54 RF mismatch errors 52–4 test port match 54 vector network analysers (VNAs) about VNAs 108–9, 266 calibration/accuracy enhancement 269–73 correctable systematic errors 270 directivity issues 270–1 frequency response (tracking) 273 isolation (crosstalk) 273 load match 272–3 non-repeatable random and drift errors 270 source match 271–2 VNA reference planes 220–1 see also calibration of automatic network analysers; MMIC; network analysers; one-port devices/error models; two-port error model for measurement; verification of automatic network analysers vector voltmeters 127–8 verification of automatic network analysers 291–304 about verification 291–3 calibration and verification 293 definition 291 see also error term verification; measurement verification; network analysers VHF measurement uncertainty 461 virtual ideal transformers 311 voltage measurement 121–43 about RF/microwave voltage measurement 121–2
capacitive loading 132–3 digital multimeters (DMMs) 122 digitising DMMs 124–5 fast sampling DMMs 124–5 input impedance effects 130–2 oscilloscopes, analogue/digital/sampling 127–9 switched input impedance 129–30 rectifier implementation 123–4 RF millivoltmeters 125–6 sampling RF voltmeters 126–7 source loading and bandwidth 132–3 thermal voltage converters (TVCs) 122–3 traceability 133–5 with micropotentiometers 134–5 with thermal converters 133–4 vector voltmeters 127–8 voltage standing wave ratio (VSWR) 129–31 wideband AC voltmeters 122–4 voltage measurement impedance matching/mismatch errors 135–43 about impedance matching/mismatch 135–6 harmonic content errors 137–8 oscilloscope calibration example 138–41 RF millivoltmeter calibration 140–3 uncertainty analysis considerations 136–7 oscilloscope bandwidth test example 137 VSWR issues 136 VSWR (voltage standing wave ratio) impedance matching issues 136 lossless transmission lines 7–8 oscilloscope voltage measurement 129–31 wave equations 3–4 waveguide, dielectric 154–5 waveguide dispersion 148 waveguide input infinity probe 231–5 waveguides, coplanar, structures and properties 153–4 waveguides, lossless 10–12 intrinsic impedance 11 permeability 10–11 phase constant/wave number 11 plane/transverse electromagnetic (TEM) waves 10–12 waveguides, rectangular metallic 12–17, 150 about rectangular waveguides 12–14
484 Index applications 150 cut-off frequency and wavelength 14–15, 17 general solution 16–17 group velocity 16 phase velocity 15 plane waves in 12–13
properties 150 reflection within 12–13 wave impedance 15–16 waveguides, ridged 150–1 wave impedance, waveguides 15–16 wave number 11 wideband AC voltmeters 122–4
Microwave Measurements 3rd Edition
Other volumes in this series: Volume 4 Volume 5 Volume 7 Volume 8 Volume 9 Volume 11
The current comparator W.J.M. Moore and P.N. Miljanic Principles of microwave measurements G.H. Bryant Radio frequency and microwave power measurement A.E. Fantom A handbook for EMC testing and measurement D. Morgan Microwave circuit theory and foundations of microwave metrology G. Engen Digital and analogue instrumentation: testing and measurement N. Kularatna
Microwave Measurements 3rd Edition Edited by R.J. Collier and A.D. Skinner
The Institution of Engineering and Technology
Published by The Institution of Engineering and Technology, London, United Kingdom © 1985, 1989 Peter Peregrinus Ltd © 2007 The Institution of Engineering and Technology First published 1985 (0 86341 048 0) Second edition 1989 (0 86341 184 3) Third edition 2007 (978 0 86341 735 1) This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted, in any form or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Inquiries concerning reproduction outside those terms should be sent to the publishers at the undermentioned address: The Institution of Engineering and Technology Michael Faraday House Six Hills Way, Stevenage Herts, SG1 2AY, United Kingdom www.theiet.org While the authors and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgement when making use of them. Neither the authors nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral rights of the author to be identified as author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
British Library Cataloguing in Publication Data Microwave measurements. – 3rd ed. 1. Microwave measurements I. Collier, Richard II. Skinner, Douglas III. Institution of Engineering and Technology 621.3’813 ISBN 978-0-86341-735-1
Typeset in India by Newgen Imaging Systems (P) Ltd, Chennai Printed in the UK by Athenaeum Press Ltd, Gateshead, Tyne & Wear
Contents
List of contributors Preface 1
Transmission lines – basic principles R. J. Collier
1
1.1 1.2
1
1.3
1.4
2
xvii xix
Introduction Lossless two-conductor transmission lines – equivalent circuit and velocity of propagation 1.2.1 Characteristic impedance 1.2.2 Reflection coefficient 1.2.3 Phase velocity and phase constant for sinusoidal waves 1.2.4 Power flow for sinusoidal waves 1.2.5 Standing waves resulting from sinusoidal waves Two-conductor transmission lines with losses – equivalent circuit and low-loss approximation 1.3.1 Pulses on transmission lines with losses 1.3.2 Sinusoidal waves on transmission lines with losses Lossless waveguides 1.4.1 Plane (or transverse) electromagnetic waves 1.4.2 Rectangular metallic waveguides 1.4.3 The cut-off condition 1.4.4 The phase velocity 1.4.5 The wave impedance 1.4.6 The group velocity 1.4.7 General solution Further reading
1 4 5 5 6 7 8 9 10 10 10 12 14 15 15 16 16 17
Scattering parameters and circuit analysis P. R. Young
19
2.1 2.2
19 19
Introduction One-port devices
vi
Contents 2.3 2.4 2.5 2.6 2.7 2.8
2.9
3
4
Generalised scattering parameters Impedance and admittance parameters 2.4.1 Examples of S-parameter matrices Cascade parameters Renormalisation of S-parameters De-embedding of S-parameters Characteristic impedance 2.8.1 Characteristic impedance in real transmission lines 2.8.2 Characteristic impedance in non-TEM waveguides 2.8.3 Measurement of Z0 Signal flow graphs Appendices 2.A Reciprocity 2.B Losslessness 2.C Two-port transforms References Further reading
22 24 27 27 28 29 30 30 33 35 36 37 37 39 40 41 41
Uncertainty and confidence in measurements John Hurll
43
3.1 3.2
43 52 52 54 54 54
Introduction Sources of uncertainty in RF and microwave measurements 3.2.1 RF mismatch errors and uncertainty 3.2.2 Directivity 3.2.3 Test port match 3.2.4 RF connector repeatability 3.2.5 Example – calibration of a coaxial power sensor at a frequency of 18 GHz References
54 56
Using coaxial connectors in measurement Doug Skinner
59
4.1
59 60 61 61 61 62 62 62 63 64 64 65
4.2
4.3 4.4 4.5
4.6
Introduction 4.1.1 Coaxial line sizes Connector repeatability 4.2.1 Handling of airlines 4.2.2 Assessment of connector repeatability Coaxial connector specifications Interface dimensions and gauging 4.4.1 Gauging connectors Connector cleaning 4.5.1 Cleaning procedure 4.5.2 Cleaning connectors on static sensitive devices Connector life
Contents 4.7 4.8 4.9 4.A 4.B 4.C 4.D 4.E
5
Adaptors Connector recession Conclusions Appendix A Appendix B Appendix C Appendix D Appendix E Further reading
65 65 66 66 66 85 86 87 88
Attenuation measurement Alan Coster
91
5.1 5.2 5.3
5.4
5.5
6
vii
Introduction Basic principles Measurement systems 5.3.1 Power ratio method 5.3.2 Voltage ratio method 5.3.3 The inductive voltage divider 5.3.4 AF substitution method 5.3.5 IF substitution method 5.3.6 RF substitution method 5.3.7 The automatic network analyser Important considerations when making attenuation measurements 5.4.1 Mismatch uncertainty 5.4.2 RF leakage 5.4.3 Detector linearity 5.4.4 Detector linearity measurement uncertainty budget 5.4.5 System resolution 5.4.6 System noise 5.4.7 Stability and drift 5.4.8 Repeatability 5.4.9 Calibration standard A worked example of a 30 dB attenuation measurement 5.5.1 Contributions to measurement uncertainty References Further reading
91 91 93 94 97 98 104 105 107 108 110 110 112 112 114 115 115 115 115 116 116 117 119 120
RF voltage measurement Paul C. A. Roberts
121
6.1 6.2
121 122 122 124
Introduction RF voltage measuring instruments 6.2.1 Wideband AC voltmeters 6.2.2 Fast sampling and digitising DMMs
viii
Contents
6.3 6.4
7
8
6.2.3 RF millivoltmeters 6.2.4 Sampling RF voltmeters 6.2.5 Oscilloscopes 6.2.6 Switched input impedance oscilloscopes 6.2.7 Instrument input impedance effects 6.2.8 Source loading and bandwidth AC and RF/microwave traceability 6.3.1 Thermal converters and micropotentiometers Impedance matching and mismatch errors 6.4.1 Uncertainty analysis considerations 6.4.2 Example: Oscilloscope bandwidth test 6.4.3 Harmonic content errors 6.4.4 Example: Oscilloscope calibrator calibration 6.4.5 RF millivoltmeter calibration Further reading
125 126 127 129 130 132 133 133 135 136 137 137 138 140 143
Structures and properties of transmission lines R. J. Collier
147
7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9
147 148 150 150 151 152 153 154 154 155 156
Introduction Coaxial lines Rectangular waveguides Ridged waveguide Microstrip Slot guide Coplanar waveguide Finline Dielectric waveguide References Further reading
Noise measurements David Adamson
157
8.1 8.2
157 158 158 159 159 160 162 162 163 163 163
8.3 8.4
Introduction Types of noise 8.2.1 Thermal noise 8.2.2 Shot noise 8.2.3 Flicker noise Definitions Types of noise source 8.4.1 Thermal noise sources 8.4.2 The temperature-limited diode 8.4.3 Gas discharge tubes 8.4.4 Avalanche diode noise sources
Contents 8.5
8.6
8.7 8.8
8.9
9
164 164 166 166 169 169 171 172 174 175 175 176 176 176
Connectors, air lines and RF impedance N. M. Ridler
179
9.1 9.2
179 180 180 181 181 182 182 185 187 188 189 190 192 193 194 198 200 201 203
9.3
9.4
9.5
9.6
10
Measuring noise 8.5.1 The total power radiometer 8.5.2 Radiometer sensitivity Measurement accuracy 8.6.1 Cascaded receivers 8.6.2 Noise from passive two-ports Mismatch effects 8.7.1 Measurement of receivers and amplifiers Automated noise measurements 8.8.1 Noise figure meters or analysers 8.8.2 On-wafer measurements Conclusion Acknowledgements References
ix
Introduction Historical perspective 9.2.1 Coaxial connectors 9.2.2 Coaxial air lines 9.2.3 RF impedance Connectors 9.3.1 Types of coaxial connector 9.3.2 Mechanical characteristics 9.3.3 Electrical characteristics Air lines 9.4.1 Types of precision air line 9.4.2 Air line standards 9.4.3 Conductor imperfections RF impedance 9.5.1 Air lines 9.5.2 Terminations Future developments Appendix: 7/16 connectors References
Microwave network analysers Roger D. Pollard
207
10.1 10.2
207 208 208 214 216
10.3
Introduction Reference plane 10.2.1 Elements of a microwave network analyser Network analyser block diagram Further reading
x 11
Contents RFIC and MMIC measurement techniques Stepan Lucyszyn
217
11.1 11.2
217 218 220 229 230 230 231 236 240 240 241 243 243 246 246 247 249 249 250 251 254 255
11.3
11.4
11.5
11.6
12
Introduction Test fixture measurements 11.2.1 Two-tier calibration 11.2.2 One-tier calibration 11.2.3 Test fixture design considerations Probe station measurements 11.3.1 Passive microwave probe design 11.3.2 Probe calibration 11.3.3 Measurement errors 11.3.4 DC biasing 11.3.5 MMIC layout considerations 11.3.6 Low-cost multiple DC biasing technique 11.3.7 Upper-millimetre-wave measurements Thermal and cryogenic measurements 11.4.1 Thermal measurements 11.4.2 Cryogenic measurements Experimental field probing techniques 11.5.1 Electromagnetic-field probing 11.5.2 Magnetic-field probing 11.5.3 Electric-field probing Summary References
Calibration of automatic network analysers Ian Instone
263
12.1 12.2 12.3 12.4 12.5
263 263 263 266 267 267 267
12.6 12.7 12.8
Introduction Definition of calibration Scalar network analysers Vector network analyser Calibration of a scalar network analyser 12.5.1 Transmission measurements 12.5.2 Reflection measurements Problems associated with scalar network analyser measurements Calibration of a vector network analyser Accuracy enhancement 12.8.1 What causes measurement errors? 12.8.2 Directivity 12.8.3 Source match 12.8.4 Load match 12.8.5 Isolation (crosstalk) 12.8.6 Frequency response (tracking)
269 269 270 270 270 271 272 273 273
Contents 12.9 12.10 12.11 12.12
12.13
13
273 273 276 279 284 284 286 287 289 289
Verification of automatic network analysers Ian Instone
291
13.1 13.2 13.3
291 291 292 292 292 293 293 293 296 299 299 299 300 301 301 302 304
13.4 13.5
13.6
14
Characterising microwave systematic errors 12.9.1 One-port error model One-port device measurement Two-port error model TRL calibration 12.12.1 TRL terminology 12.12.2 True TRL/LRL 12.12.3 The TRL calibration procedure) but to use a less precise name (i.e. 14 mm).
Table 9.3
Electrical discontinuities caused by joining mechanically compatible connectors
Connector pair
Centre conductor pin diameter for both connectors (mm)
Equivalent discontinuity capacitance (fF)
Maximum linear reflection coefficient magnitude
3.5 mm and K connector 2.4 mm and V connector
0.927 0.511
8 10
0.04 (at 33 GHz) 0.08 (at 50 GHz)
line and can be represented electrically as a single shunt capacitance at the reference plane of the connector pair [32]. This discontinuity capacitance produces a reflection at the connector interface that varies with frequency. This effect has been investigated in [33], and typical maximum values for this reflection are given in Table 9.3. In addition to the mechanical compatibility of the above precision connectors, the 3.5 mm and K connectors are also mechanically compatible with the SMA connector. In this case, the presence of a solid dielectric (e.g. Teflon) at the reference plane of the SMA connector causes an additional discontinuity capacitance (this time due to the dielectric) leading to even larger electrical reflections than those produced from a 3.5 mm to K-connection. However, as mentioned previously, the WSMA precision 3.5 mm connector was designed specifically to produce high-performance mating with SMA connectors [31]. This is achieved by deliberately setting back the position
Connectors, air lines and RF impedance 187 of the centre conductor pin by a prescribed amount, and hence introducing an amount of inductance to compensate for the additional capacitance caused by the SMA’s dielectric [34].
9.3.3 Electrical characteristics Two very important electrical characteristics of a coaxial connector are the nominal characteristic impedance and the maximum recommended operating frequency to ensure a stable, and repeatable, measurement. The characteristic impedance of coaxial air lines is discussed in detail in Section 9.4 of this chapter. This discussion is also applicable to the precision coaxial connectors used with these air lines. The maximum recommended operating frequency for a coaxial line is usually chosen so that only a single electromagnetic mode of propagation is likely to be present in the coaxial line at a given frequency. This is the dominant transverse electromagnetic (or TEM) mode and operates exclusively from DC to the maximum recommended operating frequency. Above this frequency, other higher-order modes7 can also propagate to some extent. The maximum recommended operating frequency is often called the ‘cut-off frequency’ as it corresponds to the lower frequency cut-off for these higher-order waveguide modes. The first higher-order mode in 50 0001 coaxial line is the TE11 mode (also known as the H11 mode in some references). The cut-off frequency is given by [35] c fc = √ (9.1) λ c µ r εr It has been shown in [36] that the approximate cut-off wavelength for the TE11 mode is given by λc ≈ π(a + b)
(9.2)
which corresponds to the average circumference of the line’s conductors. More precise expressions for the cut-off wavelength can be obtained from [37] and these produce the theoretical upper frequency limits (i.e. the cut-off frequencies) for each line size shown in Table 9.4. Table 9.4 also gives recommended usable upper frequency limits for each line size. These are lower than the theoretical upper frequency limits and this is due to potential higher-order mode resonances (again, the TE11 mode being the most likely) caused by solid material dielectric (e.g. Teflon) being present between the two conductors of the coaxial line. These resonances are most problematic when they occur in the vicinity of the transitions from air to solid dielectric, such as when a dielectric bead is 7 These modes are often called ‘waveguide modes’ since they are similar to the modes found in hollow waveguide. These modes are either transverse electric (TE) or transverse magnetic (TM) and have a longitudinal component to their propagation. It should be noted that the TEM mode can continue to propagate at frequencies where TE and TM modes are also possible, since the TEM mode does not actually have an upper frequency limit.
188 Microwave measurements Table 9.4
Theoretical and recommended upper frequency limits for coaxial connectors
Connector name
Theoretical upper frequency limit (GHz)
Recommended usable upper frequency limit (GHz)
14 mm (e.g. GR900) 7 mm (e.g. APC-7) Type N 3.5 mm 2.92 mm (K connector) 2.4 mm 1.85 mm (V connector) 1 mm
9.5 19.4 19.4 38.8 46.5 56.5 73.3 135.7
8.5 18.0 18.0 33.0 40.0 50.0 65.0 110.0
used to support the centre conductor of the coaxial line (as in GPCs). Such resonances can occur in single connector beads as well as in a mated connector pair containing two dielectric beads. These higher-order mode resonances can cause significant electromagnetic changes in both the reflection and transmission properties of the coaxial line. (In general, these changes cause the reflection coefficient of the line to increase whereas the transmission coefficient decreases.) These resonances are highly unpredictable and can be initiated by subtle asymmetries, eccentricities or other irregularities that may be present in the line – as can be the case at connector interfaces. For example, if dielectric beads form part of the connector interface (as in GPCs), these electromagnetic changes can vary according to the orientation of the connectors each time a connection is made. Under these conditions, even pristine precision connectors can exhibit very poor repeatability of connection. The presence of bead resonances in precision coaxial connectors has been investigated in [38], while [39] presents some methods proposed to reduce the likelihood of excitation of these modes (e.g. through connector bead design). In any case, care should be taken when performing measurements near the upper frequency limits of coaxial connectors – even the recommended usable upper frequency limits, given in Table 9.4. Acute changes in the reflection and transmission coefficients (or a lack of repeatability of these coefficients) may indicate the presence of a higher-order mode resonance.
9.4
Air lines
Precision air-dielectric coaxial transmission lines (or, air lines, for short) can be used as reference devices, or standards, for impedance measurements at RF and microwave frequencies. (The term impedance is used here to imply a wide range of
Connectors, air lines and RF impedance 189 electrical quantities, such as S-parameters, impedance and admittance parameters, VSWR, and return loss.) This includes the use of air lines as calibration and verification standards for measuring instruments such as vector network analysers (VNAs) [40]. For example, VNA calibration schemes, such as Thru-Reflect-Line (TRL) [41] and Line-Reflect-Line (LRL) [42], use air lines as standards to achieve very high accuracy impedance measurement capabilities. This is the method currently used to realise the UK primary national standard for impedance quantities [43] at RF and microwave frequencies (typically, from 45 MHz and above). Similarly, verification schemes determining the residual systematic errors in a calibrated VNA [44] use air lines as the reference devices, and these methods are currently endorsed by organisations involved in the accreditation of measurement, such as the European co-operation for Accreditation (EA) [45]. This section describes the different types of air line that are available and reviews their use as standards of characteristic impedance and/or phase change. Consideration is also given for the effects caused by imperfections in the conductors used to realise these air lines.
9.4.1 Types of precision air line There are basically three types of air line depending on the number of dielectric beads used to support the centre conductor of the line. These beads are usually to aid in the connection of the line during measurement. 9.4.1.1 Unsupported air lines These lines do not contain any support beads and therefore the connector interfaces conform to the LPC category. The ends of the centre conductor are usually fitted with spring-loaded contacting tips to facilitate connecting the line to other connectors. The line’s centre conductor is held in place by the test ports of a measuring instrument (or whatever else is being connected to the line). The centre and outer conductors of these lines come in two separate parts and are assembled during connection. These lines (which are of a calculable geometry) are used where the very highest levels of accuracy are required. Therefore, such lines are often found in VNA calibration kits used to realise TRL and LRL calibration schemes. 9.4.1.2 Partially supported air lines These lines contain a support bead at only one end of the line. This design is often used for relatively long lengths of line that may be difficult to connect if they were not supported in some way. The unsupported end of the line is usually connected first – this being the more difficult of the two connections – followed by the supported end (which connects like a conventional connector). Such a line therefore has connections that are LPC at one end and GPC at the other. The centre and outer conductors of these lines often come as two separate components, although fully assembled versions also exist where the centre conductor is held in place by the bead in the air line’s GPC. Semi-supported lines are often found in VNA verification kits where a calculable geometry is not required (although a high-electrical performance is still necessary).
190 Microwave measurements These lines can also be used in applications where minor reflections from one end of the line do not cause problems (e.g. some applications of the ‘ripple’ technique [44]). 9.4.1.3 Fully supported air lines These lines contain support beads at both ends of the line. This is equivalent to GPCs being present at both ends of the line thus making it relatively easy to connect. These lines come fully assembled with the centre conductor being held in place by both beads in the air line’s GPCs. Such lines find application where only relatively modest levels of accuracy are required or where only a part of the length of a line needs to be of a known, or calculable, impedance (e.g. when calibrating time-domain reflectometers). In such applications, the minor reflections and discontinuities caused by the presence of the beads will be inconsequential.
9.4.2 Air line standards In the above applications, the air lines are used as references of either characteristic impedance or phase change, or both. These two applications are discussed in the following subsections. 9.4.2.1 Characteristic impedance In general, the characteristic impedance of a particular electromagnetic mode supported by a coaxial line is a complex function of the dimensions and alignment of the conductors, the physical properties of the materials of the line, and the presence of discontinuities such as connectors. However, for a uniform line with lossless conductors and air between the centre and outer conductors, the characteristic impedance of the TEM mode can be approximated by 1 Z0 = 2π
0001
µ loge ε
0002 0003 0002 0003 b b ≈ 59.93904 × loge a a
(9.3)
From the above expression, it is clear that the characteristic impedance of a line can be found from measurements of the diameters of the line’s conductors. Such measurements are often made using air gauging techniques [46] that enable measurements to be made continuously along the entire lengths, and at all possible orientations, of both conductors. This is a very useful technique since the determination of an air line’s characteristic impedance can be made with direct traceability to the SI base unit of length (i.e. the metre). Similarly, it is also clear that, from the above expression, values of characteristic impedance can be established by using different diameters for a line’s conductors. This is evident from the diameter values presented in Table 9.2 that show a range of diameter values for coaxial air lines each with a nominal characteristic impedance of 50 0001. Similarly, Table 9.5 gives diameter values that achieve a nominal characteristic impedance of 75 0001 for the 14 and 7 mm line sizes, mentioned previously. These
Connectors, air lines and RF impedance 191 Table 9.5
Line diameters for 75 0001 line sizes
Connector name
Line size, i.e. the internal diameter of the outer conductor (mm)
Centre conductor diameter (mm)
GR900 Type N
14.2875 7.000
4.088 2.003
diameters are used to realise 75 0001 versions of the GR900 and Type N connectors, respectively8 . Having established that a wide range of characteristic impedance values can be achieved simply by choosing different diameters for the centre and outer conductors, this raises the question ‘Why is 50 0001 a preferred value for the characteristic impedance of coaxial lines?’ The answer appears to be that it was chosen as a compromise in performance between the theoretical characteristic impedance needed to obtain minimum attenuation in a line (which occurs at nominally 77.5 00019 ) and the theoretical characteristic impedance needed to obtain the maximum power transfer along a line (which occurs nominally at 30 0001). The average of these two values is 53.75 0001, which rounds to 50 0001 (to one significant figure). Hence, 50 0001 is a good compromise value for the characteristic impedance of lines used in many and diverse applications. 9.4.2.2 Phase change Air lines can also be used as standards of phase change since a lossless line will only introduce a phase change to a signal, which relates directly to the line’s length. The phase change is given by √ εr ϕ = 2π f l (radians) c or √ εr ϕ = 360 f l (degrees) c Air lines have been used successfully as phase change standards to calibrate reflectometers and VNAs at the very highest levels of accuracy (e.g. see [47,48]). These techniques use the lines in conjunction with high reflecting terminations (such as short-circuits and open-circuits) to produce a known phase change at the instrument 8 Caution! Great care should be taken when performing measurements where both 75 and 50 0001 versions of the same connector type are available. For the Type N connector, damage will occur to a 75 0001 female connector if an attempt is made to mate it with a 50 0001 male connector. This is due to the substantial difference in diameters of the male pin and the female socket. (Note that the same situation occurs with 50 and 75 0001 versions of BNC connectors!). 9 This may also explain why 75 0001 is also often used in some applications (such as in certain areas of the communications industry).
192 Microwave measurements test port. In recent years, the use of such techniques is beginning to re-emerge in applications where it is not practical to use unsupported air lines primarily as standards of characteristic impedance (e.g. in calibration schemes such as TRL and LRL). For example, a kit currently available for VNA calibrations in the 1 mm coaxial line size [10] uses short-circuits offset by different lengths of line to achieve calibrations from around 50 to 110 GHz. An important consideration when using air lines in conjunction with high reflecting terminations (e.g. as offset short-circuits) is that the effective electrical length of the offset line is actually double the mechanical length. This is because the electrical signal has to make a ‘there-and-back’ journey along the length of the line having been reflected back from the termination at the end of the line.
9.4.3 Conductor imperfections In the above discussion concerning using air lines as standards of characteristic impedance and phase change, it has been assumed that the line’s conductors are made up of lossless material (i.e. the conductors are perfectly conducting or, in other words, possess infinite conductivity). However, in practice, conductors are not perfectly conducting and therefore possess finite conductivity (or loss). This causes problems for the electrical properties of lines especially at low frequencies when the conductivity at the surface of the conductors becomes important. Manufacturers attempt to minimise these problems by producing lines made up of high-conductivity materials (such as alloys of copper) or by applying a plated layer of high-conductivity material (such as silver) to the surface of the conductors in the coaxial line. Even so, as frequency decreases, the finite conductivity of a line causes the propagating wave to penetrate the walls of the conductors to some extent. The attenuation constant associated with the wave propagating into the walls of the conductors10 is considerably higher than for the wave propagating in the dielectric between the conductors, and therefore the wave attenuates rapidly as it penetrates the walls of the conductors. The reciprocal of this attenuation constant is called the skin depth and is defined as the distance travelled into the walls of the conductors by the wave before being attenuated by one neper (≈8.686 dB). The skin depth is given by 0004 1 (9.4) δs = πf σ µ This indicates that skin depth increases as the frequency decreases. The skin depth will also be larger for a line with a lower value of conductivity. To illustrate this, values for skin depth are given in Table 9.6, for conductors made up of silver, brass and beryllium copper (BeCu), with assumed conductivities of 62, 16 and 13 MS m−1 , respectively, as these are materials often used to fabricate precision air lines. Further detailed discussions on skin depth effects can be found in [49]. 10 The wave decays exponentially as it penetrates the walls of the conductors.
Connectors, air lines and RF impedance 193 Table 9.6
Skin depth values as a function of frequency
Frequency (MHz)
1 10 100 1000
Skin depth (µm) Silver (σ = 62 MS m−1 )
Brass (σ = 16 MS m−1 )
BeCu (σ = 13 MS m−1 )
64 20 6 2
126 40 13 4
140 44 14 4
It is generally only necessary to accurately determine the conductivity of a line’s conductors at RF (typically, between 1 MHz and 1 GHz) in order to determine the line’s characteristics. This is because lines are rarely used as impedance standards below these frequencies and skin depth becomes less of a problem at higher frequencies. This requirement, however, is not trivial. If the line’s constitution is known then a value may be obtained from tables of physical data (e.g. from sources such as [50]). However values specified in tables usually refer to bulk material samples. These values are often different from actual values for the same material after it has been subject to manufacturing processes, as is the case for air lines (e.g. see [51,52]). An additional problem in determining a value for the conductivity of a line is caused by plating layers that may be applied by manufacturers either to increase conductivity (e.g. silver plating) or increase longevity (e.g. gold ‘flashing’). Several studies have been carried out evaluating effects of plating on the effective conductivity of conductors [53–55] but these assume prior knowledge of the material of each layer and ignore additional complications caused by impurities which will doubtlessly be present. A recent validation of theoretical predictions based on assumed conductivity values has been performed by comparison with precision attenuation measurements [56]. Finally, another consideration concerning the characteristics of a line relates to the non-uniformity of the conductor’s surfaces caused either by changes in the longitudinal dimensions of the line [57,58] or surface roughness [59]. In both cases, these effects will cause the properties of the line to depart significantly from ideal values.
9.5
RF impedance
The measurement of impedance, and impedance-related quantities, requires special consideration when the measurement frequency is in the RF region (i.e. from 1 MHz to 1 GHz). This is generally due to techniques used at the higher frequencies becoming inappropriate at these longer wavelengths. Similarly, low-frequency techniques, used
194 Microwave measurements
R
L
G
Figure 9.3
C
Distributed circuit model for a section of coaxial line
below 1 MHz, are also unsuitable – for example, because the connector configurations are often different (e.g. four-terminal pair connections). Information concerning use of air lines and terminations (i.e. one-port devices) as impedance standards at RF is given below – for example, to calibrate a VNA. More detailed information can be found in [60].
9.5.1 Air lines Air lines can be used in conjunction with terminations as calibration items for reflectometers (or VNA one-port calibrations). In this configuration, one end of the air line is connected to the instrument test port while the other end is connected to the termination. Lines can also be used for VNA two-port calibrations (such as TRL and LRL, where they act as the Line standard) and are connected between the two test ports during calibration. In either application, the accuracy achieved using modern VNAs requires that the electrical characteristics of the air lines are defined very precisely, as shown in Figure 9.3. A coaxial line can be characterised using the distributed circuit model given in Figure 9.3, where R, L, G and C are the series resistance and inductance, and the shunt conductance and capacitance, respectively, per unit length of line. Expressions for the four line elements R, L, G and C can be used to obtain further expressions for two fundamental line parameters – the characteristic impedance and the propagation constant – which are defined as follows: 0004 (R + jωL) (9.5) Z= (G + jωC) 0005 γ = α + jβ = (R + jωL)(G + jωC) (9.6) 9.5.1.1 Lossless lines For a lossless line (i.e. with conductors of infinite conductivity) both the series resistance and the shunt conductance are zero. The series inductance and the shunt
Connectors, air lines and RF impedance 195 capacitance have fixed values independent of frequency and are given by 0006 µ loge (b a) L0 = 2π 2πε 0006 C0 = loge (b a)
(9.7) (9.8)
The characteristic impedance of the lossless line is therefore (as before) 0004 Z0 =
L0 1 = C0 2π
0001
µ loge ε
0002 0003 b a
(9.9)
This shows that the line’s characteristic impedance is a purely real quantity (i.e. containing no imaginary component), is independent of frequency and determined by the ratio (b/a). For example, to achieve a characteristic impedance of 50 0001 this ratio is approximately 2.3. The propagation constant of the lossless line is 0005 ω 2π √ (rad m−1 ) γ0 = jβ = jω L0 C0 = jω µε = j = j v λ
(9.10)
This shows that the line’s propagation constant is purely imaginary (i.e. containing no real component) and is determined only by the wavelength (or equivalent) of the propagating wave. The attenuation constant is zero which is consistent with a line having no loss. The phase constant is a linear function of frequency, indicating a non-dispersive line. 9.5.1.2 Lossy lines As mentioned previously, metallic air-filled coaxial lines are not lossless. An important part of line characterisation at RF is a determination of the effects due to line loss. An attempt at dealing with this problem for RF impedance standardisation has been given in [61]. Further work has since been presented in [62], giving expressions for all four line elements – R, L, C and G – containing frequency-dependent terms for each element. Additional work has also solved this problem for frequencies below the RF region, obtaining exact field equations for lossy coaxial lines [63]. The expressions derived in [62] for the four line elements at RF are as follows: 0002
0003 k 2 a2 F 0 R = 2ωL0 d0 1 − 2 0007 0002 0003 k 2 a 2 F0 L = L0 1 + 2d0 1 − 2 G = ωC0 d0 k 2 a2 F0 2 2
C = C0 (1 + d0 k a F0 )
(9.11) (9.12) (9.13) (9.14)
196 Microwave measurements
Z change from 50 Ω(mΩ)
3000 2500 2000 1500 1000 500 0 1
10
100
1000
Frequency (MHz)
Figure 9.4
Change in characteristic impedance magnitude for a 7 mm BeCu line 0
Z phase (mDegrees)
−500 −1000 −1500 −2000
−2500
1
10
100
1000
Frequency (MHz)
Figure 9.5 where
Characteristic impedance phase angle for a 7 mm BeCu line
F0 =
0007 (b2 /a2 ) − 1 (b/a) loge (b/a) 1 b − − +1 2 loge (b/a) (b/a) + 1 2 a
(9.15)
d0 =
δs (1 + (b/a)) 4b loge (b/a)
(9.16)
These expressions can be used to calculate the characteristic impedance, which, for a line with finite conductivity, is clearly a complex quantity, material dependent and a function of frequency. Figures 9.4 and 9.5 illustrate the effect on the characteristic impedance of a nominal 50 0001 7 mm air line made up of BeCu with an assumed conductivity of 13 MS m−1 . The deviation in the characteristic impedance causes a problem for impedance measurements (such as S-parameters) since they are usually specified with respect to the lossless line value (e.g. 50 0001). Measurements made on instruments calibrated with lines of different material will vary systematically since the impedance parameters will be measured with respect to different characteristic impedances. This problem is
Connectors, air lines and RF impedance 197
Attenuation constant (dB/m)
0.25 0.20 0.15 0.10 0.05 0.00 1
10
100
1000
Frequency (MHz)
Figure 9.6
Attenuation constant for a 7 mm BeCu line
Phase constant change(Deg/m)
1.6
1.2
0.8
0.4
0.0 1
10
100
1000
Frequency (MHz)
Figure 9.7
Change in phase constant for a 7 mm BeCu line
overcome by transforming from the actual line characteristic impedance to the defined lossless value (e.g. 50 0001 for the 50 0001 line size). Further information on impedance transformations of this type is given in [64]. The above expressions can also be used to calculate the propagation constant, which, for a line with finite conductivity has both real and imaginary parts and is non-linear with frequency. Figures 9.6 and 9.7 illustrate the effect on the propagation constant for a nominal 50 0001 7 mm air line made up of BeCu. The attenuation constant is non-zero (Figure 9.6), which is consistent with a line containing loss. The increase in the phase constant from its lossless value indicates that the line’s electrical length is longer than its physical length – this discrepancy varying as a function of frequency. The line is therefore dispersive and imparts group delay to broadband signals. A comparison of parameters characterising lossless and lossy lines reveals that only one extra term is included to allow for the loss effects, that is, the conductor’s conductivity. If the conductivity is assumed to be infinite, the skin depth becomes zero and the term d0 in the expressions for the four lossy line elements vanishes. This
198 Microwave measurements causes R and G to become zero and L and C to revert to their lossless values (i.e. L0 and C0 ). The finite conductivity (and hence non-zero skin depth) of the conductors is therefore solely responsible for departures from the lossless line conditions. The √ expression given earlier for skin depth also contains a 1/ f term indicating that skin depth increases as frequency decreases, causing a subsequent increase in the values for all four line elements.
9.5.2 Terminations It is often very convenient to use terminations (i.e. one-port devices) as calibration standards for reflectometers and VNAs. These terminations can be used in both one-port and two-port VNA calibration schemes. The terminations can be connected directly to the instrument test port or separated by a length of air line called an ‘offset’. The air line section can be an integral part of the item or connected separately. The three most common terminations used for this purpose are shortcircuits, open-circuits and near-matched terminations (including so-called sliding loads). Mismatched terminations (and capacitors) can also be used, particularly at lower frequencies. 9.5.2.1 Short-circuits A coaxial line short-circuit is simply a flat metallic disc connected normally to the line’s centre and outer conductors. Its radius must exceed the internal radius of the outer conductor and be of sufficient thickness to form an effective shield for the electromagnetic wave propagating in the line. The disc is usually made up of a similar material as the line’s conductors. Short-circuits can be connected directly to an instrument test port or via a length of line producing an offset short-circuit. Short-circuits provide a good approximation to the lossless condition at RF (i.e. with both series resistance and inductive reactance being close to zero). This produces a reflection coefficient with real and imaginary parts of −1 and 0, respectively. Loss due to skin depth and surface finish of the disc can be considered for high-precision metrology applications. Such losses have been considered in [65] by analysing the effects of a TEM wave incident normally to a conducting plane. 9.5.2.2 Open-circuits In principle, a coaxial open-circuit is produced by having nothing connected to the instrument test port. However, this produces a poorly defined standard for two reasons: (1) it will radiate energy producing a reflected signal dependent on obstacles in the vicinity of the test port and (2) the test port connector’s mating mechanism affects the established measurement reference plane which limits accurate characterisation as a standard. The first of these problems can be overcome by extending the line’s outer conductor sufficiently beyond the position of the open-circuited centre conductor so that the evanescent radiating field decays to zero within the outer conductor shield – the extended outer conductor acting as an effectively infinite length of circular waveguide below cut-off.
Connectors, air lines and RF impedance 199 The second problem can be overcome either by depressing the mating mechanism using a dielectric plug or attaching a length of line to the centre conductor, terminated in an abrupt truncation. The dielectric plug technique is used as a standard with numerous VNA calibration kits. The abruptly truncated line technique has been used to realise primary national impedance standards [47,66]. In both cases, the opencircuit behaves as a frequency-dependent ‘fringing’ capacitance. Calculations for the capacitance of an abruptly truncated coaxial line can be found in the literature (i.e. [67–69]). These values have been verified for RF impedance applications using a computer-intensive equivalent circuit technique [70]. Coaxial open-circuits have a reflection coefficient of nominally unity magnitude and a phase angle dependent on the fringing capacitance and the length of any line used to fabricate the device. They can therefore be very useful as standards for calibrating reflectometers and VNAs. 9.5.2.3 Near-matched terminations A low-reflection (or near-matched) termination can be produced by mounting a cylindrical thin-film resistive load in the centre conductor of a line with a tractorially shaped outer conductor. A parabolic transition between the conventional coaxial line and the tractorial section transforms incident plane wave fronts to spherical wave fronts required to propagate in the tractorial section of the termination. This produces near-uniform power dissipation along the length of the resistive load element with minimal frequency dependence. This design of low reflecting termination has been discussed in [71]. Low-reflection terminations are usually assumed to have zero reflection during a reflectometer, or VNA, calibration (and are therefore often called ‘matched’ loads). Alternatively, low reflecting load elements can be used to ‘synthesise’ the performance of a matched termination, using sliding load techniques. This is achieved by measuring the response of a load element at several positions along a variable length of precision air line. The characteristics of a ‘perfectly’ matched termination can then be computed by fitting a circle to the measured reflection values (the centre of the fitted circle being the point in the complex reflection coefficient plane corresponding to a perfect match, i.e. zero reflection). However, problems due to imperfections in the air line section and inadequate phase differences produced by realisable lengths of air line make this technique of limited use at RF. 9.5.2.4 Mismatched terminations In principle, mismatched terminations (and capacitors) can be very useful devices for providing values of reflection that are significantly different from those achieved using short-circuit, open-circuit and near-matched terminations. Such reflection values could be used in certain calibration applications (e.g. as alternatives to the shortopen-load values used during conventional VNA calibration schemes). However, devices used for calibration (i.e. standards) are usually assumed to have ‘known’
200 Microwave measurements values based on either a calculated and/or measured performance11 . In general, it is not possible to calculate, to any degree of accuracy, the performance of a mismatched termination. Indeed, the same can be said of near-matched terminations where an assumed value (i.e. zero) is often used for calibration purposes. There have been several attempts recently at characterising near-matched terminations using measurement data at DC and RF. Some work in the 1990s [72] used equivalent circuit models for characterising these devices at lower RF (300 kHz to 30 MHz) based on measurement data at higher RF. More recent work [73,74] has concentrated on implementing interpolation schemes for characterising these devices. The interpolation schemes have the advantage that very few assumptions need to be made concerning the characteristics of the device. In principle, such schemes can be extended to characterise ‘any’ device (e.g. mismatch terminations) without requiring detailed knowledge concerning the physical (i.e. calculable) properties of the device. This is leading to the development of generalised techniques for VNA calibrations [75] that do not need to rely on the classical assumptions implicit in the short-open-load calibration schemes. Such techniques are expected to greatly enhance our knowledge of calibration devices and instruments used traditionally to perform RF impedance measurements.
9.6
Future developments
Coaxial connectors and coaxial transmission lines continue to play a crucial role in the realisation of the majority of measurements made at radio and microwave frequencies. This chapter has presented some of the important issues relating to the various types of coaxial connector currently available for making high-precision measurements. Even so, the connector itself can still be the limiting factor for the accuracy achieved by today’s measurement systems. Similarly, coaxial air lines provide very useful standard reference artefacts for realising impedance quantities for these connector types and the associated transmission lines. These devices are simple structures with well-defined electromagnetic properties. But once again, the precision at which today’s instruments can operate means that these standards will need to be defined to an even greater level of precision. This is particularly true at lower RF (and, indeed, at extremely high frequencies) where the line’s characteristics depart substantially from their idealised values. It is unlikely that future requirements for these technologies will be less demanding than they are at present. Indeed, it can be expected that most measurement applications will require broader bandwidths, improved electrical capabilities (including repeatability, insertion loss and lower passive inter-modulation) and higher levels of accuracy. These demands are likely to continue to drive developments in precision coaxial connectors, air lines and other impedance standards for the foreseeable future. 11 For example, the characteristics of unsupported air lines can be calculated based on the measured values of the diameters of the line’s conductors.
Connectors, air lines and RF impedance 201
Appendix: 7/16 connectors The 7/16 connector was developed during the 1960s primarily for high-performance military applications. In recent years, it has become a popular choice for certain applications in the mobile communications industry, such as in base stations and antenna feed lines. This is due to its suitability for uses involving high power levels, low receiver noise levels and where there are requirements for low passive intermodulation (PIM). The 7/16 connector is a sexed connector with a nominal characteristic impedance of 50 0001. It is available in both GPC and LPC versions – LPCs are found on 7/16 unsupported air lines used in VNA calibration kits to realise calibration schemes such as TRL and LRL. Terminations are also available which can be used for Short-OpenLoad calibration schemes. The nominal diameters of the centre and outer conductors are 7 and 16 mm, respectively, and this yields a recommended usable upper frequency limit of approximately 7.5 GHz. Primary national standards of impedance for 7/16 connectors have recently been introduced at the UK’s National Physical Laboratory.
Symbols a α b β γ
= = = = =
γ0 = C = C0 c δs φ e ε εr
= = = = = = =
ε0 = f = fc =
Radius of coaxial line centre conductor (m). Attenuation constant (Np m−1 ). Radius of coaxial line outer conductor (m). Phase constant (rad m−1 ). Propagation constant for coaxial line containing conductor loss. This is generally a complex-valued quantity (m−1 ). Propagation constant of lossless coaxial line. This is an imaginary-valued quantity (m−1 ). Shunt capacitance, per unit length, of coaxial line including conductor loss (F m−1 ). Shunt capacitance, per unit length, of lossless coaxial line (F m−1 ). Speed of light in vacuum (defined exactly as 299,792,458 m s−1 ). Skin depth of air line conductors (m). Phase change (in degrees or radians) introduced by a length of line, l. 2.718281828…(base of Naperian logarithms). Permittivity, ε = ε0 εr (F m−1 ). Relative permittivity of an air line’s dielectric (e.g. εr = 1.000649 for ‘standard’ air at 23 ◦ C, 50 per cent relative humidity and 1013.25 hPa atmospheric pressure). Permittivity of free space (defined exactly as (c2 µ0 )−1 = 8.854187817 . . . × 10−12 F m−1 ). Frequency (Hz). Cut-off frequency for the TEM mode (Hz).
202 Microwave measurements G = Shunt conductance, per unit length, for a coaxial line including conductor −1 √loss (S m ). j = − 1. k = Angular wave number, k = 2π/λ (rad m−1 ). l = Length of air line (m). L = Series inductance, per unit length, for a coaxial line including conductor loss (H m−1 ). L0 = Series inductance, per unit length, for a lossless coaxial line (H m−1 ). λ = Wavelength = v/f (m). λc = Cut-off wavelength for the TEM mode (m). µ = Permeability, µ = µ0 µr (H m−1 ). µr = Relative permeability of an air line’s dielectric (e.g. µr = 1 for ‘standard’ air, to six decimal places). µ0 = Permeability of free space (defined exactly as 4π × 10−7 H m−1 ). π = 3.141592653. . . R = Series resistance, per unit length, for a coaxial line including conductor loss (0001 m−1 ). σ = Conductivity of an air line’s conductors (S m−1 ). √ v = Speed of the electromagnetic wave in the air line [v = c/ εr (m s−1 )]. ω = Angular frequency, ω = 2π f (rad s−1 ). Z = Characteristic impedance of a coaxial line containing conductor loss. This is generally a complex-valued quantity (0001). Z0 = Characteristic impedance of a coaxial line with lossless conductors. This is a real-valued quantity (0001).
References 1 Hertz, H.: Electric waves, being researches on the propagation of electric action with finite velocity through space, Trans. Jones, D. E. (Dover Publications Inc, New York, 1962), Chapter 10 2 Maxwell, J. C.: A treatise of electricity and magnetism, 3rd edn, vol. 2 (Oxford University Press, London, 1892) 3 Bryant, J. H.: ‘Coaxial transmission lines, related two-conductor transmission lines, connectors, and components: A US historical perspective’, IEEE Transactions on Microwave Theory and Techniques, 1984;32 (9):970–83 4 G-IM Subcommittee on Precision Coaxial Connectors: ‘IEEE standard for precision coaxial connectors’, IEEE Transactions on Instrumentation and Measurement, 1968;17 (3):204–18 5 Adam, S. F., Kirkpatrick, G. R., Sladek, N. J., and Bruno, S. T.: ‘A high performance 3.5 mm connector to 34 GHz’, Microwave Journal, 1976;19 (7):50–4 6 Maury, M. A., and Wambach, W. A.: ‘A new 40 GHz coaxial connector’, Millimeter Waves Techniques Conference Digest (NELC, San Diego, CA, 1974) 7 Browne, J.: ‘Precision coaxial cables and connectors reach 45 GHz’, Microwaves & RF, Sep 1983;131–6
Connectors, air lines and RF impedance 203 8 Kachigan, K., Botka, J., and Watson, P.: ‘The 2.4 mm connector vital to the future of 50 GHz coax’, Microwave Systems News, 1986;16 (2):90–4 9 Manz, B.: ‘Coaxial technology vies for emerging V-band applications’, Microwaves & RF, Jul 1989;35–41 10 Howell, K., and Wong, K.: ‘DC to 110 GHz measurements in coax using the 1 mm connector’, Microwave Journal, 1999;42 (7):22–34 11 Weinschel, B. O.: ‘Air-filled coaxial lines as absolute impedance standards’, Microwave Journal, Apr 1964;47–50 12 Harris, I. A., and Spinney, R. E.: ‘The realization of high-frequency impedance standards using air spaced coaxial lines’, IEEE Transactions on Instrumentation and Measurement, 1964;13:265–72 13 Rayleigh, L.: ‘On the self-inductance and resistance of straight conductors’, Philosophical Magazine S5, 1886;21 (132):381–94 14 Russell, A.: ‘The effective resistance and inductance of a concentric main, and methods of computing the Ber and Bei and allied functions’, Philosophical Magazine, 1909;17:524–52 15 Wheeler, H. A.: ‘Formulas for the skin effect’, Proceedings of the Institute of Radio Engineers, 1942;30:412–24 16 Stratton, J. A.: Electromagnetic theory (McGraw-Hill Book Company Inc, New York and London, 1941), Chapter 9 17 Harris, I. A.: ‘The theory and design of coaxial resistor mounts for the frequency band 0-4000 Mc/s’, Proc. Inst. Electr. Eng., 1956;103 Part C(3):1–10 18 MacKenzie, T. E., and Sanderson, A. E.: ‘Some fundamental design principles for the development of precision coaxial standards and components’, IEEE Transactions on Microwave Theory and Techniques, 1966;14 (1):29–39 19 Ridler, N. M., and Medley, J. C.: ‘Improvements to traceability for impedance measurements at RF in the UK’, IEE Engineering, Science and Education Journal, 1997;6 (1):17–24 20 Ridler, N. M., and Medley, J. C.: ‘Improving the traceability of coaxial impedance measurements at lower RF in the UK’, IEE Proceedings Science Measurement and Technology, 1996;143 (4):241–45 21 Skinner, A. D.: ANAMET connector guide, ANAMET Report 032, 2001 (Available at: www.npl.co.uk/anamet) 22 ‘Coaxial Systems. Principles of microwave connector care (for higher reliability and better measurements)’, Hewlett Packard Application Note 326, July 1986 23 ‘Coaxial connectors in radio frequency and microwave measurements’, NAMAS Information Sheet 4303, edn 1, December 1991 24 Maury, M. A.: ‘Microwave coaxial connector technology: a continuing evolution’, Microwave Journal (State of the Art Preference Supplement), Sep 1990; 39–59 25 Weinschel, B. O.: ‘Coaxial connectors: a look to the past and future’, Microwave Systems News, 1990;20 (2):24–31 26 Anderson, T. N.: ‘Evolution of precision coaxial connectors’, Microwave Journal, Jan 1968;18–28
204 Microwave measurements 27 Huber, F. R., and Neubauer, H.: ‘The Dezifix connector – a sexless precision connector for microwave techniques’, Microwave Journal, Jun 1963;79–85 28 Weinschel, B. O.: ‘Standardization of precision coaxial connectors’, Proceedings of the IEEE, 1967;55 (6):923–32 29 Sladek, N. J., and Jesch, R. L.: ‘Standardization of coaxial connectors in the IEC’, Proceedings of the IEEE, 1986;74 (1):14–18 30 Botka, J.: ‘Major improvement in measurement accuracy using precision slotless connectors’, Microwave Journal, 1988;31 (3):221–26 31 ‘Connector relieves nagging SMA measurement problems’, Microwaves, Jan 1979;97–9 32 Whinnery, J. R., Jamieson, H. W., and Robbins, T. E.: ‘Coaxial line discontinuities’, Proceedings of the Institute of Radio Engineers, 1944;32:695–709 33 Ide, J. P.: ‘Estimating the electrical compatibility of mechanically compatible connectors’, Microwave Engineering Europe, 1994;43:39–40 34 Oldfield, W. W.: ‘Comparing miniature coaxial connectors’, Microwaves and RF, 1985;24 (9):171–74 35 Dimitrios, J.: ‘Exact cutoff frequencies of precision coax’, Microwaves, Jun 1965; 28–31 36 Ramo, S., and Whinnery, J.: Fields and waves in modern radio (John Wiley & Sons, New York, 1959) 37 Marcuvitz, N.: Waveguide handbook, MIT Radiation Laboratory Series 10 (McGraw-Hill Book Company, New York, 1951), pp. 72–80 38 Gilmore, J. F.: ‘TE11 -mode resonances in precision coaxial connectors’, GR Experimenter, 1966;40 (8):10–13 39 Neubauer, H., and Huber, R. F.: ‘Higher modes in coaxial RF lines’, Microwave Journal, 1969;12 (6):57–66 40 Wong, K. H.: ‘Using precision coaxial air dielectric transmission lines as calibration and verification standards’, Microwave Journal, Dec 1998; 83–92 41 Engen, G. F., and Hoer, C. A.: ‘Thru-Reflect-Line: an improved technique for calibrating the dual six-port automatic network analyzer’, IEEE Transactions on Microwave Theory Techniques, 1979;MTT-27 (12):987–93 42 Hoer, C. A., and Engen, G. F.: ‘On-line accuracy assessment for the dual six-port ANA: extension to nonmating connectors’, IEEE Transactions on Instrumentation and Measurement, 1987;IM-36 (2):524–29 43 Ridler, N. M.: A review of existing national measurement standards for RF and microwave impedance parameters in the UK, IEE Colloquium Digest No 99/008, 1999, pp. 6/1–6/6 44 Baxter, W., and Dunwoodie, D.: An easy-to-use method for measuring small SWRs to better than computer-aided accuracy levels, Wiltron Technical Review, No 8, 1978 45 EA: Guidelines on the evaluation of Vector Network Analysers (VNA), EA-10/12, 2000 (Available at www.european-accreditation.org) 46 Ide, J. P.: ‘Traceability for radio frequency coaxial line standards’, NPL Report DES 114, 1992
Connectors, air lines and RF impedance 205 47 Ridler, N. M., and Medley, J. C.: An uncertainty budget for VHF and UHF reflectometers, NPL Report DES 120, 1992 48 Ridler, N. M.: ‘Improved RF calibration techniques for network analyzers and reflectometers’, Microwave Engineering Europe, Oct 1993;35–39 49 Zorzy, J.: ‘Skin-effect corrections in immittance and scattering coefficient standards employing precision air-dielectric coaxial lines’, IEEE Transactions on Instrumentation and Measurement, 1966;IM-15 (4):358–64 50 Kaye, G. W. C., and Laby, T. H.: Tables of physical and chemical constants, 15th edn (Longman, London and New York, 1986), pp. 117–20 51 Gray, D. A.: Handbook of coaxial microwave measurements (General Radio Company, Massachusetts, USA, 1968), Chapter 1 52 Weinschel, B. O.: ‘Errors in coaxial air line standards due to skin effect’, Microwave Journal, 1990;33 (11):131–43 53 Faraday Proctor, R.: ‘High-frequency resistance of plated conductors’, Wireless Engineer, 1943;20:56–65 54 von Baeyer, H. C.: ‘The effect of silver plating on attenuation at microwave frequencies’, Microwave Journal, 1960;3 (4):47–50 55 Somlo, P. I.: The computation of the surface impedance of multi-layer cylindrical conductors, CSIRO National Standards Laboratory (Australia), Report No APR 12, 1966 56 Kilby, G. J., and Ridler, N. M.: ‘Comparison of theoretical and measured values for attenuation of precision coaxial lines’, IEE Electronics Letters, 1992;28 (21):1992–94 57 Hill, D. A.: ‘Reflection coefficient of a waveguide with slightly uneven walls’, IEEE Transactions on Microwave Theory Techniques, 1989;MTT-37 (1):244–52 58 Holt, D. R.: ‘Scattering parameters representing imperfections in precision coaxial air lines’, Journal of Research of NIST (USA), 1989;94 (2):117–33 59 Sanderson, A. E.: ‘Effect of surface roughness on propagation of the TEM mode’, in Young, L. (ed.), Advances in Microwaves, vol. 7 (Academic Press Inc, New York, 1971), pp. 1–57 60 Ridler, N. M.: VHF impedance – a review, NPL Report DES 127, 1993 61 Nelson, R. E., and Coryell, M. R.: ‘Electrical parameters of precision, coaxial, airdielectric transmission lines’, NBS Monograph 96, National Bureau of Standards (USA), 1966 62 Daywitt, W. C.: ‘First-order symmetric modes for a slightly lossy coaxial transmission line’, IEEE Transactions on Microwave Theory Techniques, 1990;MTT-38 (11):1644–51 63 Daywitt, W. C.: ‘Exact principal mode field for a lossy coaxial line’, IEEE Transactions on Microwave Theory Techniques, 1991;MTT-39 (8):1313–22 64 Woods, D.: ‘Relevance of complex normalisation in precision reflectometry’, IEE Electronics Letters, 1983;19 (15):596–98 65 Collin, R. E.: Foundations for microwave engineering, (McGraw-Hill Book Company, New York, 1966) 66 Ridler, N. M., and Medley, J. C.: ‘Calibration technique using new calculable standard for RF reflectometers fitted with GPC-7 connectors’, Conference on
206 Microwave measurements
67 68 69 70 71 72 73
74
75
Precision Electromagnetic Measurements (CPEM) Digest, Boulder, CO, 1994, pp. 117–18 Somlo, P. I.: ‘The computation of coaxial line step capacitances’, IEEE Transactions on Microwave Theory Techniques, 1967;MTT-15 (1):48–53 Razaz, M., and Davies, J. B.: ‘Capacitance of the abrupt transition from coaxialto-circular waveguide’, IEEE Transactions on Microwave Theory Techniques, 1979;MTT-27 (6):564–69 Bianco, B., Corana, A., Gogioso, L., and Ridella, S.: ‘Open-circuited coaxial lines as standards for microwave measurements’, IEE Electronics Letters, 1980;16 (10):373–74 Ridler, N. M., Medley, J. C., Baden Fuller, A. J., and Runham, M.: ‘Computer generated equivalent circuit models for coaxial-line offset open circuits’, IEE Proceedings A, Science, Measurement and Technology, 1992;139 (5): 229–31 Fantom, A. E.: Radio frequency and microwave power measurement (Peter Perigrinus Ltd, London, 1990), Appendix A Ridler, N. M., and Medley, J. C.: Traceable reflection coefficient measurements in coaxial line at MF and HF, IEE Colloquium Digest No 1994/042, 1994, pp. 8/1–8/4 Cox, M. G., Dainton, M. P., and Ridler, N. M.: ‘An interpolation scheme for precision reflection coefficient measurements at intermediate frequencies. Part 1: theoretical development’, IMTC’2001 Proceedings of the 18th IEEE Instrumentation and Measurement Technology Conference, Budapest, Hungary, 21–23 May 2001, pp. 1720–25 Ridler, N. M., Salter, M. J., and Young, P. R.: ‘An interpolation scheme for precision reflection coefficient measurements at intermediate frequencies. Part 2: practical implementation’, IMTC’2001 Proceedings of the 18th IEEE Instrumentation and Measurement Technology Conference, Budapest, Hungary, 21–23 May 2001, pp. 1731–35 Morgan, A. G., Ridler, N. M., and Salter, M. J.: ‘Generalised calibration schemes for RF vector network analysers’, IMTC’2002 Proceedings of the 18th IEEE Instrumentation and Measurement Technology Conference, Anchorage, AL, 21–23 May 2002
Chapter 10
Microwave network analysers Roger D. Pollard
10.1
Introduction
This chapter is intended to cover the basic principles of measuring microwave networks by using a network analyser. The objectives are to discuss the kind of measurements which can be made and the major components in a network analyser covering the basic block diagram, the elements and the advantages and disadvantages of different hardware approaches. Material on error correction is the subject of another chapter. The fundamental concept of microwave network analysis involves incident, reflected and transmitted waves travelling along a transmission line. It must be appreciated, at the outset, that measurement in terms of impedance, which is the ratio of voltage to current, implies knowledge of the characteristic impedance Z0 which describes the mode of propagation in the transmission line. Microwave network analysis is concerned with measuring accurately the incident, reflected and transmitted signals associated with a linear component in a transmission line environment. It is important to appreciate that the same quantities may be defined as different values, for example, return loss, reflection coefficient, VSWR, S11 , impedance and admittance are all ways of describing reflection coefficient, and, similarly, gain, insertion loss, transmission, group delay and insertion phase are all ways of describing transmission coefficient. It is also necessary to understand the fundamental difference between a network analyser and a spectrum analyser. Network analysers are used to measure components, devices and circuits, but a network analyser is always looking at a known signal in terms of frequency and is described as a stimulus–response system. With a network analyser, for example, it is very hard to get an accurate trace on the display, for reasons which will be explained later, but very easy to interpret the results using vector error correction. A network analyser can provide much higher accuracy than a spectrum analyser. Spectrum analysers on the other hand are used to measure signal
208 Microwave measurements characteristics on unknown signals. They are usually a single channel receiver without a source and have a much wider range of IF bandwidths than a network analyser. With a spectrum analyser it is easy to get a trace on the display, but interpreting the results can often be much more difficult than with a network analyser.
10.2
Reference plane
The measurements under consideration are those which characterise travelling waves on a uniform transmission line and the (usually voltage) ratios which are detected are functions of position on the lines. Furthermore, any change in the cross section of the transmission line will give rise to a reflection and the launch of evanescent modes. It is therefore necessary to be able to specify a reference plane which is appropriately located in a sufficient length of uniform transmission line. The reference plane often, but not necessarily, is the plane of contact of the outer conductors of a mating pair of coaxial connectors or a pair of waveguide flanges.
10.2.1 Elements of a microwave network analyser Figure 10.1 shows the general block diagram of a network analyser showing the major signal processing parts.
DUT
Reflected
Source
Signal separation
Incident (R)
Reflected (A)
Transmitted (B)
Receiver/detector
Processor/display
Figure 10.1
General block diagram of a network analyser
Microwave network analysers 209 50 Ω
6 dB Main signal
50 Ω
6 dB Coupled signal
Figure 10.2
Separation of reference signal using power splitter or directional coupler
Four elements are present: (1) source to provide a stimulus, (2) signal separation devices, (3) a receiver for detecting the signals, and (4) a processor and display for calculating and showing the results. 10.2.1.1 Source The signal source supplies the stimulus for the test system and can either sweep the frequency of the source or its power level. Traditionally, most network analysers had a separate source but nowadays the source is often a built-in part of the instrument. The source may be either a voltage-controlled oscillator or a synthesised sweeper. 10.2.1.2 Signal separation This is normally described as the test set, which can be a separate box or integrated into a network analyser. The signal separation hardware must provide two functions. The first is to separate a portion of the incident signal to provide the reference signalling for ratioing. This can be done with a power splitter or a directional coupler (Figure 10.2). Power splitters are usually resistive, non-directional devices and can be very broadband; the trade-off is that they have some loss (usually 6 dB or more) in each port. Directional couplers can be built to have very low loss through the main arm and offer good isolation and directivity, but it is difficult to make them operate at very low frequencies. The second function is to separate the incident and reflected travelling waves at the input to the device under test (DUT). Directional couplers are ideal because they have the necessary directional properties, low loss in the main arm and good reverse isolation. However, owing to the difficulty of making very broadband couplers, directional bridges are often used. Bridges can operate over a very wide range of frequency but exhibit more loss to the transmitted signal resulting in less power delivered to the DUT. A directional coupler is a device that separates a component of the signal travelling in one direction only. In the diagrams in Figure 10.3, the signal flowing through the main arm is shown as a solid line, the coupled signal as a dotted line. Note that the fourth port of the coupler is terminated with a matched load. The signal appearing at the coupled port is a fraction of the input signal; this fraction is the coupling factor. In the example in Figure 10.3, the coupling factor is 20 dB and therefore when 1 mW (0 dBm) is supplied to the input port, 0.01 mW (−20 dBm) will appear at the coupled
210 Microwave measurements Coupling, forward − 20 dBm 0.01 mW Source Z0 0 dBm 1 mW Coupling reverse − 50 dBm 0.00001 mW
−0.046 dBm 0.99 mW This is an error signal during measurements
Source Z0 0 dBm 1 mW
Figure 10.3
−0.046 dBm 0.99 mW
Directional coupler: coupling and directivity
port. Note that as a result there is a small loss through the main arm. The coupling factor is rarely constant with frequency and the frequency response can become a significant measurement error term. In an ideal coupler, there will be no component of a signal travelling in the reverse direction at the coupled port, but in practice a coupler has finite isolation and some energy will leak in the reverse direction. In the example in Figure 10.3, the coupler is reversed and the isolation measured at −50 dB. The most important single parameter for a directional coupler is its directivity, which is a measure of a coupler’s ability to separate signals flowing in opposite directions. It can be thought of as the dynamic range for reflection measurements. By definition, directivity is the ratio between the reverse coupling factor (isolation) and the forward coupling factor. In the example of Figure 10.3, the coupler has a directivity of 30 dB. During a reflection measurement the error signal can be, at best, the directivity below the desired signal. The better the match of the DUT the greater measurement error the directivity error will cause. Directivity error is the main reason that will be seen as a large ripple pattern in many measurements of return loss. At the peak of the ripple, directivity is added in phase with the signal reflected from the device. In other cases the directivity will cancel the DUT reflection, resulting in a sharp dip in the response (Figure 10.4). The directional bridge is similar in operation to the Wheatstone bridge. If all four arms have equal resistance and 50 0001 is connected to the test port then a voltage null will be measured at the detector and the bridge is balanced. If the load at the test port is not 50 0001 then the voltage across the detector is proportional to the mismatch presented by the DUT. If both magnitude and phase are measured at the detector, the complex impedance of the test port can be calculated. A bridge also has an
Microwave network analysers 211 0 Data Max Directivity
Device
Return loss
DUT RL = 40 dB
30
Add in phase
60
Figure 10.4
Device
Directivity
Device
Frequency Data Min
Data = Vector sum
Directivity
Cancel ∴ Data ≈ 0
Return loss ripple caused by coupler directivity
50 Ω
50 Ω standard
50
Ω
50
50 Ω
Ω 50 Ω source
50 Ω detector
Detector
50
Ω
50 Ω
Figure 10.5
Test port Γ
Directional bridge: theoretical and actual circuit
equivalent directivity that is the ratio between the best balance measuring a perfect load and the worst balance measuring an open circuit or a short circuit. The effect of bridge directivity on measurement accuracy is exactly the same as for a directional coupler. The basic arrangement of a directional bridge is shown in Figure 10.5. Notice that in a microwave system there is generally a requirement that one terminal of each component is connectable to ground; the key therefore to designing a successful broadband directional bridge to operate at microwave frequencies is the provision of a suitable balun as shown in Figure 10.5. 10.2.1.3 Detectors and receivers There are two basic ways of providing detection in network analysers – diode detectors, which simply convert the RF to a proportional DC level, or tuned receivers. Diode
212 Microwave measurements
RF R A B
Detector
Bridge
Termination
DUT
Reflection
RF R A B
Detector Detector Transmission
Figure 10.6
DUT
Scalar network analyser measurements using diode detectors
detection is inherently scalar and loses phase information. The main advantages of diode detection are low cost and broadband frequency range which is a significant benefit when measuring frequency translating devices (Figure 10.6). Offset against this is the limited sensitivity and dynamic range and susceptibility to source harmonics and spurious signals. Drift in a diode detector, a major source of measurement error, can be eliminated by the use of AC detection that also reduces noise and susceptibility to unwanted signals. However, the necessary modulation of the RF signal can affect the measurements of some devices (e.g. amplifiers with AGC). The tuned receiver uses a local oscillator (LO) to mix the RF down to an intermediate frequency (IF). The LO is locked either to the RF or to the IF so that the receiver in the network analyser is always correctly tuned to the RF present at the input (Figure 10.7). The IF signal is filtered, which narrows the receiver bandwidth, allows large amounts of gain and greatly improves the sensitivity and the dynamic range. A modern network analyser uses an analogue-to-digital converter (ADC) and digital signal processing to extract the magnitude and phase information from the IF signal. Tuned receivers not only provide the best sensitivity and dynamic range but also provide harmonic and spurious signal rejection. The narrow band IF filter produces a considerably lower noise floor resulting in significant improvement in sensitivity and dynamic range. For example, a microwave network analyser might have a 3 KHz IF bandwidth and an achievable dynamic range, better than 100 dB. The dynamic range can be improved by increasing the input power by decreasing the IF bandwidth
Microwave network analysers 213 IF = FLO ± FRF
RF
ADC / DSP
IF filter
LO
Figure 10.7
Downconverting tuned receiver
or by averaging. This provides a trade-off between noise floor and measurement speed. Averaging reduces the noise floor of the network analyser because complex data are being averaged. Without phase information, as in, for example, a spectrum analyser, averaging only reduces the noise amplitude and does not improve sensitivity. Also because the RF signal is downconverted and filtered before it is measured, any harmonics associated with the source appear at frequencies outside the IF bandwidth and are removed. This eliminates response to harmonics and spurious signals and results in increased dynamic range. A tuned receiver can be implemented with a mixer or a sampler based front-end. It is often cheaper and easier to make wide band front-ends using samplers instead of mixers. The sampler uses diodes to sample very short time slices of the incoming RF signal. Conceptually the sampler can be thought of as a mixer with an internal pulse generator. The pulse generator creates a broadband frequency spectrum (often known as a ‘comb’) composed of harmonics of a local oscillator. The RF signal mixes with one of the spectral lines (or ‘comb-tooth’) to produce the desired IF. Figure 10.8 shows the block diagram of a sampler system. The local oscillator is tuneable and drives a harmonic generator. The output from the harmonic generator drives a diode that can be thought of simply as a switch. In terms of frequency behaviour the output from the harmonic generator provides a comb of harmonics of the local oscillator and by tuning the local oscillator to the right frequency, the difference between the incoming RF and one of the comb-teeth will be exactly the IF frequency which can pass through the IF filter. A phase lock loop will ensure that the local oscillator is always correctly tuned as the source frequency changes. In most modern designs the local oscillator is pre-tuned to ensure that the same comb-tooth of the local oscillator is used every time that the same frequency is input. Compared to a mixer-based network analyser the LO in a sampler-based front-end covers a much smaller frequency range and a broadband mixer is no longer needed. The trade-off is that the phase lock algorithms for locking the various comb-teeth are much more complex. Sampler based front-ends also have a somewhat lower dynamic range than those based on mixers and fundamental local oscillators because the additional noise is converted into the IF from all of the comb-teeth. Nonetheless, network analysers
214 Microwave measurements
IF output
IF filter
Source
Reference oscillator
LO Harmonic generator
IF filter IF = nfLO −fRF LO harmonics
Frequency
Figure 10.8
Principle of operation of a sampling receiver in a network analyser
with narrow band detection based on samplers still have far greater dynamic range than analysers based on diode detection. Dynamic range is usually defined as the maximum power the receiver can measure accurately minus the receiver noise floor. There are many applications requiring large dynamic range, the most common being filter applications. Also the presence of harmonics from the source may create a false response which will be removed by a tuned receiver.
10.3
Network analyser block diagram
Figure 10.9 shows the general schematic of an S-parameter measurement system whilst Figure 10.10 is the block diagram of a modern microwave vector network analyser. The schematic diagram shown in Figure 10.10 is a RF system which has an integrated source and a tuned receiver based on samplers (labelled S). The system can be configured with a three-channel or four-channel receiver and consequently the test set can be either a transmission/reflection type or capable of full S-parameters. There are two basic types of test set that are used with network analysers for transmission/reflection (TR) test sets. The RF power always comes out of test port 1 and test port 2 is always connected to a receiver. To measure reverse transmission
Microwave network analysers 215 RF source
a0
a3 IF
IF
LO source IF
IF b0
b3
Port - 1
Port - 2 a1
Cable
b2
Cable
DUT b1
IF
a2
Figure 10.9
Proc display
A/D
BPF
Schematic of an S-parameter measurement system Synthesiser 15 MHz to 60 MHz
996 kHz
MUX Reference
RF
detector
Test set
300 kHz to 3 GHz Phase lock
DUT
Source
Figure 10.10
Test set
A
S
B
S
R
S
4 kHz
4 kHz
4 kHz
ADC
CPU Digital control
Receiver
Block diagram of an RF network analyser
Display
216 Microwave measurements or output reflection the device must be disconnected, turned around and reconnected again. TR-based network analysers offer only response and one-port calibration so measurement accuracy is not as good as the one that can be achieved using S-parameter test sets. An S-parameter test set allows both forward and reverse measurements without reconnection and allows characterisation of all four S-parameters. RF power can come out of either test port 1 or test port 2 and either test port can be connected to a receiver. The internals rearrangement is carried out by switches inside the test set. These are usually solid-state switches which are fast and do not wear out. Although it is possible to configure an S-parameter test set with only three samplers or mixers the architecture provides fewer choices for calibration as does a four receiver architecture. The display and processor section allows in current systems is usually an in-built, full-featured PC that not only the reflection and transmission data to be formatted in many ways to allow for easy display, comparison and interpretation but also supports algorithms for calibration, data storage and various other features.
Further reading Warner, F. L.: ‘Microwave vector network analysers’ in Bailey, A. E. (ed.), Microwave Measurements, 2nd edn (Peter Peregrinus Ltd, London, 1989), Chapter 11
Chapter 11
RFIC and MMIC measurement techniques Stepan Lucyszyn
11.1
Introduction
All electronic sub-systems are made up of devices and networks. In order to simulate the overall performance of a sub-system under development, all the components that make up the sub-system must be accurately characterised. To this end, precision measurement techniques must be employed at component level. Not only do precision measurements enable a manufacturer to check whether devices are within their target specifications, and to monitor variations in parameter tolerances due to process variations, they also allow more accurate empirical models to be extracted from the measurements and help new modelling techniques to be validated. Also, the operation and performance of some experimental devices can often only be understood from accurate measurements and subsequent modelling. Conversely, poor measurements could result in the needless, and therefore expensive, redesign of high-performance components or sub-systems. Devices and networks are traditionally characterised using Z, Y or h-parameters. To measure these parameters directly, ideal open and short circuit terminations are required. These impedances can be easily realised at low frequencies. However, at microwave frequencies such impedances can only be achieved over narrow bandwidths (when tuned circuits are employed) and can also result in circuits that are conditionally stable (when embedded within a ‘matched load’ reference impedance environment) becoming unstable. Fortunately, scattering- (or S)- parameters can be determined at any frequency. To perform such measurements, the device under test (DUT) is terminated with matched loads. This enables extremely wideband measurements to be made and also greatly reduces the risk of instability; however, only when the DUT is terminated with near ideal matched loads (this is irrespective of whether the measurement system is calibrated or not). S-parameter measurements
218 Microwave measurements also offer the following advantages: (1) Any movement in a measurement reference plane along an ideal transmission line will vary the phase angle only. (2) For a linear device or network, voltage or current and measured power are related through the measurement reference impedance (normally 75 or 50 0001 for coaxial lines and 1 0001 for rectangular waveguides). (3) With some passive and reciprocal structures, ideal S-parameters can be deduced from spatial considerations, enabling the measurements of the structure to be checked intuitively. By applying a known incident wave to the DUT and then measuring the reflected and transmitted wave amplitudes, S-parameters can be calculated from the resulting wave amplitude ratios. The equipment most commonly used to perform this measurement is called a vector network analyser (VNA) [1]. The DUT can now be characterised using complete S-parameter measurements (along with DC measurements). The element values associated with the small-signal equivalent circuit model of the DUT can be determined using direct calculations, iterative optimisation and intuitive tuning. This process is referred to as parameter extraction. With a radio frequency integrated circuit (RFIC), also known as a monolithic microwave integrated circuit (MMIC), either a test fixture or probe station is employed to secure the MMIC in place and to provide a stable means of electrically connecting the MMIC to the measurement system [2]. In this chapter, the use of test fixtures and probe stations at ambient room temperature is reviewed and their role at thermal and cryogenic temperatures is discussed. Finally, with the increasing need for performing non-invasive (or non-contacting) measurements, experimental field probing technologies are introduced.
11.2
Test fixture measurements
Although probe stations result in much more accurate and reproducible measurements, test fixtures are still widely used. The principal reasons are that they are very much cheaper than probe stations and they offer a greater degree of flexibility, such as facilitating larger numbers of RF ports and enabling DC bias circuitry and any offchip resonators to be located next to the chip. Also, the heat dissipation required when testing monolithic power amplifiers can be easily provided with test fixtures. In addition, test fixtures are ideally suited when RF measurements are required during temperature-cycling and when cryogenic device characterisation is required [3–5]. An illustration of a basic two-port test fixture is shown in Figure 11.1. Most test fixtures are, in principle, based on this generic design, typically consisting of four different components: (1) a detachable metal chip carrier with high-permittivity substrate, (2) a rigid metal housing, (3) connector/launchers and (4) bond wires. The MMIC is permanently attached to the chip carrier with either conductive epoxy glue or solder. The metal housing is employed to hold the chip carrier and the connector/launchers in place. The launcher is basically an extension of the coaxial
RFIC and MMIC measurement techniques 219 50 Ω microstrip transmission line Microstrip launcher
Bond wires
Housing Ridge-mounted MMIC under test
50 Ω coaxial cable/connector to the VNA Coaxial calibration VNA reference plane
50 Ω flange-mounted coaxial connector Chip carrier High permittivity ground plane chip carrier substrate
Figure 11.1
Chip carrier
Generic design of a two-port test fixture
connector’s centre conductor, which passes through the housing wall to make electrical contact with the associated chip carrier’s microstrip transmission line. Bond wires or straps are used to connect the other end of the microstrip line to the MMIC under test. The parasitic element values associated with a test fixture are typically an order of magnitude greater than those of the MMIC under test. Before any accurate measurements can be performed, measurement systems must first be calibrated, in order to correct for the systematic errors resulting from the numerous reflection and transmission losses within the measurement system. A calibration kit is required to perform this calibration procedure. This ‘cal. kit’ has a number of electrical reference standards and software that must be downloaded into the VNA’s non-volatile memory or associated PC/workstation controller. For a two-port measurement system, the calibration standards must: (1) define the primary reference planes; (2) remove any phase ambiguity using open circuit and/or short circuit reflection standard(s); and (3) define the reference impedance using delay line, matched load or attenuator impedance standard(s). Some of the various combinations of different standards that can be employed in a two-port calibration procedure are listed in Table 11.1. The software should contain accurate models for the associated standards and the algorithms required to implement the chosen calibration method. The accuracy of subsequent measurements ultimately depends on how well all the standards remain characterised. Any deviation in the electrical parameters of the standards will degrade the magnitudes of the effective directivity and source match for the measurement system. As a result, great care must be taken to look after these calibration standards. The non-idealities of a measurement system are characterised using mathematical error correction models, represented by flow diagrams (also known as error adapters or boxes). The function of the calibration procedure is to solve for the error coefficients in these models by applying the raw, uncorrected, S-parameter measurements of the
220 Microwave measurements Table 11.1
Common calibration methods
Method
Calibration standard Through L=0
TRL LRL TRM LRM TRA LRA TSD
• • • •
Reflect
L 0002= 0
• • •
Reference impedance
ρ1 = ρ2
Line
• • • • • • ρ = −1
• •
•
Match
• •
Atten.
• •
standards to a set of independent linear equations. The basic two-port calibration procedures have an eight-term error model (four terms associated with each port) and require only three standards. These error terms should correspond directly to the raw hardware performance, including the directivity, source match and frequency tracking. A more accurate 12-term error model, as used in two-port coaxial calibration, takes crosstalk and the effects of impedance mismatches at the RF switches within the VNA’s test-set into account. Once the calibration procedure has been performed, it can be verified by measuring separate verification standards.
11.2.1 Two-tier calibration One method of calibrating the measurement system is to split the process into two tiers [6]. Initially, a coaxial calibration is performed, where the VNA reference planes are located at the end of its cable connectors. Historically, the VNA was calibrated using short-open-load-through (SOLT) standards. These lumped-element standards can give high-quality coaxial calibrations across an ultra-broad bandwidth (e.g. DC to 50 GHz), so long as all the standards remain accurately characterised across the entire bandwidth. Since test fixtures are far from ideal, a second process is required to shift the initial VNA reference planes to the MMIC under test, in order to eliminate the effect of the test fixture. This second process is known as de-embedding or deconvolution [7]. To perform de-embedding it is necessary to accurately characterise the test fixture [8]. Another reason why you may need to characterise a test fixture is when multiple RF port MMICs are to be measured using a two-port VNA [9]. Here, power reflected from impedance-mismatched loads on the auxiliary ports of the MMIC can result in significant measurement errors. These errors will increase as the mismatch losses increase and/or the number of RF ports increases. As a result, MMICs that have more RF ports than the VNA require all the loads to be individually characterised, and a further process of matrix renormalisation [9–13] in order to remove the effects of
RFIC and MMIC measurement techniques 221 the mismatched loads on the auxiliary ports. Three methods that can, in principle, be employed to characterise a test fixture are (1) time-domain (T-D) gating, (2) in-fixture calibration and (3) equivalent circuit modelling. 11.2.1.1 Time-domain gating Some VNAs can be upgraded with a synthetic-pulse T-D reflectometry (TDR) option [14–20]. Here, the discrete form of the inverse Fourier transform (IFT) is applied to a real sequence of harmonically related frequency-domain (F-D) measurements; in our case, of the MMIC embedded within its test fixture. This is directly equivalent to mathematically generating synthetic unity-amplitude impulses (or unity-amplitude steps), which are then ‘applied’ to the embedded MMIC. The resulting T-D reflection and transmission responses can then be analysed to provide information about the MMIC and test fixture discontinuities. In reflection measurements, it is possible to remove the effects of unwanted impedance mismatches or else isolate and view the response of an individual feature. With a multiple port test fixture, transmission measurements can give the propagation delay and insertion loss of signals travelling through a particular path by removing the responses from the unwanted paths. With an MMIC fed with transmission lines that only support a pure TEM mode of propagation, time and actual physical distance are simply related: 0001 c0003tζ /2 with reflection measurements Physical distance = c0003tζ with transmission measurements where c is the speed of light in free space; 0003t is the time difference, relative to a √ reference (e.g. t = 0); and ζ = 1/ εr is the velocity factor. Also, F-D nulls in |S11 | are at frequency harmonics of 1/0003t, where 0003t is the time difference between two reflected impulses. If the feed lines are non-TEM, and therefore dispersive, impulse spreading will occur, which could significantly distort the impulse shape (in time and amplitude). If the dispersive nature is known, the frequency sweep can be pre-warped [20]. With either a banded VNA (which may cover just one of the main waveguide bands), or a broadband VNA, the band-pass T-D mode can be selected, where only synthetic impulses are generated. This is useful for band-limited guided-wave structures (e.g. rectangular waveguides). In general, in this mode, only the magnitudes of the individual reflection and transmission coefficients are available. As a result, the exact nature of any discontinuity (e.g. resistive, inductive and capacitive) cannot be identified. However, it is still possible to extract some information about the nature of a defect in band-pass mode with a phasor impulse. With a broadband VNA, a low-pass T-D mode is also available where both synthetic impulses and synthetic steps can be generated. The low-pass mode is used to emulate a real-pulse TDR measurement system. This allows the user to identify the nature of any discontinuity. F-D measurements are taken from the start frequency, f1 , to the stop frequency, f2 . When compared with band-pass, for the same bandwidth (i.e. frequency-span) B = f2 − f1 , the low-pass mode offers twice the response resolution in the T-D. However, with the low-pass mode, the F-D measurements must be
222 Microwave measurements harmonically related, from DC to f2 , such that f2 = nfd f1 , where nfd is the number of points in the F-D (e.g. 51, 101, 201, 401 and 801). The DC data point is extrapolated from the f1 measurement. However, if the measurement at f1 is noisy, the T-D trace will be unstable and difficult to interpret. In TDR, the width of a band-limited unit impulse (or window function) is defined as the interval between its two half-amplitude (i.e. −6 dB power) points. The corresponding response resolution is defined as the interval between two impulses that are just distinguishable from each other as separate peaks. With equal amplitude impulses, the response resolution is equal to the 6 dB impulse width. With no window function applied to the F-D measurements: 1.2 for band-pass B 6 dB Impulse width = 0.6 for low-pass B 2 for band-pass B Main Lobe’s null-to-null width = 1 for low-pass B The time range is the length of time that measurements can be made without encountering a repetition of the same response. The range must be set longer than the furthest discontinuity, otherwise aliasing will occur, where out-of-range discontinuities will fold-over and appear in-range at (two range – target position) Range =
1 0003f
where 0003f = B/(nfd − 1). If a feature lies exactly midway between two T-D points then the energy associated with the discontinuity will be distributed between the two points, resulting in the displayed amplitude being reduced by almost 4 dB [20]. Therefore, care must be taken to ensure there is sufficient range resolution (or point spacing) in the T-D. Range resolution =
Range ntd
where ntd is the number of points in the T-D. The point spacing can be reduced to any desired level, at the expense of processing time, by using a chirp-Z fast Fourier transform algorithm. This allows range to be replaced by an arbitrary display time-span in the above range resolution equation. It is worth noting that with range and range resolution, either the one-way time or round-trip time may be quoted, depending on the manufacturer. De-embedding using synthetic-pulse TDR is not de-embedding in the true sense. It is specifically T-D gating, which can isolate a time feature and emphasise its frequency response. With time-gating, a mathematical window (called a gate or time filter) is used to isolate the embedded MMIC,so that only the MMIC’s frequency
RFIC and MMIC measurement techniques 223 response can be emphasised. When the gate is switched on, all reflections outside the gate are set to zero. This is equivalent to terminating the MMIC with the complex conjugate of its respective port impedance(s). The synthetic-pulse TDR option can be a very useful tool, although it can suffer from a number of sources of errors [15,19,20]; some of these are listed as follows: (1) Noise errors [15]. (a) Sweep mode: The VNA’s synthesised source can be operated in either the ramp-sweep or step-sweep mode. With the former, small non-linearities and phase discontinuities generate low-level noise sidebands on the T-D impulse and step stimuli. However, with the step-sweep mode, the improved source stability eliminates these noise sidebands and improves the T-D’s dynamic range by as much as 30 dB. Moreover, to reduce the noise floor of the T-D measurements further, the step-sweep mode enables more averaging of the F-D measurements, compared with the ramp-sweep mode, without greatly increasing the sweep time. (b) Bandwidth: The noise floor in the T-D response is directly related to noise in the F-D data. Therefore, the number of F-D data points taken at, or below, the system’s noise floor can be minimised by reducing the frequency-span to the bandwidth of the MMIC. (c) Test-set: If the test-set does not have a flat response down to the start frequency then the reduction in the F-D’s dynamic range towards f1 will cause an increase in the T-D’s noise floor, the resulting trace bounce, in the low-pass mode, can be improved by turning on T-D trace averaging. (2) Frequency-domain window errors. There is usually a choice of F-D window functions (e.g. Kaiser–Bessel) that can be applied prior to the IFT, for example, minimum (0th order), normal (6th order) and maximum (13th order). The minimum window has a rectangular function that produces the sin x/x impulse shape, having the minimum 6 dB impulse width and also the maximum sidelobe levels (with a minimum sidelobe suppression of only 13 dB in its power response). The other two window functions reduce the sidelobe levels (with a minimum suppression of 44 and 98 dB, respectively) at the expense of a wider impulse (by a factor of 1.6 and 2.4, respectively). It will be seen that a trade-off has to be made when choosing the F-D’s windowing function, between the desired resolution and dynamic range in the T-D. Note that this windowing function does not affect the displayed F-D response. (a) Time resolution errors: With narrow bandwidth VNAs, the impulse may be too wide. As a result, it may be difficult to resolve the MMIC and the connector/launchers features, down to the baseline, when the associated discontinuities are too close to one another. In practice, the MMIC should be separated by at least two 6 dB impulse widths from the connector/launcher.
224 Microwave measurements (b) Dynamic range errors: Impulse sidelobes limit the dynamic range of the T-D responses, since the sidelobes from a large impulse can hide a small adjacent target impulse. (c) Moding errors: If the bandwidth of the VNA is too high, such that overmoding in transmission lines or box mode resonances occur in the test jig, the T-D responses become un-interpretable. (d) Out-of-band response: The amplitude of the impulses represents the average value over the entire frequency-span. Therefore, the displayed amplitude of an impulse can be different from the expected value if the frequency-span includes an MMIC with a non-flat frequency response; for example, having highly abrupt out-of-band characteristics. (3) Discontinuity errors. (a) Masking errors: If the target discontinuity is preceded by other discontinuities that either reflect or absorb energy, then these other discontinuities may remove some of the energy travelling to and emanating from the target discontinuity. The trailing edge of earlier features can also obscure the target feature. (b) Multi-reflection aliasing errors: Multiple reflections between discontinuities can cause aliasing errors. For example, if a two-port MMIC is positioned midway between two connector/launchers, reflection from the furthest connector/launcher will be corrupted by multiple reflections between the MMIC and the nearest connector/launcher. (4) Time-domain window errors. In practice, a time filter having a non-rectangular response is used for gating, otherwise the sin x/x weighting would be conveyed to the F-D. There is usually a choice of T-D window functions that can be applied before the Fourier transform: minimum, normal, wide and maximum. The minimum window has the fastest roll-off and largest sidelobes, while the maximum window has the slowest roll-off and smallest sidelobes. (a) Baseline errors: The gate-start and gate-stop times, which define the −6 dB gate-span of the filter, must be set at the baseline if low frequency distortion in the F-D is to be minimised [14]. (b) Truncation errors: A limited gate width may truncate lengthy target features. To minimise truncation error, the wider gates are preferred. (c) Sidelobe errors: The time filter sidelobes may ‘see’ earlier or subsequent features. This could significantly corrupt the F-D response of the target feature. To minimise sidelobe errors, the wider gates are preferred. (d) Gate offset errors: F-D distortion can occur if the gate-centre is offset from the centre of the target feature(s). This is because a nearsymmetrical target response may lose its symmetry when applied to a time-offset gate that has significant in-gate attenuation. To minimise gate offset errors, the wider gate shapes are preferred.
RFIC and MMIC measurement techniques 225 (e) Minimum gate-span errors: The gate-span must be set wider than the minimum value, otherwise the gate will have no passband and may have high sidelobe levels. (f) Attenuation errors: For a fixed gate-span, the level and duration of in-gate attenuation may be excessive with wider gates. (g) Reflection/transmission switching errors: If gating is performed on a voltage reflection coefficient response then the associated return loss F-D measurement is valid. If the same gating times are applied to the voltage transmission coefficient response(s) then this may not be appropriate. For example, when a two-port MMIC is not placed midway between connectors, the transmission pulse may not be fully enclosed within the reflection response’s gate. The resulting insertion loss F-D measurement will not represent accurate de-embedding. As an example, a gallium arsenide (GaAs) MMIC with a 2.9 mm length of 55 0001 microstrip through-line was placed at the centre of a 25.4 mm alumina chip carrier. An Agilent Technologies 8510B VNA was calibrated with a 20 GHz bandwidth and 401 frequency points. The band-pass mode was selected with a minimum F-D windowing function. This combination provides a minimum response resolution and maximum range values of 60 ps and 20 ns, respectively. The F-D power responses are shown in Figure 11.2a. The corresponding T-D response of the input port’s voltage reflection coefficient is shown in Figure 11.2b. Here, the first and last peaks correspond to the impedance mismatches associated with the coaxial-to-microstrip transitions of the input and output ports, respectively. The two centre peaks correspond to the reflections associated with the microstrip-to-MMIC transitions. It will be apparent from Figure 11.2b that accurate de-embedding would not be possible using T-D gating. This is because the unwanted reflections cannot be resolved down to the baseline. If de-embedding was attempted in the above example then the ripples in the F-D responses would be smoothed out, as one would expect, although this would not constitute accurate de-embedded measurements. In order to achieve accurate deembedded measurements, a VNA with more bandwidth, or alternatively, a real-pulse TDR system having ultra-short impulses, can be used. 11.2.1.2 In-fixture calibration In general, a quality test fixture is much cheaper to buy than a probe station. Suitably designed quality test fixtures can be accurately characterised using in-fixture calibration techniques. As with coaxial calibration, the most appropriate algorithms use a combination of through, reflection and delay line standards, with common methods being through-reflect-match (TRL), TSD and line-reflect-line (LRL). The main reason for employing these types of calibration is that only one discrete impedance standard is required, such as an open or short, which is relatively easy to implement. The matched load is avoided; this is advantageous, as it is more difficult to fabricate non-planar 50 0001 loads to the same level of accuracy that can be
226 Microwave measurements achieved with low dispersion transmission lines. However, there are still significant disadvantages with in-fixture calibration: (1) Multiple delay lines may be required for wideband calibration (any one line must introduce between about 20 and 160 of electrical delay to avoid phase ambiguity, limiting the bandwidth contribution of each line to an 8:1 frequency range). (2) The use of multiple lines can add uncertainty to the measurements, since the launchers are continually being disturbed during calibration, although freely available software (called MultiCal™) can eliminate the effects of non-repeatability, by measuring either the same line a number of times or different lengths of line, in order to reduce the uncertainty [21]. (3) A frequency-invariant measurement reference impedance must be taken from the characteristic impedance, Z0 , of the delay lines, however, frequency dispersion in microstrip lines may not always be corrected for. In practice, the Z0 of the lines can be determined using TRL calibration [22,23] and then subsequent measurements can be renormalised to any measurement reference impedance. (4) The high level of accuracy is immediately lost with test fixtures that employ poor quality components and/or non-precision assembly. (5) The calibration substrates dictate and, therefore, restrict the location of the RF ports. (6) For devices with more than two ports the calibration procedure must be significantly extended and all the results from this routine must be easily stored and retrieved. (7) The microstrip-to-MMIC transition is not taken into account. 11.2.1.3 Equivalent circuit modelling Test fixtures made in-house tend to be simple in design, such as the type shown in Figure 11.1, and cost only a small fraction of the price of a good quality commercial test fixture. Unfortunately, these non-ideal test fixtures suffer from unwanted resonances [24], poor grounding [25] and poor measurement repeatability. The problem of unwanted resonances can be clearly seen in the F-D responses of Figure 11.2a. Here, the resonances at 3 and 12 GHz are attributed to the production grade coaxial connectors used in the test fixture. Because of poor repeatability, employing elaborate and expensive calibration techniques to characterise such fixtures would appear unjustified, because significant measurement degradation is inherent. As an alternative, equivalent circuit models (ECMs) can provide a crude but effective means of de-embedding. This ‘stripping’ process results in about the same level of degradation as would be found if in-fixture calibration was used with a non-ideal test fixture, but with minimal expense and greater flexibility. Also, ECMs based on the physical structure of the fixture have demonstrated a wide bandwidth performance. The ECMs can be easily incorporated into conventional F-D simulation software packages. They can also be employed to simulate packaged MMICs. An example of an ECM for a test fixture similar to the one in Figure 11.1 is shown in Figure 11.3. This model has
RFIC and MMIC measurement techniques 227 (a)
(b)
Figure 11.2
Embedded 55 0001 MMIC through-line: (a) frequency-domain power responses and (b) corresponding time-domain response for the input voltage reflection coefficient
228 Microwave measurements SMA connector/wedge-shaped launcher model
Coaxial connector
Lossy microstrip line model
Coax-to-microstrip transition C2
VNA reference plane
Figure 11.3
R1 TLINE 1 TLINE 2 TLINE 3
Z01 0001r1 00021 I1
Bond wire model
Z02 0001r2 00022 I2
Z03 0001r3 00023 I3
Wire 1 TLINE 4
R2 L1
Wire 2 L2 C1
Z04 0001r4
Im(i)
MMIC reference plane
Cf
I4
Equivalent circuit model of a microstrip test fixture
demonstrated a sufficient degree of accuracy from DC to 19 GHz for the popular Omni-Spectra SMA connector/wedge-shaped launcher [9], which is similar to the more popular SMA printed circuit board socket. The exact nature of the ECM, the element values and the microstrip parameter data are extracted from through-line measurements of the test fixture. Both a direct microstrip through-line and an MMIC through-line should be used in order to provide more information for the parameter extraction process, and to make it possible to model the microstrip-to-MMIC transition accurately. De-embedding can be carried out with most F-D CAD packages by converting the ECM into a series of negative elements connected onto the ports of the measured data. Some CAD packages provide a ‘negation’ function that allows the ECM sub-circuit to be directly stripped from the measured data. With either method, the order of the node numbers is critical, and the de-embedding routine should be verified. In addition to those already mentioned, de-embedding using equivalent circuit modelling has the following advantages: (1) dispersion in the microstrip lines does not have to be corrected for in the VNA’s calibration; (2) there is no restriction by the calibration procedure on the location of the RF ports; (3) systematic errors resulting from variations in the characteristic impedance of the chip carrier’s microstrip lines, due to relaxed fabrication tolerances, can easily be corrected for; (4) bond wires [26] and the microstrip-to-MMIC transition can be modelled [27]; (5) resonant mode coupling between circuit components, due to a package resonance, can also be modelled [24]. Better still, package resonances can, in some instances, be removed altogether [28,29].
RFIC and MMIC measurement techniques 229
Figure 11.4
Photograph of the Anritsu 3680V universal test fixture
11.2.2 One-tier calibration Improved contact repeatability and prolonged contact lifetime are two considerations that favour the two-tier process [6], as they are only assembled once with T-D gating and ECMs. In practice, however, to achieve the best performance, in-fixture TRL or line–network–network [30] calibration is applied directly to a quality test fixture, without the need for the two-tier coaxial calibration/de-embedding process. This onetier calibration procedure gives more accurate measurements than the two-tier method, since de-embedding is inherently prone to errors, and the propagation of measurement errors is reduced [6]. Using this approach, the Anritsu 3680 V universal test fixture, shown in Figure 11.4, can perform repeatable measurements up to 60 GHz. At the time of writing, a number of other companies produce test fixtures for accurate in-fixture calibration, including Agilent Technologies, Intercontinental Microwave, Argumens and Design Techniques. They are either split-block fixtures, with a removable centre section, or they use launchers attached to sliding carriages. With the high levels of accuracy that can be achieved using quality test fixtures, the poor characterisation of bond wires, due to the poor repeatability of conventional manually operated wire-bonding machines, becomes significant. Improvements in the modelling accuracy and physical repeatability of the microstrip-to-MMIC transition when using automatic wire-bonding assembly techniques have been reported [27]. In addition, flip-chip technology (also known as solder-bump technology) is now well established [31–39]. Here, a tiny bead of solder is placed on all the MMIC bond pads and the MMIC is placed upside down directly onto the chip carrier. When heated to the appropriate temperature, the solder flows evenly and a near perfect connection
230 Microwave measurements is made between the MMIC pad and its associated chip carrier pad. The advantages of this technology over bond wire technology, for the purposes of measurements, are its ultra-broad bandwidth, superior contact repeatability and high characterisation accuracy of the carrier’s transmission line-to-MMIC transition.
11.2.3 Test fixture design considerations The following guidelines are useful when selecting, designing or using a test fixture: (1) Split-block test fixtures [5,40] are ideal for two-port in-fixture TRL calibration, since they can provide good repeatability. Here, a short circuit standard is preferred, since significant energy may be radiated with an open circuit standard. (2) Side walls can form a waveguide or resonant cavity. The size of the waveguide/cavity should be made small enough so that the dominant mode resonant frequency is well above the maximum measurement frequency. Carefully placed tuning screws and/or multiple RF absorbing pads can eliminate or suppress unwanted modes [28,29]. (3) Poor grounding, due to excessively long ground paths and ground path discontinuities, must be avoided. (4) Avoid thick chip carrier substrates, wide transmission lines (sometimes used for off-chip RF de-coupling) and discontinuities, in order to minimise the effects of surface wave propagation and transverse resonances at millimetric frequencies. Transverse currents can be suppressed by introducing narrow longitudinal slits into the low impedance lines. (5) Use substrates with a high dielectric constant to avoid excessive radiation losses and to minimise unwanted RF coupling effects. (6) New precision connector/launchers should be used whenever possible, and measurements should be performed below the connector’s dominant TEM mode cut-off frequency. (7) Launchers should be separated from the DUT by at least three or four times the substrate thickness, so that any higher-order evanescent modes, generated by the non-ideal coax-to-microstrip transition, are sufficiently attenuated at the DUT.
11.3
Probe station measurements
Until relatively recently, the electrical performance of an MMIC was almost always measured using test fixtures. Nowadays, extremely accurate MMIC measurements can be achieved using probe stations. Such techniques were first suggested for use at microwave frequencies in 1980 [41], demonstrated experimentally in 1982 [42], and introduced commercially by Cascade Microtech in 1983. During the past two decades there have been rapid developments in probe station measurement techniques. Today, the partnership between Cascade Microtech and Agilent Technologies provides a total solution for on-wafer probing, which can perform repeatable
RFIC and MMIC measurement techniques 231 F-D measurements at frequencies as high as 220 GHz [43], although single-sweep measurements from 45 MHz to 110 GHz are routinely undertaken. When compared with test fixtures, commercial probe station measurements have the following advantages: (1) they are available in a single-sweep system from DC to 110 GHz; (2) they are more accurate and much more repeatable, since they introduce much smaller systematic errors; (3) they have a simpler calibration procedure, which can be automated with on-wafer calibration and verification standards [12,44]; (4) they enable the VNA measurement reference planes to be located at the probe tips or at some distance along the MMIC’s transmission line; in the latter case, transition effects can be removed altogether; (5) they provide a fast, non-destructive means of testing the MMIC, thus allowing chip selection prior to dicing and packaging; and (6) banded measurements are possible up to 220 GHz. Overall, the microwave probe station can provide the most cost effective way of measuring MMICs when all costs are taken into account.
11.3.1 Passive microwave probe design At frequencies greater than a few hundred megahertz, DC probe needles suffer from parasitic reactance components, due to the excessive series inductance of long thin needles and shunt fringing capacitances. If the needles are replaced by ordinary coaxial probes that are sufficiently grounded, measurements up to a few gigahertz can be achieved. The upper frequency is ultimately limited by the poor coax-to-MMIC transition. A tapered coplanar waveguide (CPW) probe provides a smooth transition with low crosstalk. Cascade Microtech have developed tapered CPW probes and microstrip hybrid probes (Infinity) that enable measurement to be made from DC to 110 GHz with a single coaxial input. With waveguide input, 50–75 GHz (V-band) or 75–110 GHz (W-band) [43] probes are available in both the tapered waveguide and Infinity versions, as shown in Figure 11.5. The Infinity probes are also available for 90–140 GHz (F-band), 110–170 GHz (D-band) and 140–220 GHz (G-band) operation. The maximum frequency limit for coaxial-input probes is imposed by the onset of higher-order modes propagating in the conventional coaxial cables and connectors. For W-band operation, Agilent Technologies developed a coaxial cable and connector that has an outer screening conductor diameter of only 1 mm, while Anritsu have their own 1.1 mm coaxial technology. A photograph illustrating the use of Agilent’s 1 mm coaxial technology to give state-of-the-art performance up to 110 GHz, with a Cascade Microtech Summit 12000 probe station, is shown in Figure 11.6. This arrangement uses the latest Agilent N5250 110 GHz VNA. Fully automatic calibration of the probing system can be performed up to 110 GHz. The D-band version is shown in Figure 11.7.
232 Microwave measurements
Figure 11.5
Photograph of a waveguide input Infinity probe
In the past, the tapered coplanar waveguide probe was made from an alumina substrate or an ultra-low-loss quartz substrate. The probe tips that made the electrical contacts consisted of hard metal bumps that were electroplated over small cushions of metal, allowing individual compliance for each contact. As the probes were overtravelled (in the vertical plane) the probe contacts wiped or ‘skated’ the MMICs’ probe pads (in the horizontal plane). One of the major limitations of these tapered CPW probes was their short lifetime, since the substrate had limited compliance and the probe contacts could wear down quite quickly. As a result, the more the probe was used, the more over-travel had to be applied to them. Eventually, either the probe substrate begins to crack or the probe tips fall apart. For this reason, GGB Industries developed the Picoprobe™. This coaxial probe is more compliant and can achieve operation between DC and 120 GHz, with a coaxial input, and between 75 and 120 GHz with a waveguide input [45]. From DC to 40 GHz, this probe has demonstrated an insertion loss of less than 1.0 dB and a return loss better than 18 dB. However, one potential disadvantage of coaxial probes is that the isolation between probes may be limited when operating above V-band. For even better compliancy, durability, ruggedness and flexibility, Cascade Microtech developed the Air Coplanar™ tipped coaxial probe [46]. This probe has demonstrated an insertion loss of less than 1.0 dB from DC to 110 GHz and can operate at temperatures from −65 to +200 ◦ C. A cross-sectional view and photograph can be seen in Figure 11.8.
RFIC and MMIC measurement techniques 233
Figure 11.6
Single-sweep, 10 MHz to 110 GHz, on-wafer probing system with Agilent’s N5250 110 GHz PNA series network analyser and the Summit 12971 probe
Cascade Microtech still produce the ACP probe, as it is useful for applications that require high power/bias use (above 500 mA), poor contact planarity, large pitches (above 250 µm) or temperatures above 125 ◦ C. Cascade Microtech’s latest generation of Infinity probes, shown in Figure 11.9, was initially designed to improve the contact resistance characteristics of probing onto aluminium pads but it also has significant advantages for probing onto gold pads. Figure 11.10 shows a comparison between the resistance characteristics of the tungsten ACP probe and Infinity probe, when probing onto aluminium. Inherent to the design is a coaxial-to-microstrip transition. This, in turn, uses vias to connect to extremely small contacts. The microstrip construction ensures vastly improved isolation between the underside of the probe and the measurement of the substrate underneath, allowing adjacent devices to be placed closer to the test structure. This design also dramatically improves the calibration and crosstalk characteristics. Moreover, as a result of the reduced contact size, as shown in Figure 11.11, the damage to the contact pads is also greatly reduced; this is very useful for tests that require multiple tests or with applications where very little pad damage is allowed.
234 Microwave measurements
Figure 11.7
Photograph of the banded, 110–170 GHz, on-wafer probing system Coaxial connector (b) (2.92, 2.4, 1.85 or 1mm)
(a)
Block
Hard absorber Absorber
Air coplanar waveguide
Figure 11.8
Soft absorber Low-loss cable
APC probe: (a) cross-sectional view of construction and (b) photograph
When selecting the type of microwave probe required, it is necessary to supply the vendor with the following specifications: (1) Footprint: Ground–signal–ground (GSG) is the most common for MMICs, although ground–signal (GS) probes are used below 10 GHz. (2) Probe tip contact pitch (i.e. distance between the mid-points of adjacent contacts): For microwave applications, 200 µm is very common, although
RFIC and MMIC measurement techniques 235 (a)
(b) Coax
Thin-film microstrip
Figure 11.9
Infinity tip: (a) illustration and (b) contact bumps in contact with wafer 0.25
Contact resistance, Ω
Conventional tungsten ACP
0.2 0.15 0.1 0.05
Infinity probe
0 0
1000
2000
3000
4000
5000
Figure 11.10
Variation of contact resistance with touchdowns for conventional tungsten ACP and Infinity probes
Figure 11.11
Contact damage from Infinity probes, typically 12 × 25µm2
236 Microwave measurements
(3) (4) (5) (6)
probes are commercially available with pitches ranging from 50 to 1250 µm. Smaller pads result in smaller extrinsic launcher parasitics. A 100 µm pitch is commonly used from applications in the 40–120 GHz frequency range, while 75 µm is used above 120 GHz. Probe tip contact width: 40 and 25 µm are typical for operation up to 65 and 110 GHz, respectively. Probe tip contact metal-plating: BeCu is optimised for GaAs chips (having gold pads) and tungsten is optimised for silicon and SiGe chips (having aluminium pads). Launch angle, φ. Coaxial connector type: The 3.5 mm Amphenol Precision Connector (APC3.5) is used for operation to 26.5 GHz; the Anritsu K-connector (2.92 mm), for single-mode operation to 46 GHz, is compatible with 3.5 mm connectors; the APC2.4 can be used for measurements up to 50 GHz, while the Anritsu V-connector (1.85 mm), for single-mode operation to 67 GHz, is compatible with 2.4 mm connectors; the Agilent Technologies 1 mm connector is used for operation up to 120 GHz, while the Anritsu W-connector (1.1 mm) has a cut-off frequency of either 110 or 116 GHz, depending on the coaxial dielectric used.
Cascade Microtech now sells probes that are capable of making on-wafer measurements in dual configurations, such as GSGSG. In the case of the dual infinity, this allows dual measurements up to 67 GHz. Such probes may be used in conjunction with modern four-port VNAs, such as Agilent’s N5230A PNA-L. If the launch angle is too small, unwanted coupling between the probe and adjacent on-wafer components may occur. For this reason, it is recommended that adjacent components have at least 600 µm of separation for 110 GHz measurements. On the other hand, if the angle is too large there will not be enough skate on the probe pads. It has been found analytically and empirically that the best angle occurs when the horizontal components of the phase velocity for the probe and MMIC transmission lines match one other [44]. Therefore 0006 0007 εeff . probe −1 φ = cos εeff . MMIC where εeff . probe is the effective permittivity of probe line and εeff . MMIC is the effective permittivity of MMIC line. For example, a CPW line on GaAs has εeff. MMIC ≈ 6.9 at 76.5 GHz and, therefore, φ = 68◦ with Air Coplanar™ probes, since εeff . probe = 1. However, in practice, the launch angle is approximately 20◦ . This may raise questions as to the possibility of launching unwanted parasitic modes, due to uncompensated velocity mismatches at the RF probe tip, and also fringe fields coupling from the RF probe tip into the wafer.
11.3.2 Probe calibration During the placement of probes onto an MMIC, there are two mechanisms by which the probe tips become soiled. First, since the probe tip contact’s metal-plating is
RFIC and MMIC measurement techniques 237 designed to be much harder than the MMIC probe pad ohmic contact’s metal, particles of either gold or aluminium will be deposited onto the respective BeCu or tungsten contacts. Second, it is not uncommon for the probe tip contacts to overshoot the unpassivated probe pads and scratch off some of the Si2 N3 (silicon nitride) passivation material surrounding the pads. Without regular cleaning, a build-up of gold/aluminium and Si2 N3 particles can form around the probe tip contacts. This build-up is likely to degrade the performance of measurements at millimetric frequencies. Therefore, prior to calibrating the measurement system, it is recommended that the probe tips be very gently cleaned. Here, forced-air can be blown onto the probe tip – in a direction parallel to the tip and towards its open contact end – in order to remove any particles. For more stubborn objects, a lint-free cotton bud, soaked in isopropanol (IPA), can be carefully brushed in a direction parallel to the tip and towards its open contact end. After the probe tips have been inspected for any signs of damage and cleaned, a planarity check must be made between the probes and the ultra-flat surface of the wafer chuck. A contact substrate, consisting of a polished alumina wafer with defined areas of patterned gold, is used to test that all three of the probe tip contacts (e.g. ground–signal–ground) make clear and even markings in the gold. Once this procedure is complete, the probe tip contacts can be cleaned of any residual gold by simply probing onto the exposed, un-metallised, areas of alumina. This is particularly important for tungsten contacts, because tungsten oxidises, and therefore the contact resistance would otherwise increase. However, this is not the case for BeCu contacts as they do not oxidise. Probe stations use a one-tier calibration procedure, with the standards located either on an impedance standard substrate (ISS) or on the test wafer. With a precision ISS, the standards can be fabricated to much tighter tolerances. For example, a pair of 100 0001 resistors are used to implement the CPW 50 0001 load reference impedance. Here, these resistors can be laser-trimmed to achieve an almost exact value of 50 0001, but at DC only. For D- and G-band operation, in order to reduce the effects of moding from the underside of the calibration substrate, Cascade Microtech produce a 250 µm thin ISS that, when used in conjunction with their ISS absorber blocks, drastically reduces the effects of substrate moding. It should be noted, however, that if a calibration is performed using a 635 µm thick alumina ISS and the verification is performed using 200 µm thick GaAs on-wafer standards (which is a realistic measurement scenario), then problems may be encountered at millimetric frequencies. This is because the probe-to-ISS interface is electromagnetically different from that of the probe-to-wafer interface. As a result, even though the specifications for corresponding calibration and verification standards may be identical, their measured characteristics may differ significantly. For this reason, the use of on-wafer standards is by far the best choice. This is because the probe-to-wafer interface can be electromagnetically the same for calibration, verification and all subsequent measurements. Moreover, on-chip launch transition discontinuities (e.g. probe pads and their transmission lines) can be treated as part of the overall measurement system to be calibrated. Ideally, the reference planes within the on-wafer standards should have the same line geometries as those at the on-chip
238 Microwave measurements DUT. The UK National Physical Laboratory (NPL) and the US National Institute of Standards and Technology (NIST) have developed GaAs ISS wafers with calibration standards and verification components of certified quality [47,48]. There are a number of calibration techniques that are used for on-wafer measurements [44,47–52]. The SOLT technique is not used at upper-microwave frequencies due to the poor quality of planar open standards. For TRL, the reflect standards (either an open or short circuit) must be identical at both ports, but they can be non-ideal and unknown. The TRL technique also requires a minimum of two transmission lines. The reference impedance is taken from the characteristic impedance, Z0 , of these lines [53]. Since a 50 0001 load is not required for TRL calibration, only transmission line standards are needed, and these are easily realisable on-wafer. In practice, in order to cover a useful frequency range, it is necessary to employ a number of different delay line lengths to overcome phase ambiguity at all the measurement frequencies. This means that the probe separation has to be adjusted during the calibration procedure. For many applications such as automated test systems this is a major limitation, and for these applications the line-reflect-match (LRM) calibration [49] is preferred to TRL. The multiple CPW delay lines required with the TRL calibration are effectively replaced by the CPW 50 0001 load, to theoretically represent an infinitely long delay line. This results in the following advantages: (1) (2) (3) (4) (5)
an ultra-wideband calibration can be achieved (e.g. DC to 120 GHz), the probes can be set in a fixed position, automatic calibration routines can be applied, reflections and unwanted modes in long CPW delay lines are avoided and a considerable saving of wafer/ISS area can be made.
With SOLT and LRM, the accuracy to which the load is known directly determines the accuracy of the measurement. In other words, perfect models are required for the load impedances. These loads inevitably have some parasitic shunt capacitance (which is equivalent to having negative series inductance), and furthermore, have frequencydependent resistance due to the ‘skin effect’. In addition, with microstrip technology there will be significant series inductance associated with the short and load standards. Cascade’s line-reflect-reflect-match (LRRM) calibration is a more accurate version of the standard LRM calibration, in which load-inductance correction is incorporated by including an extra reflection standard. NIST recently released some public domain software on the worldwide web called MultiCal™. This software provides a new method for the accurate calibration of VNAs [21–23]. Here, multiple and redundant standards are used to minimise the effects of random errors caused by imperfect contact repeatability. Moreover, with split-band methods (e.g. LRL and TRL), the calibration discontinuities at the frequency break points can be eliminated. With MultiCal™-TRL, only the physical lengths of the standards and the DC measurement of the line resistance per unit length (by applying a least-square error fit to the multiple shorted line lengths) are required. The Z0 of the lines can then be determined and subsequent measurements can be renormalised to the 50 0001 measurement reference impedance.
RFIC and MMIC measurement techniques 239 For the ultimate in ultra-wideband calibration, verification and measurement accuracy, there is strong support for having MultiCal™-TRL calibration for frequencies above a few gigahertz (say 1 GHz), combined with LRM for the frequencies below 1 GHz, using on-wafer standards. The LRM’s standards should be characterised at DC and at 1 GHz (using MultiCal™-TRL); conventional modelling techniques can be used to interpolate the results. A recent comparison was made between the calibration coefficients obtained from a NIST multiline calibration and those obtained from an assortment of other techniques; the results are shown in Figure 11.12. A two-port probe station traditionally uses a 12-term error model, although a 16-term error model has been introduced that requires five two-port calibration standards [54]. This more accurate model can correct for poor grounding and the additional leakage paths and coupling effects encountered with open-air probing. With the extremely high levels of accuracy that are possible with modern probe stations, the effects of calibration errors become more noticeable. Calibration errors can result from the following (in the order of greatest significance): (1) probe placement errors – position, pressure and planarity variations; (2) degradation with use in the probe tips and the standards’ probe pads surface wave effects on calibrations [55]; and (3) ISS manufacturing variations. It has been found that the effects of probe misplacement are greatly reduced when calibration is carried out on an automated probe. Cascade Microtech produce an automated calibration package, called WinCal, which allows full automation of the calibration on a Cascade semi-automatic probe station, such as the Summit 12000 or the 300 mm S300. Manual calibration is also possible. WinCal incorporates all the main family of calibrations (e.g. TRL, SOLT, LRM and also has LRM/LRRM
Figure 11.12
Comparison of calibration coefficients obtained from LRRM, LRM, SOLT and NIST multiline
240 Microwave measurements with auto load inductance compensation). Another routine, called Short Open Load Reflect, is included that allows accurate calibration to be conducted with non-ideal through-line standards. Such situations are almost unavoidable when device ports are orthogonal in nature. WinCal has the ability to measure, record and display S-parameters in a variety of formats and also carry out compensation to remove the effects of pad parasitics. A stability checker is also provided in order to determine the validity of the calibration at any given moment. With the extremely high level of measurement accuracy that can be achieved, the effects of on-chip launch transition discontinuities can be significant above a few gigahertz. So far, it has been assumed that the effects of probe pads and their associated transmission lines have been calibrated out. Here, the on-wafer calibration standards would have the same launch transition discontinuities as the on-chip DUT. However, effective de-embedding techniques can still be performed within the MMIC. If ECMs are to be employed, the foundry that fabricates the MMIC should provide very accurate models for probe pads and transmission lines. The metrologist must use these foundry-specific models to determine the actual measurements of the on-chip DUT. When de-embedding is performed using equivalent circuit modelling, these foundry-specific models can be easily incorporated into conventional F-D simulation software packages.
11.3.3 Measurement errors Even when the system has been successfully calibrated, measurement errors (or uncertainty) can still occur. Some of the more common sources of errors are as follows: (1) (2) (3) (4) (5) (6) (7)
probe placement errors, temperature variation between calibration and measurement, cable-shift induced phase errors between calibration and measurement, radiation impedance changes due to the probes/wafer chuck moving, matrix renormalisation not being performed with multiple port MMICs, resonant coupling of the probes into adjacent structures [56], low frequency changes in the characteristic impedance and effective permittivity of both microstrip and CPW transmission lines [56] and (8) optically induced measurement anomalies associated with voltage-tunable analogue-controlled MMICs [57].
11.3.4 DC biasing Depending on the nature and complexity of the device or circuit under test, DC bias can be applied to an MMIC in a number of ways: (1) through the RF probes, via bias-tees in the VNA’s test set; (2) through single DC needles mounted on probe station positioners; and (3) with multiple DC needles attached to a DC probe card, which may in turn be mounted on a positioner.
RFIC and MMIC measurement techniques 241 The DC probe needle has significant inductance, and as a result, provides RF de-coupling for the bias lines that helps to prevent stability problems. However, additional off-chip de-coupling capacitors and resistors can usually be added to the card to further minimise the risk of unwanted oscillations. With bias-tees and DC needles, the maximum DC bias voltage and current are approximately 40 V and 500 mA, respectively. With multiple DC needles, standard in-house DC footprints are recommended wherever possible, in order to provide card re-use. This will reduce measurement costs considerably. There is a limit to the maximum number of needles per card, but ten is typical. One needle is normally required to provide a ground reference.
11.3.5 MMIC layout considerations The foundry’s design guidelines will define a minimum distance between the centres of probe pad vias and the minimum distance from the vias to the edge of the MMIC’s active area. Generally, a particular company or institute may standardise on a certain pad size and pitch for a particular probe tip specification. In order to save expensive chip area, probing directly onto via-hole grounds is tempting. However, the probe tip contacts may puncture the gold pads on top of the via-holes, which could damage the probe tips and destroy the MMIC. While on-via probing can be used, in principle, it is likely that the chip would fail a subsequent QA inspection. As a result, when designing MMICs for on-wafer probed measurement, it is important to consult the foundry design guidelines for the probe pad specifications. The location and orientation of the probe pads must also be considered. If the pads associated with one port are too close to those of another port, the very fragile probe tips are at risk of severe damage if they accidentally touch one another during the probe alignment procedure. The minimum separation distance between probe tips is determined by the design rule on probe pad spacing (typically 250 µm with vias or 200 µm without vias, depending on the thickness of the chip). Moreover, if the spacing between port pads is less than 200 µm, there could be significant measurement errors due to RF crosstalk effects between probes. Finally, if three or four RF probe positioners are attached to the probe station then they will be oriented orthogonal to one another. As a result, the RF probe pads for a three- or four-port MMIC must also be orthogonal to one another. On the MMIC, launch transitions are required to interface between the probes and the DUT. In many cases, the DUT is in the microstrip medium, and so transitions from CPW-to-microstrip must be employed before and after the DUT. With reference to Figure 11.13a, microstrip launchers require through-GaAs vias to provide a low inductance earth path from the probe to the MMIC’s backside metallisation layer. A microstrip launcher should be long enough for the higher-order evanescent modes, resulting from the CPW-to-microstrip transition, to be sufficiently attenuated and have minimum interaction with the DUT. As a rule of thumb, the microstrip launchers should ideally have a length of three to four times the substrate thickness. With reference to Figure 11.13b, when the DUT is in the CPW medium, through-GaAs vias are not required and a matched taper from the probe pads to the DUT is used. Even though this taper is very short, if the 50 0001 characteristic impedance is not maintained throughout the transition, significant parasitic capacitance or inductance
242 Microwave measurements
Probe tip
G
Via to ground
G
G
S
S
S
G Source Drain
S
Source G
G (a)
Figure 11.13
G (b)
G (c)
Common launcher techniques: (a) microstrip, (b) coplanar waveguide and (c) direct probing onto a FET device
can be introduced. In special cases, launchers are not required at all for some devices. One example of this is with a simple FET structure, as shown in Figure 11.13c, where two GSG probes are placed directly onto the source–gate–source and source– drain–source pads. This approach eliminates the need for de-embedding the effects of launchers from the measurements, but the effects of the bond pads should still be considered. At this point, it is important to note that for frequencies above a few gigahertz, the equivalent circuit model of a device that has been characterised in one medium (e.g. microstrip or CPW) should only be used in circuits designed in the same medium. Single devices such as transistors and diodes can be biased through the bias-tees of the network analyser. However, in order to test a complete circuit using a probe station, special consideration has to be given to the layout of the DC bias pads and the design of the bias networks. When using DC needles to bias a circuit, the following points should be considered: (1) The foundry may impose minimum pad sizes and centre-to-centre pitch. (2) For ease of DC probe card fabrication and probe alignment, the DC probe pads should be arranged in a linear array along the edge of the chip’s active area, and should be kept away from the RF pads. A common method is to have the RF probe pads on the east and west edges of the chip, and the DC bias pads on the north and/or south edges. If layout constraints suggest that orthogonal RF inputs and outputs would be more convenient, first check that suitable positioners are available. (3) The bias networks of the circuit should be modelled separately to ensure that oscillations will not occur. Off-chip de-coupling capacitors cannot always be placed as near to the chip as they can be in a test fixture. (4) High-value resistors can be added on-chip to prevent RF leakage and catastrophic failure resulting from excess forward biasing of diodes and transistors. With varactor diodes, cold-FETs and switching-FETs, a trade-off may have to be made in the value of these bias resistors. If the resistance is too small there may not be enough RF isolation. If the resistance is too high the maximum switching speed may not be reached, due to an excessive R-C time
RFIC and MMIC measurement techniques 243 constant. In practice, a minimum resistance value of approximately 300 0001 should suffice for most applications.
11.3.6 Low-cost multiple DC biasing technique Conventional DC probe cards may need to be replaced for every new MMIC design, unless standard DC probe footprints can be used. This throwaway approach is very costly, especially when the DC probe cards are supplied by a commercial vendor (as automated and precision manufacturing techniques generally have to be used for aligning multiple needles). Moreover, the cost of the cards increases with the number of needles, as the individual needles are themselves precision-made components. A flexible, low-cost technique has been developed for providing an experimental active filter with multiple DC bias connections [58]. The MMIC is attached to a gold-plated chip carrier using conductive epoxy glue. An array of single-layer microwave capacitors is then attached to the chip carrier in close proximity to the MMIC. BAR-CAPS™, made by Dielectric Labs Inc., are ideal for this purpose since they are available as single-chip strips of three, four or six 100 pF shunt capacitors, each having a probeable area of approximately 650 × 325 µm2 and separated by approximately 170 µm. A gold bond wire is then used to connect the MMIC’s DC probe pad to its off-chip capacitor. As an example of this technique, a microphotograph of the experimental MMIC, requiring 15 DC bias lines, is shown in Figure 11.14. It has been found that this low-cost solution has a number of important advantages for use in the R & D laboratory. (1) The high-inductance bond wires and off-chip de-coupling capacitors minimise the risk of unwanted oscillations. (2) When designing the MMIC layout, the DC probe pads do not need to be arranged in a linear array along the edges of the chip. This provides greater design layout flexibility. (3) The linear array of off-chip capacitors automatically provides a standard in-house DC footprint, reducing long-term measurement costs considerably. (4) The probeable area of the off-chip capacitors is approximately 15 times larger than that of the MMIC probe pads and the capacitors can withstand greater mechanical forces. As a result, in-house DC probe cards can be made by hand because of the relaxation in manufacturing precision, reducing short-term costs considerably.
11.3.7 Upper-millimetre-wave measurements The past few years have seen considerable developments in the proposed uses of the millimetric frequency range above 75 GHz for new civil applications; for example, collision avoidance radar at 77 GHz. Also, the 94 GHz band is no longer dominated by military applications. High-resolution radiometric imaging at 94 and 140 GHz has a number of important applications, including aircraft landing systems, finding victims trapped in fires and locating concealed weapons without the use of X-rays. Ultra-high
244 Microwave measurements
Figure 11.14
Microphotograph of an experimental MMIC with multiple DC biasing using the low-cost technique [58]
data rate optical communications – using a ‘radio-fibre’ system at 180 GHz – could transform the way domestic computer networks are distributed. Future EC directives on environmental air pollution monitoring will require cheap high-performance terahertz sensors to be mass-produced. Sensors for sub-cellular probing are opening up new areas of medical research. Finally, passive tagging/identification systems are possible, which are both easy to conceal and extremely difficult to forge. With most (if not all) of these applications, monolithic technology will be sought. To this end, there have been major advances in both high electron mobility transistor (HEMT) and heterojunction bipolar transistor (HBT) technologies, both of which have attained values of fmax greater than 500 GHz [59,60]. Today, VNAs are commercially available that can operate in either broadband or banded configurations up to 110 GHz. The Agilent Technologies N5250 and the Anritsu ME7808B are examples of two broadband VNAs that are able to measure small-signal S-parameters from about 45 MHz to 110 GHz in a single-sweep. Both systems use coaxial cables between the test-sets and the probes. As frequency increases, the combined losses of all the components between the test-sets’ reflectometers and the MMIC under test (e.g. test-set combiners, transmission lines, probes, transitions and connectors) also increase. As a result, the overall system suffers from a reduction in both accuracy and stability [61]. The Anritsu 360B employs two test-sets: one rack-mounted (operating from 40 MHz to 67 GHz) and the other mounted on the probe station (operating from 67 to 110 GHz). Here, a test-set
RFIC and MMIC measurement techniques 245 combiner (or forward wave MUX coupler) is used to combine the signals from both test-sets. The drawback with this approach is the considerable losses associated with test-set combiners, which will degrade the effective directivity, source match and frequency tracking of the system at W-band. Ultimately, this will have an impact on the quality of calibrations and the system’s ability to hold a calibration in the presence of drift. The Agilent Technologies 8510XF minimises this problem by removing the need for a test-set combiner. Here, ultra-broadband (45 MHz to 110 GHz) directional couplers are utilised to create a single test-set [61]. In order to minimise the losses between the test-set’s reflectometer and the MMIC under test, a banded VNA is preferred. This can utilise coaxial cables up to W-band and metal-pipe rectangular waveguides at and/or above W-band. The UK’s National Physical Laboratory has recently established a new primary national standard measurement facility for S-parameters with rectangular waveguide operating over the frequency range of 75–110 GHz, using such a banded VNA system [62]. This facility represents a significant extension to the existing UK national standards for S-parameter and impedance measurements [63]. To date, there are still no traceable standards for on-wafer measurements above 75 GHz, from either NPL or NIST. This is due to a multitude of issues (e.g. mechanical precision, multi-moding, radiation effects, dielectric and surface wave propagation, ohmic losses in the dielectric and anomalous skin-effect losses in the conductors) associated with accurate calibration and verification measurements using non-ideal standards. However, there is a great deal of experimental work being undertaken to find the optimum calibration strategy for W-band [64–66]. With the ever-increasing interest in performing on-wafer measurements above 110 GHz, Oleson Microwave Laboratories Inc. can now supply frequency extension modules for the commercial market to include the following waveguide bands: WR-8 for F-band (90–140 GHz) [67]; WR-5 for G-band (140–220 GHz); and WR-3 for H-band (220–325 GHz). Cascade Microtech and GGB Industries supply the Infinity and Picoprobe™ on-wafer probes, respectively, for frequencies up to 220 GHz. In addition to these commercial systems, the University of Kent has developed an experimental passive on-wafer probing system. Here, ultra-low loss PTFE dielectric waveguides are used to avoid the problem of the skin-effect altogether [68–72]. The dielectric waveguide has been used to implement the multistate reflectometer, interconnecting transmission lines, and even the on-wafer probes. In principle, this system can operate from 118 to 178 GHz [72]. However, the ultimate challenge is to remove all the losses between the test-set’s reflectometer and MMIC under test. In an experimental set-up, a full two-port VNA has been implemented with active probes, enabling S-parameter measurements to be made from DC up to 120 GHz [73]. Here, high-speed non-linear transmission line (NLTL)-gated directional T-D reflectometers (which are essentially directional samplers) were realised using GaAs MMIC technology [74]. More recently, a 70–230 GHz VNA has been demonstrated that also employs MMIC reflectometers located on the on-wafer probes [75,76]. The NLTL-based active probes serve as S-parameter test-sets for the Agilent Technologies 8510 VNA. Using the Agilent Technologies 8510XF system, good agreement has been demonstrated from 70 to 120 GHz [75].
246 Microwave measurements
11.4
Thermal and cryogenic measurements
11.4.1 Thermal measurements In real-life applications, microwave circuits can be exposed to temperatures other than ambient room temperature (i.e. 23 ◦ C or approximately 296 K). For example, some components in geostationary orbiting satellites (e.g. within the antenna subsystem) may be periodically exposed to temperatures ranging from −150 to +80 ◦ C, depending on the amount of visible sunlight, the levels of localised heat generated within the satellite and the effectiveness of the thermal control sub-system. Also, Gunn diodes can have junction temperatures in excess of +200 ◦ C. At the other extreme, cryogenically cooled LNAs can operate at −196 ◦ C, with a liquid nitrogen cryogen having a boiling point temperature of 77 K. During the development of a sub-system, the levels of performance degradation while operating over a predefined temperature range must be known. Therefore, the temperature-dependent characteristics of all the MMIC components that make up a sub-system must be determined. Once the complete sub-system has been assembled, temperature-cycling is performed so that the measured levels of performance degradation can be compared with those predicted during simulation. The Cascade Microtech Summit S300-863 semi-automatic probing system, in conjunction with the Microchamber™ enclosure, enables very fast set-up and measurements to be performed up to 110 GHz in a dark, temperature controlled and electromagnetic interference-isolated environment. The Summit S300-973 thermal probing system [77] can be seen in Figure 11.15. The MMIC under test sits on a temperature controlled wafer chuck, which can be subjected to temperatures ranging from −65 to +200 ◦ C or from 0 to +300 ◦ C. Across these temperature ranges, the parameter values within, say, a FET’s equivalent circuit model exhibit a linear temperature dependency. Here, all the resistive and capacitive elements have a positive temperature coefficient, while Ids , gm and fT have negative temperature coefficients. Also, as the temperature drops, the gain of an active device can increase significantly. Therefore, to ensure linear operation, and thus avoid oscillation, the input RF power levels need to be reduced accordingly. Also, if the RF probes and cables exhibit large temperature gradients, significant phase changes will be found, even at low microwave frequencies. As a result, an air flow purge is introduced into the chamber in order to minimise the thermal coupling between the chuck and the probe/connector/cables. The air-flow purge also creates a dry, frost-free environment. The system is calibrated for every new wafer chuck temperature setting. An LRRM calibration is used, with the ISS located on a separate thermally isolated stage. The at-temperature calibration procedure can be performed 15 min after the chuck temperature has been changed. This short wait corresponds to approximately three thermal time constants for the probe/connector/cable assembly. Since all but the matched load impedance standards are insensitive to temperature, the ISS chuck temperature can be set at −5 ◦ C, for a wafer chuck temperature of −65 ◦ C. This approach results in less than a 1 per cent error in measurements between DC and 65 GHz.
RFIC and MMIC measurement techniques 247
Figure 11.15
Photograph of the Summit S300-973 thermal probing system, capable of over temperature measurements from −65 to 200 ◦ C
As a wafer chuck changes temperature it expands or contracts. For example, the total chuck expansion, from −65 to +200 ◦ C, can be about 230 µm. As a result, probe placement errors will become significant. Therefore, at each temperature, the overtravel of the probe tips may need to be adjusted. In addition, as the wafer diameter changes with temperature, there will be small changes in the spacing between devices. Cascade Microtech’s Summit series of semi-automatic thermal probe stations include control software that automatically compensates for such changes. This minimises the impact of measurement accuracy. Cascade Microtech now has a new microscopy system called Evue. This enables the contact height to be adjusted dynamically to ensure that the chuck is maintained at a constant height. This has the potential to enable fully automatic over temperature probing. Moreover, the technology employed in this system allows for an extremely large field of view that can be zoomed into a far smaller field of view at a single software command.
11.4.2 Cryogenic measurements Cryogenic hybrid MICs, employing high-performance active semiconductor and passive superconductor components, are being more widely used in applications ranging from radio astronomy, to space communications, to medical nuclear magnetic
248 Microwave measurements resonance scanners. Therefore, it is important to be able to determine the cryogenic temperature characteristics of these components [3–5,78–82]. At cryogenic temperatures, the noise figures of conventional GaAs transistors are reduced dramatically from their ambient room temperature values. For example, at 10 GHz the measured noise figure of a typical 0.6 × 100 µm MESFET is 0.8 dB at 300 K and only 0.4 dB at 35 K [80]. With HEMT technology, electron mobility can increase by a factor of 5 when the lattice temperature is reduced from 300 to 77 K [80], resulting in a considerable improvement in gain and noise performance. Furthermore, measurements made at temperatures as low as 10 K may provide information that can give a unique insight into the physics of experimental devices. Also, in addition to the advances being made in new semiconductor devices, there is considerable interest in the developments of ultra-low loss high temperature superconducting microwave components that currently have to be refrigerated below around 100 K. The first microwave test fixture to be used in cryogenic measurements was reported in 1976 [3]. The fixture was designed to be immersed in liquid nitrogen (LN2 ), which has a boiling point of 77 K. This approach suffers from the problems of poor accuracy and poor repeatability due to the changing temperature gradients exhibited by the cable/connector/launcher assembly, and requires a complicated calibration procedure. Accurate measurements have been reported using a TRL calibrated split-block test fixture mounted on the cold-head of an RMC Cryosystems™ LTS-22-IR helium refrigerator [5]. This approach enables small-signal S-parameter measurements to be made at 300 and 77 K. Cryogenic probe stations have either the MMIC under test and the probes immersed in liquid nitrogen or a liquid cryogen-cooled copper stage with a dry nitrogen vapour curtain. The former approach suffers from poor repeatability (due to varying amounts of LN2 ), a short measurement duration (in order to limit the build-up of ice formation) and a limited lifetime due to the degradation of the probes in contact with the LN2 . With the latter approach, accuracy is limited by mechanical stress, caused by the large thermal gradients between the microwave hardware and the MMIC under test. Also, reliability is limited by moisture and the build-up of ice, which increases the wear and tear on manipulators and requires extensive re-planarisation of the mechanical apparatus. Researchers at the University of Illinois have, however, demonstrated the design and operation of a cryogenic vacuum microwave probe station, for the measurement of S-parameters from DC to 65 GHz, which minimises the problems of limited accuracy and repeatability [80]. Within a vacuum chamber, the vacuum probe station has high-frequency CPW probes connected to cable feeds via a custom bellows and manipulator system. A liquid helium cryogen, with a boiling point temperature of 4.2 K, enables measurements to be performed at temperatures as low as 20 K. The copper stage is continually fed with liquid cryogen, and the system is then left to stand for 15–20 min in order to achieve temperature equilibrium. Once the at-temperature calibration has been performed, the actual device measurements can be taken for up to 4 h before having to recalibrate. Today, complete on-wafer cryogenic characterisation (from 20 to 300 K) can be performed for S-parameters, noise parameters and load-pull measurements [82].
RFIC and MMIC measurement techniques 249
11.5
Experimental field probing techniques
So far only invasive MMIC measurement techniques have been discussed, which generally do not perform internal function and failure analysis. However, one simple technique that can perform such tasks is to realise a coaxial probe with a highimpedance tip. Here, a 500 0001 resistor is used to create a potential divider with the 50 0001 oscilloscope. The internal node voltage can be measured without perturbing the operation of the circuit. This technique has been demonstrated on an MMIC power amplifier [83]. Alternatively, non-contacting methods also exist. Again, all the RF ports of the MMIC under test are terminated with matched loads. An RF signal is injected into the MMIC’s input port and a micron-level probing system is used to detect the internal signal strength. In the case of non-contacting techniques, different types of field are detected along transmission lines and at discontinuities. Field probing can detect current crowding, standing waves and unwanted modes of propagation, and S-parameters can be determined from T-D network analysis measurements.
11.5.1 Electromagnetic-field probing The simplest method of field detection uses a semiconductor diode. At microwave frequencies, however, it becomes difficult to match the diode because its impedance varies with power level. At low power levels, bolometers are traditionally employed for use above 1 GHz. The device is similar to a thin-film resistor, where a highresistivity bismuth film is evaporated onto metallic electrodes. When exposed to microwave radiation, the bolometer absorbs the electromagnetic energy and converts it into heat energy. As the film heats up, its resistivity decreases. Since the bolometer is inherently a square law detector, the measured voltage change across the device is proportional to the change in incident RF power. In practice, however, since the signal levels are so small, the incident microwave signal must be pulsed. This causes the resistance of the bolometer to change at the pulse repetition frequency, which is usually below 100 kHz. With a DC bias current applied, the low-frequency voltage signal across the bolometer is applied to a lock-in amplifier that acts as a coherent detector. This technique exhibits a high degree of sensitivity; as an example, a 4 × 5µm device with a noise equivalent power of 160 pW/Hz1/2 has been reported [84]. With the use of conventional probe microfabrication techniques, microbolometers can be employed to detect power levels as low as a few nanowatts along MMIC transmission lines. A microbolometer probe that can be used for microstrip and CPW transmission lines is illustrated in Figure 11.16. With a perfectly symmetrical probe positioned directly above a CPW line, the wanted CPW (or even) mode will be detected and the unwanted slotline (or odd) mode will not. As well as their simple fabrication and calibration, microbolometer probes can be designed to operate in the terahertz frequency range. Unfortunately, the attainable stability and uniformity of the resistive film does not yet appear to be sufficient for the commercial production of these probes. A more recent development uses a dielectric rod probe, with a thin copper strip at its end face that helps to pick up the electromagnetic field and couple it to the dielectric
250 Microwave measurements
Ι
Ι
To bias and lock-in amplifier
Bolometer
Figure 11.16
Illustration of an electromagnetic-field probe
waveguide [85]. Using this technique, measured results have been demonstrated between 200 and 220 GHz to show standing wave patterns on a mismatched dielectric waveguide [85].
11.5.2 Magnetic-field probing The simplest magnetic-field probing technique is to connect a conventional spectrum analyser to a magnetic-field probe. Using wafer probe microfabrication techniques, a miniature magnetic quadrupole antenna can be configured to match the magnetic fields associated with microstrip and CPW transmission lines, as illustrated in Figure 11.17. Placed directly above the transmission line, the lines of magnetic flux will come up through one loop and back down through the other loop. As a result, the induced signals add. From a distance, the probe sees a near uniform magnetic field which induces signals that tend to cancel each other out. In addition to amplitude, phase measurements can also be measured. A reference signal at the same frequency, with a variable amplitude and phase, is combined with the measured signal. The measured phase is equal to the reference phase when the amplitude displayed on the spectrum analyser is at its peak. Therefore, the probe can be used to measure the amplitude and phase of currents at any node within an MMIC. An experimental system has been reported that can operate in the 26.5–40 GHz frequency range [86]. Here, a 25–50 µm separation distance provides sufficient coupling and discrimination, while providing a negligible effect on the MMIC under test. One of the major sources of error is electrostatic pickup. Increasing the width of the loops increases the ratio of magnetic to electric coupling, but it also increases the random radiation picked up from other circuit elements. Reducing the width of the metal conductors reduces capacitive pickup, but increases the conductor’s resistance and self-inductance. In practice, an effective method of limiting the errors due to electrostatic pickup is to rotate the probe and average the measurements. This problem can be avoided by having just a single-loop probe [87].
RFIC and MMIC measurement techniques 251 To spectrum analyser
CPW feed line
Dielectric Quadrupole antenna
Figure 11.17
Illustration of a magnetic-field probe
11.5.3 Electric-field probing The simplest electric-field probing technique is to connect a conventional spectrum analyser to a near electric-field (i.e. capacitive) probe. This technique was first demonstrated on MICs in 1979 [88], but it is still being used today [89]. The probe can be simply realised by removing a small section of the outer screening conductor and dielectric from the end of the analyser’s coaxial feed line. Unfortunately, these probes have significant unwanted parasitic reactances at high microwave frequencies, which can severely perturb the operation of the circuit under test, thus causing measurement errors. However, micromachining techniques can be adopted to limit this problem, to realise dipole and monopole antennas [90]. In practice, this technique is only accurate when used with shielded transmission lines. As a result, it is unsuitable for micron-level features found in MMICs. Over the past decade, a number of alternative electric-field probing techniques have been investigated, with varying degrees of success. 11.5.3.1 Electron beam probing The voltage-contrast scanning electron microscope (SEM) was developed in the late 1960s for detecting voltages on the conductor tracks of integrated circuits. A pulsed electron beam stimulates secondary electron emissions from the irradiated surface of metals. For conductors at a negative potential, the secondary electrons have more energy than for conductors at a more positive potential. Commercial SEMs suffer from a poor millivolt potential sensitivity and limited bandwidths of only a few gigahertz [91], although larger bandwidths have been reported [92]. Also, apart from its very high complexity and cost, the electron beam may affect the operation of GaAs MMICs due to charging of deep levels in the GaAs substrate. However, the major advantage of this technique is that the attainable spatial resolution that can be achieved is in the order of a few angstroms.
252 Microwave measurements 11.5.3.2 Photo-emissive sampling Instead of using an electron beam to stimulate secondary electron emissions, another approach uses a high-intensity pulsed laser beam to illuminate the surface of the metals [91]. This T-D sampling technique offers an improved potential sensitivity and a greatly extended bandwidth. However, as with the SEM, the performance of GaAs MESFETs may be affected by charging of deep level traps. 11.5.3.3 Opto-electronic sampling Time-domain network analysis can be performed using opto-electronic sampling techniques. Here, electrical pulses can be generated on an MMIC by illuminating DC biased photoconductive switches with a pulsed laser beam. The optical excitation of a photoconductive switch can also perform signal sampling. By comparing the Fourier transforms of the sampled incident and reflected or transmitted waveforms, the complex two-port S−parameters can be determined for the DUT [91,93–99]. Sub-picosecond electrical pulse generation with a photoconductive switch has been reported, enabling terahertz measurement bandwidth [100]. This T-D opto-electronic sampling technique (also known as photoconductive sampling) requires the DUT to be embedded in a single-chip GaAs test fixture. Each RF port of the DUT is connected to a test structure consisting of a 50 0001 matched load termination, photoconductive switches, DC bias lines and a length of transmission line. These test components are not only wasteful of expensive chip space, but they must also be de-embedded from the measurements. In addition, the fabrication process of the photoconductive switches must be compatible with that of the MMIC under test. However, a DC to 500 GHz measurement system has been demonstrated [99]using this technique. 11.5.3.4 Electro-optic sampling The most promising electric-field probing technique is electro-optic sampling. A variety of non-centrosymmetric crystals, such as gallium arsenide and indium phosphide, exhibit Pockel’s electro-optic effect. The presence of an electric field will induce small anisotropic variations in the crystal’s dielectric constant, and therefore, its refractive index. If a laser beam passes through this material it will experience a voltage-induced perturbation in its polarisation, which is directly proportional to the change in the electric-field strength. As a result, this linear electro-optic effect can be used to provide a non-invasive means of detecting electric fields [91,93,94,101–111]. With internal (or direct) electro-optic probing the laser beam penetrates the GaAs MMIC in a reflection mode, as illustrated in Figure 11.18a, giving good beam access and requiring only a single focusing lens [91,93,94,101–103,107–111]. However, optical polishing of the MMIC substrate is required for best results. With front-side probing, the beam is reflected off the back-side ground plane metallisation, adjacent to the circuit conductor. With back-side probing, the beam is reflected off the back of the circuit conductor itself, making this scheme ideal for conventional CPW or coplanar strip lines and slotlines. Today, internal electro-optic sampling can achieve a spatial resolution down to less than 0.5 µm [110]. Centrosymmetric crystals, such as silicon and germanium, do not exhibit the linear electro-optic effect. Therefore, silicon MMICs must employ external (or indirect)
RFIC and MMIC measurement techniques 253 Back-side probing Slotline
Front-side probing
Electric-field lines
Probe beam
Ground plane
Microstrip line GaAs substrate
Probe beam
Ground plane (a) Probe beam
Fused silica needle Electro-optic crystal
(b)
Figure 11.18
Illustration of electric-field probe: (a) internal and (b) external
electro-optic probing [91,93,104–106]. This technique uses an extremely small electric field sensor, consisting of a 40 × 40 µm2 electro-optic crystal (lithium tantalate) at the end of a fused silica needle, placed in close proximity to the circuit conductor, as shown in Figure 11.18b. Sending a laser beam down the needle and measuring the induced change in the refractive index of the crystal from the returning beam can detect the conductor’s fringing fields. Since the beam can be focused down to a spot size of 3–5 µm in diameter, excellent spatial resolution is achieved. Also, there is no need for MMIC substrate polishing. With electro-optic probing, picosecond optical pulses (generated by a laser with an output power level that is lower than the band-gap energy of the MMIC’s semiconductor) pass through the electric fields associated with the MMIC’s circuit conductors. After being passed through a common beam splitter, the incident and return beams are combined, before being passed through a polarising beam splitter. Two photodiodes detect the intensity of the orthogonally polarised components and lock-in amplifiers are then used to determine the electric-field vectors. As a result, internal node voltage measurements can be determined and impressive two-dimensional mappings of the amplitude [105,107–109] and phase angles [109]
254 Microwave measurements of microwave fields within the MMIC can be obtained. T-D network analysis can also be performed using electro-optic sampling. Here, picosecond electrical pulses are applied to the input port of the MMIC under test, with the generator connected to the MMIC using traditional invasive techniques. By comparing the Fourier transform of the detected incident and reflected or transmitted waveforms, the complex two-port S-parameters can be determined. To date, a 50–300 GHz network analyser has been demonstrated using this technique [106]. A European consortium (which includes NPL and the Fraunhofer Institute for Applied Solid State Physics) has developed the first optical instrument capable of testing terahertz circuits and tracing the measurements back to international standards [111]. 11.5.3.5 Electrical sampling scanning-force microscopy A number of non-invasive measurement techniques have been introduced that can perform internal function and failure analysis of MMICs. The electron beam probing technique is well established and has excellent spatial resolution, but the temporal resolution is limited because of electron transit time effects. Optical probing techniques have a superior temporal resolution, but because of the micron-beam diameters they have a limited spatial resolution. Scanning-force microscopy, in the electrical sampling mode, is a relatively new non-contacting measurement technique that has high spatial, temporal and voltage resolutions [112,113]. Here, an atomically sharp needle is mounted on one end of a cantilever. When the needle is placed at a fixed working distance of between 0.1 and 0.5 µm above the MMIC, it will be subjected to attraction or repulsion forces, causing a detectable bending of the cantilever. This very experimental technique has so far demonstrated a spatial resolution of 0.5 µm and a bandwidth of 40 GHz [112].
11.6
Summary
A wide range of techniques has been briefly introduced for the measurement of MMICs. A summary of the main features associated with the most practical invasive techniques is given in Table 11.2. In general, the level of accuracy and repeatability Table 11.2
Comparison of the invasive measurement technologies Commercial test fixture
On-wafer probe station
1-tier
1-tier
1-tier
High Moderate Wideband Poor Low
High High Wideband Poor High
Very high Very high Ultra-wideband Poor Very high
In-house test fixture Calibration Accuracy Repeatability Bandwidth Flexibility Cost
2-tier with ECM de-embedding Moderate Moderate Wideband Excellent Very low
RFIC and MMIC measurement techniques 255 obtainable is proportional to the initial investment costs of the measurement system. Compared with traditional invasive on-wafer measurement techniques, optical systems have so far demonstrated a lower dynamic range and inferior frequency resolution. In addition, optical techniques have complicated and lengthy calibration procedures. However, with its excellent spatial resolution and extremely wide bandwidth capabilities, electro-optic probing may become commonplace in the not too distant future.
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260 Microwave measurements 82 Laskar, J., Murti, M. R., Yoo, S. Y., Gebara, E., and Harris, H. M.: ‘Development of complete on-wafer cryogenic characterization: S-parameters, noise-parameter and load-pull’, Gallium Arsenide and its Applications Symposium Digest, 1998, pp. 33–38 83 Wei, C.-J., Tkachenko, Y. A., Hwang, J. C. M., Smith, K. R., and Peake, A. H.: ‘Internal-node waveform analysis of MMIC power amplifiers’, IEEE Transactions on Microwave Theory and Techniques, 1995;MTT-43 (12):3037–42 84 Schwarz, S. E., and Turner, C. W.: ‘Measurement techniques for planar highfrequency circuits’, IEEE Transactions on Microwave Theory and Techniques, 1986;MTT-34 (4):463–7 85 Basu, A., and Itoh, T.: ‘A new field-probing technique for millimeter-wave components’, IEEE MTT-S International Microwave Symposium Digest, 1997, pp. 1667–70 86 Osofsky, S. S., and Schwarz, S. E.: ‘Design and performance of a non-contacting probe for measurements on high-frequency planar circuits’, IEEE Transactions on Microwave Theory and Techniques, 1992;MTT-40 (8):1701–8 87 Gao, Y., and Wolff, I.: ‘A new miniature magnetic field probe for measuring three-dimensional fields in planar high-frequency circuits’, IEEE Transactions on Microwave Theory and Techniques, 1996;MTT-44 (6):911–18 88 Dahele, J. S., and Cullen, A. L.: ‘Electric probe measurements on microstrip’, IEEE Transactions on Microwave Theory and Techniques, 1980;MTT-28 (7):752–5 89 Gao, Y., and Wolff, I.: ‘Electric field investigations on active microwave circuits’, Proceedings of 26th European Microwave Conference, 1996, pp. 662–4 90 Budka, T. P., Waclawik, S. D., and Rebeiz, G. M.: ‘A coaxial 0.5–18 GHz near electric field measurement system for planar microwave circuits using integrated probes’, IEEE Transactions on Microwave Theory and Techniques, 1996;MTT-44 (12):2174–82 91 Bloom, D. M., Weingarten, K. J., and Rodwell, M. J. W.: ‘Probing the limits of traditional MMIC test equipment’, Microwaves & RF, 1987; 101–06 92 Kubalek, E., and Fehr, J.: ‘Electron beam test system for GHz-waveform measurements on transmission-lines within MMIC’, Proceedings of 22nd European Microwave Conference, 1992, pp. 163–8 93 Bierman, H.: ‘Improved on-wafer techniques evolve for MMIC testing’, Microwave Journal, 1990; 44–58 94 Lee, T. T., Smith, T., Huang, H. C., Chauchard, E., and Lee, C. H.: ‘Optical techniques for on-wafer measurements of MMICs’, Microwave Journal, 1990; 91–102 95 Huang, S.-L. L., Chauchard, E. A., Lee, C. H., Hung, H.-L. A., Lee, T. T., and Joseph, T.: ‘On-wafer photoconductive sampling of MMICs’, IEEE Transactions on Microwave Theory and Techniques, 1992;MTT-40 (12):2312–20 96 Kim, J., Son, J., Wakana, S. et al.: ‘Time-domain network analysis of mm-wave circuits based on a photoconductive probe sampling technique’, IEEE MTT-S International Microwave Symposium Digest, 1993, pp. 1359–61
RFIC and MMIC measurement techniques 261 97 Golob, L. P., Huang, S. L., Lee, C. H. et al.: ‘Picosecond photoconductive switches designed for on-wafer characterization of high frequency interconnects’, IEEE MTT-S International Microwave Symposium Digest, 1993, pp. 1395–98 98 Armengaud, L., Gerbe, V., Lalande, M., Lajzererowicz, J., Cuzin, M., and Jecko, B.: ‘Electromagnetic study of an electronic sampler for picosecond pulse measurements’, Proceedings of 23rd European Microwave Conference, 1993, pp. 751–4 99 Frankel, M. Y.: ‘500-GHz characterization of an optoelectronic S-parameter test structure’, IEEE Microwave and Guided Wave Letters, 1994;4 (4):118–20 100 Valdmanis, J. A., and Mourou, G.: ‘Subpicosecond electrooptic sampling: principles and applications’, IEEE Journal of Quantum Electronics, 1986;QE-22: 69–78 101 Bloom, D. M., Weingarten, K. J., and Rodwell, M. J. W.: ‘Electrooptic sampling measures MMICs with polarized light’, Microwaves & RF, 1987; 74–80 102 Mertin, W., Bohm, C., Balk, L. J., and Kubalek, E.: ‘Two-dimensional field mapping in MMIC-substrates by electro-optic sampling technique’, IEEE MTT-S International Microwave Symposium Digest, 1992, pp. 1443–6 103 Lee, C. H., Li, M. G., Hung, H.-L. A., and Huang, H. C.: ‘On-wafer probing and control of microwave by picosecond optical beam’, Proceedings of IEEE Asia-Pacific Microwave Conference, 1992, pp. 367–370 104 Wu, X., Conn, D., Song, J., and Nickerson, K.: ‘Calibration of external electro-optic sampling using field simulation and system transfer function analysis’, IEEE MTT-S International Microwave Symposium Digest, 1993, pp. 221–4 105 Mertin, W., Roths, C., Taenzler, F., and Kubalek, E.: ‘Probe tip invasiveness at indirect electro-optic sampling of MMIC’, IEEE MTT-S International Microwave Symposium Digest, 1993, pp. 1351–54 106 Cheng, H., and Whitaker, J. F.: ‘300-GHz-bandwidth network analysis using time-domain electro-optic sampling’, IEEE MTT-S International Microwave Symposium Digest, 1993, pp. 1355–58 107 Hjelme, D. R., Yadlowsky, M. J., and Mickelson, A. R.: ‘Two-dimensional mapping of the microwave potential on MMIC’s using electrooptic sampling’, IEEE Transactions on Microwave Theory and Techniques, 1993;MTT-41 (6/7):1149–58 108 David, G., Redlich, S., Mertin, W. et al.: ‘Two-dimensional direct electro-optic field mapping in a monolithic integrated GaAs amplifier’, Proceedings of 23rd European Microwave Conference, 1993, pp. 497–99 109 Mertin, W., Leyk, A., David, G. et al.: ‘Two-dimensional mapping of amplitude and phase of microwave fields inside a MMIC using the direct electro-optic sampling technique’, IEEE MTT-S International Microwave Symposium Digest, San Diego, 1994, vol. 3, pp. 1597–1600 110 David, G., Tempel, R., Wolff, I., and Jager, D.: ‘Analysis of microwave propagation effects using 2D electro-optic field mapping techniques’, Optical and Quantum Electronics, 1996;28:919–31
262 Microwave measurements 111 ‘Maps of electric fields traced back to standards’, Optics and Laser Europe (OLE) Magazine, 1997; 31–2 112 Bohm, C., Roths, C., and Kubalek, E.: ‘Contactless electrical characterization of MMICs by device internal electrical sampling scanning-force microscopy’, IEEE MTT-S International Microwave Symposium Digest, 1994, pp. 1605–8 113 Mueller, U., Boehm, C., Sprengepiel, J., Roths, C., Kubalek, E., and Beyer, A.: ‘Geometrical and voltage resolution of electrical sampling scanning force microscopy’, IEEE MTT-S International Microwave Symposium Digest, 1994, pp. 1005–8
Chapter 12
Calibration of automatic network analysers Ian Instone
12.1
Introduction
Network analysers are very complex instruments so it is important to define terms such as calibration to avoid confusion. The two dictionary definitions of calibration that can be applied to network analysers are ‘to mark (a gauge) with a scale of readings’ [1], and ‘to correlate the readings of (an instrument, etc.) with a standard to find the calibre of’ [1]. Unfortunately neither of these expressions defines the term calibration as it is applied to network analysers, instead they relate better to verification which is the process where the network analyser’s measurements are compared with those performed in a higher level laboratory.
12.2
Definition of calibration
Calibration in the network analyser sense is the process by which the errors within the instrument are compensated for, whereas verification checks that the resultant corrections have been properly assessed and applied. The extent of calibration used will depend on the desired measurement accuracy and the type of network analyser employed. To a large extent the available time will influence the type of calibration. There are two basic types of network analyser, both of them having their own advantages and limitations.
12.3
Scalar network analysers
The scalar network analyser usually consists of a source, display/processor and a transducer. Earlier scalar network analysers rarely included a receiver, instead they
264 Microwave measurements
Figure 12.1
Photograph of a typical wideband detector based scalar network analyser and accessories
normally employ wide band diode detectors that have the advantage of being able to make measurements over a very wide frequency range at high speed (Figure 12.1). Because this type operates over such a wide range the noise floor usually limits their low amplitude response to around −70 dBm. Diode detectors do not have a linear response to amplitude so the display/processor will also include a table of corrections (within the memory) that are applied to the measured values before being displayed. A very useful application of the scalar network analyser is its ability to characterise the transmission properties of mixers where the incident signal will be at a different frequency to the output signal. Filters might need to be selected to reject any unwanted signals generated by the mixer. More modern scalar network analysers are based on spectrum analysers (with one or more inputs) with a tracking generator (or two) included (Figure 12.2). With the rapidly decreasing costs of electronic equipment both the sources and receiver sections of these instruments are usually synthesised. A scalar network analyser of this design will be similar in complexity to its vector cousin, although it will lack many of the useful features (due to it being unable to measure the phase component of any signal). It will often have the advantage that it can be used as a standalone source or spectrum analyser, in some cases making it a more cost-effective solution.
Calibration of automatic network analysers 265
Figure 12.2
Photograph of a high-performance spectrum analyser based scalar network analyzer, which uses a high-performance external source as the tracking generator
Figure 12.3
Network, spectrum, impedance analyser combined with a test-set used for making a wide range of RF and LF measurements
Due to it using a spectrum analyser as the detector this type of scalar network analyser will usually have a very large dynamic range, and depending on the quality of the included spectrum analyser, will often have a good linearity characteristic. With the inclusion of digital filters this type of scalar network analyser can have a speed performance similar to that obtained using wideband detectors, but with a linearity and selectivity performance similar to that of the vector network analyser. Fully integrated analysers (Figure 12.3) are now available combining vector network, spectrum, impedance, gain, phase, group delay, distortion, harmonics, spurious
266 Microwave measurements and noise measurements in one instrument. When combined with a test set, these instruments provide reflection measurements, such as return loss, VSWR, voltage reflection coefficient and S-parameters in both real and imaginary units that can be displayed as magnitude and phase if desired. These instruments combine tremendous dynamic range (>140 dB is normal) with good linearity and full vector or scalar error-correction creating the ability to perform accurate measurements very quickly. At present these, due their complexity, useful instruments are limited to radio frequencies (RFs).
12.4
Vector network analyser
The vector network analyser consists of a display/processor, source, test set and receivers. Modern vector network analysers are usually encompassed in one compact enclosure (Figure 12.4). They are capable of measuring all of the small signal scattering parameters of a two-port device connected to it in near real time. Because the instrument employs a receiver (often with an adjustable bandwidth) it is able to make reliable measurements over a much wider amplitude range than with the wide band detector based scalar network analyser. The term ‘vector’ also demonstrates that the analyser is able to measure the quantity in terms of phase and magnitude. By using vector measurements we are able to fully characterise the analyser and then apply corrections when an item is measured. The major part of any errors introduced by the loading effects of the item being measured, or the analyser itself, can be effectively removed by calculation thereby producing very accurate values with reasonable speed. Modern analysers are able to display the measurements in a variety of formats including phase and magnitude, real and imaginary, impedance co-ordinates, etc. Despite their relatively high-cost vector network analysers are employed to make a variety of measurements where accuracy and speed are important.
Figure 12.4
Modern vector network analyser covering the frequency range 10 MHz to 67 GHz
Calibration of automatic network analysers 267
12.5
Calibration of a scalar network analyser
12.5.1 Transmission measurements Because scalar network analysers are unable to measure the phase component of any signal the calibration process is much simpler and faster than that necessary with the vector network analyser. Calibration for transmission measurements is simply a process of establishing a reference level to which the measured values will be referred. This is accomplished by connecting the detector to the source, allowing the instrument to sweep through the range of frequencies, and storing the values in the instrument’s memory. The device to be measured is then connected between the source and the detector and the instrument swept through the range of frequencies again. The difference between the first set of measurements (stored in memory) and the second set will be due to the device being tested plus any errors within the measurement system. Large potential errors with this type of measurement occur due to the mismatch loss uncertainties where the detector is connected to the source, and where the device being measured is connected to the source and detector. These uncertainties can be reduced by performing measurements through well-matched attenuators or couplers, but it is still likely that the mismatch loss uncertainties will dominate the uncertainty budget. In addition, where attenuators or couplers are used their value has to be chosen very carefully. High-value attenuators often have the best match and provide the best isolation against re-reflections and mismatch effects, but they also allow less of the signal to pass through, therefore reducing the effective dynamic range of the measurement. It is usually not practical to increase the source power as the higher power attenuators required to improve the match at the insertion point are often a poorer match than their lower power counterparts. Another alternative is to use a second detector and a power splitter. The ratio of the power appearing at the output ports of the power splitter is recorded (in the analyser’s memory) and the device to be measured is connected between one output port and its detector. The measurements are performed again and the difference between the first and the second measurements will be due to the device being tested. Using this configuration and by connecting an appropriate attenuator between the reference detector and the power splitter, and then, perhaps by using an amplifier increasing the signal generator’s amplitude between the first and second measurement it is possible to make measurements using the analyser over a much wider amplitude range than is specified. Spectrum analyser based instruments will enable a wider variety of attenuators or couplers to be used in the matching process as this type of analyser has a much wider dynamic range which copes with the additional losses much better.
12.5.2 Reflection measurements Calibrating prior to making reflection measurements follows a similar process of setting a reference and performing measurements relative to it. The input port of the bridge is connected to the generator and a short circuit connected to the bridge’s test port. The generator is swept through the range of desired frequencies and the values stored in the scalar network analyser’s memory.
268 Microwave measurements The short circuit is then replaced with an open circuit and the source is swept again through the range of desired frequencies and the values stored again in the analyser’s memory. The mean of these two sets of measurements is used as a reference and all measured values of reflection referred to it. It is important that the open circuit and short circuit are exactly 180◦ apart throughout the frequency range or further errors will be present in the measurement. Because an open circuit will always have a capacitance term associated with it and a short circuit effectively shunts any capacitance it is not normally possible to satisfy this requirement over the entire frequency range. The resultant errors are normally included as contributions to the uncertainty budget, having the most effect on the bridge’s source match estimate. As with transmission measurements, compromises are often made to ensure that the best quality measurement is performed without compromising speed or cost, etc. For instance, it is good practice to include a power splitter at the input to the bridge and connect a detector to the other output port of the power splitter. The scalar network analyser is then set to measure the ratio of the bridge over the detector’s output. The power splitter and detector perform three functions: (1) They measure and compensate for any variations in the generator’s output power which may not have been compensated for with the generator’s automatic level control. (2) When the directional bridge output port is loaded with different impedance devices connected to it (such as the short and open circuits and device being tested) it may cause the generator’s output amplitude to change. This phenomenon is almost eliminated by this arrangement. (3) The mismatch looking into the directional bridge’s test port is a contribution to the measurement uncertainties; if it can be improved the uncertainties will reduce. A typical microwave generator has a fairly poor mismatch, whereas power splitters have a fairly good mismatch in comparison. The mismatch of the generator or power splitter is transmitted through the bridge and will have an effect upon the resultant measurement uncertainties. When used in this configuration the effective output match of the power splitter is at its best, therefore transferring the best measurement conditions through the bridge. Unfortunately, as with transmission measurements, there is a downside. Every power splitter has loss and inserting more loss into the measuring system will reduce the dynamic range thereby increasing the noise floor. Power splitters and detectors also cost money and each item will have a maintenance cost associated with it so including additional items in the measurements will increase costs. Inserting a good quality attenuator between the directional bridge and the source will also improve the ‘effective source match’. To be effective the attenuator will need to have at least 20 dB transmission loss so it will not be suitable for most wideband detector systems. This method could be the most cost-effective for the spectrum analyser based system. A reasonably high value of attenuator will perform exactly the same function as the power splitter above but at a fraction of the cost.
Calibration of automatic network analysers 269
12.6
Problems associated with scalar network analyser measurements
The scalar network analyser measurement system consists of a microwave generator, detector (or a bridge and detector) and a scalar network analyser. The scalar network analyser is very similar to an oscilloscope in construction and operation. It has an input for the x-scale and several inputs for the detectors which display on the y-axis. The time base or x-axis is usually derived from the sweep output of the signal generator. Modern scalar network analysers also have a digital connection to the signal generator so that the display can be annotated with the start and stop frequencies, enabling easier control of the instruments. In addition, the digital connection is often used to connect to printers, plotters and disk drives to provide a permanent record of the test results. It can also be used to connect a computer so that the entire measurement process, presentation and archiving of results can be automated. The biggest problem with any measurement system employing diode type detectors is that they have different responses depending on the applied power level. At low powers (less than −30 dBm) they typically have a response proportional to the square of the applied power. As the power level increases their response becomes closer to a linear response. The designers of the early scalar network analysers tried to compensate for this effect by having active feedback loops in the conditioning amplifiers in the analyser; more modern instruments compensate for these effects digitally. Another problem is the limited dynamic range when compared to network analyser with a tuned front end. The diode detector often has a very wide frequency response (10 MHz to 26.5 GHz is common and 10–50 MHz is becoming more popular) which results in its ability to detect and add many very small signals across its operating spectrum. Where each of these signals might have a very small amplitude when they are all combined they effectively produce a noise floor of around −70 dBm. At this level the random component in the measurements is usually too large for sensible measurements to be performed so scalar network analyser measurements are often limited to −60 dBm. At the higher powers the detectors might suffer from being over loaded so most diode detectors are limited to a maximum input power of about +16 dBm.
12.7
Calibration of a vector network analyser
The vector network analyser as the name suggests also has the capability to measure the relative phase of the signals. The measurement system employs several receivers (usually three or four) to make the measurements as fast as possible without the need for extensive switching of the signals. On modern instruments the ‘resolution bandwidth’ is switchable allowing the user to make compromises between accuracy and speed. A process known as ‘accuracy enhancement’ is usually employed to reduce the errors in measurement due to the network analyser. Expressed simply, accuracy enhancement is the process whereby the network analyser is characterised using known standards so the errors within the measurement are removed mathematically. Each device, which is used for this characterisation, is manufactured to be excellent
270 Microwave measurements for only one parameter or purpose (e.g. a short should have 100 per cent reflection or a load should have 100 per cent absorption) so it is a lot easier to manufacture these ‘simple’ devices than the perfect couplers which might otherwise be required. A potential confusion in terms often occurs, the term ‘calibration’ when applied to vector network analysers is usually intended to describe the ‘accuracy enhancement’ process. The following paragraphs are taken from the Agilent Technologies 8722ES operating manual [2] and the Hewlett-Packard HP8753A operating manual [3] and describe in some detail the process of ‘accuracy enhancement’.
12.8
Accuracy enhancement
12.8.1 What causes measurement errors? Network analysis measurement errors can be separated into systematic, random and drift errors. Correctable systematic errors are the repeatable errors that the system can measure. These are errors due to mismatch and leakage in the test setup, isolation between the reference and test signal paths, and system frequency response. The system cannot measure and correct for the non-repeatable random and drift errors. These errors affect both reflection and transmission measurements. Random errors are measurement variations due to noise and connector repeatability. Drift errors include frequency drift, temperature drift, and other physical changes in the test setup between calibration and measurement. The resulting measurement is the vector sum of the test device response plus all error terms. The precise effect of each error term depends on its magnitude and phase relationship to the actual test device response. In most high-frequency measurements the systematic errors are the most significant source of measurement uncertainty. Since each of these errors can be characterised, their effects can be effectively removed to obtain a corrected value for the test device response. For the purpose of vector accuracy enhancement, these uncertainties are quantified as directivity, source match, load match, isolation (crosstalk) and frequency response (tracking). The description of each of these systematic errors follows. Random and drift errors cannot be precisely quantified, so they must be treated as producing a cumulative uncertainty in the measured data.
12.8.2 Directivity Normally a device that can separate the reverse from the forward travelling waves (a directional bridge or coupler) is used to detect the signal reflected from the test device. Ideally the coupler would completely separate the incident and reflected signals, and only the reflected signal would appear at the coupled output (Figure 12.5). However, an actual coupler is not perfect. A small amount of the incident signal appears at the coupled output due to leakage as well as reflection from the termination in the coupled arm (Figure 12.6). Also, reflections from the coupler output connector appear at the coupled output, adding uncertainty to the signal reflected from the device.
Calibration of automatic network analysers 271 Coupled output
Main coupler output
Input
Incident Reflected
Figure 12.5
Diagrammatic representation of an ideal directional coupler or directional bridge Coupled output
Main coupler output
Input Incident Reflected
Figure 12.6
Diagrammatic representation of an actual directional coupler or directional bridge showing the various error paths
The figure of merit for how well a coupler separates forward and reverse waves is directivity. The greater the directivity of the device, the better the signal separation. System directivity is the vector sum of all leakage signals appearing at the analyser receiver input. The error contributed by directivity is independent of the characteristics of the test device and it usually produces the major ambiguity in measurements of low reflection devices.
12.8.3 Source match Source match is defined as the vector sum of signals appearing at the analyser receiver input due to the impedance mismatch at the test device looking back into the source, as well as to adapter and cable mismatches and losses (Figure 12.7). In a reflection measurement, the source match error signal is caused by some of the reflected signal from the test device being reflected from the source back towards the test device and re-reflected from the test device. In a transmission measurement, the source match error signal is caused by reflection from the test device that is re-reflected from the source.
272 Microwave measurements Coupled output
Main coupler output
Input
DUT
Re-reflected
Reflected from the source
Reflected Incident
Figure 12.7
Diagrammatic representation of the constituent parts in the formation of source match
Input
Reflected Incident
Port 1
Port 2 DUT Reflected from load match Transmitted
Figure 12.8
Diagrammatic representation of the constituent parts in the formation of load match
The error contributed by source match is dependent on the relationship between the actual input impedance of the test device and the equivalent match of the source. It is a factor in both transmission and reflection measurements. Source match is a particular problem in measurements where there is a large impedance mismatch at the measurement plane (e.g. reflection devices such as filters with stop bands).
12.8.4 Load match Load match error results from an imperfect match at the output of the test device. It is caused by impedance mismatches between the test device output port and port 2 of the measurement system. Some of the transmitted signal is reflected from port 2 back to the test device. A portion of this wave may be re-reflected to port 2, or part may be transmitted through the device in the reverse direction to appear at port 1. If the test device has low insertion loss (e.g. a filter pass band), the signal reflected from port 2 and re-reflected from the source causes a significant error because the test device does not attenuate the signal significantly on each reflection (Figure 12.8). The error contributed by load match is dependent on the relationship between the actual output impedance of the test device and the effective match of the return port (port 2). It is a factor in all transmission measurements and in reflection measurements of two-port devices.
Calibration of automatic network analysers 273 The interaction between load match and source match is less significant when the test device insertion loss is greater than about 6 dB. However, source match and load match still interact with the input and output matches of the DUT, which contributes to transmission measurement errors (these errors are largest for devices with highly reflective ports).
12.8.5 Isolation (crosstalk) Leakage of energy between analyser signal paths contributes to error in a transmission measurement, much like directivity does in a reflection measurement. Isolation is the vector sum of signals appearing at the analyser samplers due to crosstalk between the reference and test signal paths. This includes signal leakage within the test set and in both the RF and IF sections of the receiver. The error contributed by isolation depends on the characteristics of the test device. Isolation is a factor in high-loss transmission measurements. However, analyser system isolation is more than sufficient for most measurements, and correction for it may be unnecessary. For measuring devices with high dynamic range, accuracy enhancement can provide improvements in isolation that are limited only by the noise floor. Generally, the isolation falls below the noise floor, therefore, when performing an isolation calibration the performer should use a noise reduction function such as averaging or reducing the IF bandwidth.
12.8.6 Frequency response (tracking) This is the vector sum of all test setup variations in which magnitude and phase change as a function of frequency. This includes variations contributed by signal π separation devices, test cables, adapters, and variations between the reference and test signal paths. This error is a factor in both transmission and reflection measurements.
12.9
Characterising microwave systematic errors
12.9.1 One-port error model In a measurement of the reflection coefficient (magnitude and phase) of a test device, the measured data differs from the actual, no matter how carefully the measurement is made. Directivity, source match and reflection signal path frequency response (tracking) are the major sources of error (Figure 12.9). To characterise the errors, the reflection coefficient is measured by first separating the incident signal (I) from the reflected signal (R), then taking the ratio of the two values. Ideally, (R) consists only of the signal reflected by the test device (S11A , for S11 actual) (Figure 12.10). However, all of the incident signal does not always reach the unknown. Some of (I) may appear at the measurement system input due to leakage through the test set or through a signal separation device. Also, some of (I) may be reflected by imperfect adapters between a signal separation device and the measurement plane. The vector
274 Microwave measurements
Measurement errors Directivity Frequency tracking Source match
S11M
S11A
Measured data
Figure 12.9
Unknown
Sources of error in reflection measurement
Incident power (I) R S11m = — I
S11A Reflected power (R)
Unknown
Figure 12.10
Reflection coefficient model
Effective directivity I
EDF
S11A
R
Unknown
Figure 12.11
Effective directivity (EDF ) model
sum of the leakage and the miscellaneous reflections is the effective directivity, EDF (Figure 12.11). Understandably, the measurement is distorted when the directivity signal combines with the actual reflected signal from the unknown, S11A. Since the measurement system test port is never exactly the characteristic impedance (50 0003), some of the reflected signal bounces off the test port, or other
Calibration of automatic network analysers 275
Source match I
EDF
S11A
ESF
R
Unknown
Figure 12.12
Source match (ESF ) model ERF frequency tracking
S11M
EDF
ESF
S11A
I
Figure 12.13
Reflection tracking (ERF ) model
impedance transitions further down the line, and back to the unknown, adding to the original incident signal (I). This effect causes the magnitude and phase of the incident signal to vary as a function of S11A and frequency. Levelling the source to produce a constant incident signal (I) reduces this error, but since the source cannot be exactly levelled at the test device input, levelling cannot eliminate all power variations. This re-reflection effect and the resultant incident power variation are caused by the source match error, ESF (Figure 12.12). Frequency response (tracking) error is caused by variations in magnitude and phase flatness versus frequency between the test and reference signal paths. These are mainly due to coupler roll off, imperfectly matched samplers, and differences in length and loss between the incident and test signal paths. The vector sum of these variations is the reflection signal path tracking error, ERF (Figure 12.13). These three errors are mathematically related to the actual data, S11A , and measured data, S11M , by the following equation: S11M = EDF +
(S11A ERF ) (1 − ESF S11A )
(12.1)
276 Microwave measurements
50 Ω
S11M = 0 EDF +
Figure 12.14
S11A = 0
(0) (ERF) 1–ESF (0)
‘Perfect load’ termination model
If the value of these three ‘E’ errors and the measured test device response were known for each frequency, this equation could be solved for S11A to obtain the actual test device response. Because each of these errors changes with frequency, their values must be known at each test frequency. These values are found by measuring the system at the measurement plane using three independent standards whose S11 is known at all frequencies. The first standard applied is a ‘perfect load’, which assumes S11 = 0 and essentially measures directivity (Figure 12.14). ‘Perfect load’ implies a reflection-less termination at the measurement plane. All incident energy is absorbed. With S11A = 0 the equation can be solved for EDF , the directivity term. In practice, of course, the ‘perfect load’ is difficult to achieve, although very good broadband loads are available in the compatible calibration kits. Since the measured value for directivity is the vector sum of the actual directivity plus the actual reflection coefficient of the ‘perfect’ load, any reflection from the termination represents an error (Figures 12.15 and 12.16). System effective directivity becomes the actual reflection coefficient of the near ‘perfect load’. In general, any termination having a return loss value greater than the uncorrected system directivity reduces reflection measurement uncertainty. Next, a short circuit termination whose response is known to a very high degree is used to establish another condition (Figures 12.17 and 12.18. The open circuit gives the third independent condition (Figures 12.19 and 12.20). In order to accurately model the phase variation with frequency due to fringing capacitance from the open connector, a specially designed shielded open circuit is used for this step (the open circuit capacitance is different for each connector type). Now the values for EDF , directivity, ELF , source match, and ERF , reflection frequency response, are computed and stored. This completes the calibration procedure for one-port devices.
12.10 One-port device measurement The unknown one-port device is measured to obtain values for the measured response, S11M , at each frequency.
Calibration of automatic network analysers 277 Actual directivity before correction (DA)
Γ of load (ΓL)
(–DM) Measured directivity before correction (DM) Effective directivity after correction (DA–DM = –ΓL)
Figure 12.15
Vector diagram showing how effective directivity (EDF ) is resolved
Figure 12.16
Network analyser display with a sliding load on port 1 (S11 ) and a lowband load connected to port 2 (S22 )
This is the one-port error model equation solved for S11A (Figure 12.21). Since the three errors and S11M are now known for each test frequency, S11A can be computed using the following equation: S11A =
(S11M − EDF ) ESF (S11M − EDF ) + ERF
(12.2)
278 Microwave measurements
S11A = 1∠180°
S11M = EDF +
(−1) (ERF) 1–ESF (−1)
Figure 12.17
Short circuit termination model
Figure 12.18
Network analyser display with short circuits connected to both ports (S11 and S22 )
S11A = 1∠
S11M = EDF +
Figure 12.19
(1∠
fc)
(ERF)
1–ESF (1∠
fc)
Open circuit termination model
fc
Calibration of automatic network analysers 279
Figure 12.20
Network analyser display with open circuits connected to both ports (S11 and S22 )
S11A
S11M = EDF +
Figure 12.21
S11A =?
(S11A) (ERF) 1–ESFS11A
Flow diagram representing the individual constituents of an S11 reflection measurement
For reflection measurements on two-port devices, the same technique can be applied, but the test device output port must be terminated in the system characteristic impedance. This termination should have as low a reflection coefficient as the load used to determine directivity. The additional reflection error caused by an improper termination at the test device’s output port is not usually incorporated into the one-port error model.
12.11
Two-port error model
The error model for measurement of the transmission coefficients (magnitude and phase) of a two-port device is derived in a similar manner. The potential sources of
280 Microwave measurements
Measurement errors Tracking
S21M Source match
S21A
Load match Measured value
Isolation Directivity Unknown
Figure 12.22
Major sources of error in transmission measurements of a two-port device (I)
(T)
Forward
S21M S21A
ETF
S12A =
S12M S12A
S21M ETF
(I) Reverse
(T)
Figure 12.23
S21A =
ETR
S12M ETF
Constituent parts of the transmission coefficient model
error are frequency response (tracking), source match, load match and isolation as shown in Figure 12.22. On a two-port network analyser these errors are effectively removed using the full two-port error model. The transmission coefficient is measured by taking the ratio of the incident signal (I) and the transmitted signal (T) (Figure 12.23). Ideally, (I) consists only of power delivered by the source and (T) consists only of power emerging at the test device output. As in the reflection model, source match can cause the incident signal to vary as a function of test device S11A . Also, since the test setup transmission return port is never exactly the characteristic impedance, some of the transmitted signals are reflected from the test set port 2, and from other mismatches between the test device output and the receiver input, to return to the test device. A portion of this signal may be re-reflected at port 2, thus affecting S21M , or part may be transmitted through the device in the reverse direction to appear at port 1, thus affecting S11M . This error term, which causes the magnitude and phase of the transmitted signal to vary as a function of S22A , is called load match, ELF (Figure 12.24). The measured value, S21M , consists of signal components that vary as a function of the relationship between ESF and S11A as well as ELF and S22A , so the input and
Calibration of automatic network analysers 281 Port 1
Port 2
S21
(I)
ESF
S11
(T)S21M
S22
Load match
Source match
ERF
Figure 12.24
ELF
S12
Load match error model
output reflection coefficients of the test device must be measured and stored for use in the S21A error-correction computation. Thus, the test setup is calibrated as described for reflection to establish the directivity, EDF , source match, ESF , and reflection frequency response, ERF , terms for reflection measurements on both ports. Now that a calibrated port is available for reflection measurements, the thru is connected and load match, ELF , is determined by measuring the reflection coefficient of the thru connection. Transmission signal path frequency response is then measured with the thru connected. The data are corrected for source and load match effects, then stored as transmission frequency response, ETF . Note: It is very important that the exact electrical length of the thru be known. Most calibration kits assume a zero length thru. For some connection types such as Type-N, this implies one male and one female port. If the test system requires a non-zero length thru, for example, one with two male test ports, the exact electrical delay of the thru adapter must be used to modify the built-in calibration kit definition of the thru.
Isolation, EXF , represents the part of the incident signal that appears at the receiver without actually passing through the test device (Figures 12.25 and 12.26). Isolation is measured with the test set in the transmission configuration and with terminations installed at the points where the test device will be connected. Since isolation can be lower than the noise floor, it is best to increase averaging by at least a factor of 4 during the isolation portion of the calibration. Note: If the leakage (isolation) falls below the noise floor, it is best to increase averaging before calibration. If it is not possible to increase the averaging it will be better to omit the isolation measurement.
Thus there are two sets of error terms, forward and reverse, with each set consisting of six error terms, as follows: • Directivity, EDF (forward) and EDR (reverse) • Isolation, EXF and EXR • Source match, ESF and ESR
282 Microwave measurements EXF
Isolation
EFT S21M
(I)
Port 1
Port 2
Figure 12.25
Isolation error model
Figure 12.26
Typical network analyser display during the isolation measurement
• • •
Load match, ELF and ELR Transmission tracking, ETF and ETR Reflection tracking, ERF and ERR
Network analysers equipped with S-parameter test sets can measure both the forward and reverse characteristics of the test device without the performer having to manually remove and physically reverse the device. A full two-port error model is illustrated in Figure 12.28. This illustration depicts how the analyser effectively removes both the forward and reverse error terms for transmission and reflection measurements.
Calibration of automatic network analysers 283
Figure 12.27
Typical network analyser display during the ‘through’ measurement Forward
EXF 1
S21A
ETF
S11A S22A
ELF
ESF ERF
S12A
RF IN
EDF S11M
Port 1 Reverse
Port 2
S21A S11A
S12M
ELR ETR
S21M
ERR ESR
S22A S12A
1
S22M EDR RF IN
EXR
Figure 12.28
Full two-port error model
The equations for all four S-parameters of a two-port device are shown in Figure 12.29. Note that the mathematics for this comprehensive two-port error model use all forward and reverse error terms and measured values. Thus, to perform full error-correction for any one parameter, all four S-parameters must be measured.
284 Microwave measurements
Figure 12.29
Mathematical representation of the full two-port error model algorithms
12.12 TRL calibration 12.12.1 TRL terminology Notice that the letters TRL, LRL, LRM etc. are often interchanged, depending on the standards used. For example ‘LRL’ indicates that two lines and a reflect standard are used and LRM indicates that a reflection and match standards are used. All of these refer to the same basic method. TRL∗ calibration is a modified form of TRL calibration. It is adapted for a receiver with three samplers instead of four samplers. The TRL∗ calibration is not as accurate as the TRL calibration because it cannot isolate the source match from the load match, so it assumes that load match and source match are equal. 12.12.1.1 How TRL∗ /LRL∗ calibration works The TRL/LRL calibration used in the network analyser relies on the characteristic impedance of simple transmission lines rather than on a set of discrete impedance
Calibration of automatic network analysers 285
R
B
A
Error adapter
(SA)
Error adapter
8 Error terms
Figure 12.30
Functional block diagram for a two-port error corrected network analyser measurement system employing only three receivers
standards. Since transmission lines are relatively easy to fabricate (e.g. in microstrip or co-axial), the impedance of these lines can be determined from the physical dimensions and substrate’s dielectric constant. For the analyser TRL∗ two-port calibration, a total of ten measurements are made to quantify eight unknowns (not including the two isolation error terms). Assume the two transmission leakage terms, EXF and EXR are measured using the conventional technique. The eight error terms are represented by the error adapters shown in Figure 12.30. Although this error model is slightly different from the traditional Full two-port 12-term model, the conventional error terms may be derived from it. For example, the forward reflection tracking (ERF ) is represented by the product of ε10 and ε01 . Also notice that the forward source match (ESF ) and reverse load match (ELR ) are both represented by ε11 while both the reverse source match (ESR ) and forward load match (ELF ) are represented by ε22 . In order to solve for these eight unknown TRL error terms, eight linearly independent equations are required. The first step in the TRL∗ two-port calibration process is the same as the transmission step for a full two-port calibration. For the thru step, the test ports are connected together directly (zero length thru) or with a short length of transmission line (non-zero length thru) and the transmission frequency response and port match are measured in both directions by measuring all four S-parameters. For the reflect step, identical high-reflection coefficient standards (typically open or short circuits) are connected to each test port and measured (S11 and S22 ). For the line step, a short length of transmission line (different in length from the thru) is inserted between port 1 and port 2 and the frequency response and port match are measured in both directions by measuring all four S-parameters.
286 Microwave measurements In total, ten measurements are made, resulting in ten independent equations. However, the TRL error model has only eight error terms to solve for. The characteristic impedance of the line standard becomes the measurement reference and, therefore, has to be assumed ideal (or known) and defined precisely. At this point the forward and reverse directivity (EDF and EDR ), transmission tracking (ETF and ETR ) and reflection tracking (ERF and ERR ) terms may be derived from the TRL error terms. This leaves the isolation (EXF and EXR ), source match (ESF and ESR ) and load match (ELF and ELR ) terms to discuss. 12.12.1.2 Isolation Two additional measurements are required to solve for the isolation terms (EXF and EXR ). Isolation is characterised in the same manner as the full two-port calibration. Forward and reverse isolation are measured as the leakage (or crosstalk) from port 1 to port 2 with each port terminated. The isolation part of the calibration is generally only necessary when measuring high-loss devices (greater than 70 dB). 12.12.1.3 Source match and load match A TRL calibration assumes a perfectly balanced test set architecture as shown by the term which represents both the forward source match (ESF ) and reverse load match (ELR ) and by the (ε22 ) term which represents both the reverse source match (ESR ) and forward load match (ELF ). However, in any switching test set, the source and load match terms are not equal because the transfer switch presents a different terminating impedance as it is changed between port 1 and port 2. In network analysers based on a three-sampler receiver architecture, it is not possible to differentiate the source match from the load match terms. The terminating impedance of the switch is assumed to be the same in either direction. Therefore, the test port mismatch cannot be fully corrected. An assumption is made, such that Forward source match (ESF ) = reverse load match (ELR ) = ε11 Reverse source match (ESR ) = forward load match (ELF ) = ε22 For a fixture, TRL∗ can eliminate the effects of the fixture’s loss and length, but does not completely remove the effects due to the mismatch of the fixture. Note: Because the technique relies on the characteristic impedance of transmission lines, the mathematically equivalent method (for line-reflect-match) may be substituted for TRL. Since a well matched termination is, in essence, an infinitely long transmission line, it is well suited for low-frequency calibrations. Achieving a long line standard for low frequencies is often physically impossible.
Most of the latest network analysers are equipped with four receiver test-sets. In this configuration they are able to implement the full TRL algorithm.
12.12.2 True TRL/LRL Implementation of TRL calibration with a network analyser which employs four receivers requires a total of fourteen measurements to quantify ten unknowns as
Calibration of automatic network analysers 287 opposed to only a total of twelve measurements for TRL∗ (both include the two isolation error terms). Because of the four-sampler/receiver architecture, additional correction of the source match and load match terms is achieved by measuring the ratio of the two ‘reference’ receivers during the thru and line steps. These measurements characterise the impedance of the switch and associated hardware in both the forward and reverse measurement configurations. They are then used to modify the corresponding source and load match terms (for both forward and reverse). The four receiver configuration with TRL calibration establishes a higher performance calibration method over TRL∗ , because all significant error terms are systematically reduced. With TRL∗ , the source and load match terms are essentially that of the raw, ‘uncorrected’ performance of the hardware where as with TRL the source and load match terms are reduced in line with the quality of calibration kit components used.
12.12.3 The TRL calibration procedure When building a set of standards the requirements for each of the standard types specified in Table 12.1 must be satisfied. Table 12.1
TRL calibration procedure: requirements for each of the standard types
Standard types
Requirements
Thru
No loss Impedance (Z0 ) need not be known S21 = S12 = 1∠0◦ S11 = S22 = 0
Thru (non-zero length)
Z0 of the thru must be the same as the line. Attenuation of the thru need not be known. If the thru is used to set the reference plane, the insertion phase or electrical length must be well known and specified
Reflect
Reflection coefficient 0007 magnitude is optimally 1.0, but need not be known. Phase of 0007 must be known and specified to be within ±1/4 wavelength or 90◦ . 0007 must be identical on both ports. If the reflect is used to set the reference plane, the phase response must be well known and specified.
Line/match (line)
Z0 of the line establishes the impedance of the measurement (i.e. S11 = S22 = 0). Insertion phase of the line must be different from the thru. Difference between thru and line must be >20◦ and <160◦ . Attenuation need not be known. Insertion should be known
Line/match (match)
Z0 of the match establishes the reference impedance of the measurement. 0007 must be identical on both ports
288 Microwave measurements When calibrating a network analyser, the actual calibration standards must have known physical characteristics. For the reflect standard, these characteristics include the offset in electrical delay (seconds) and the loss (0003 per second of delay). The characteristic impedance, Z0 , is not used in the calculations in that it is determined by the line standard. The reflection coefficient magnitude should optimally be 1.0, but need not be known since the same reflection coefficient magnitude must be applied to both ports. The thru standard may be a zero ss-length or known length of transmission line. The value of length must be converted to electrical delay, just like that done for the reflect standard. The loss term must also be specified. The line standard must meet specific frequency-related criteria, in conjunction with the length used by the thru standard. In particular, the insertion phase of the line must not be the same as the thru. The optimal line length is 14 wavelength (90◦ ) relative to a zero length thru at the frequency of interest, and between 20◦ and 160◦ of phase difference over the frequency range of interest. (Note: these phase values can be ±N × 180◦ , where N is an integer.) If two lines are used the difference in electrical length of the two lines should meet these optimal conditions. Measurement uncertainty will increase significantly when the insertion phase nears zero or is an integer multiple of 180◦ , and this condition is not recommended. For a transmission medium that exhibits linear phase over the frequency range of interest, the following expression can be used to determine a suitable line length of 1 4 wavelength at the frequency (which equals the sum of the start frequency and stop frequency divided by 2): Electrical length (cm) = (Line − Zero length thru) Electrical length (cm) =
(15,000 × VF) f1 (MHz) + f2 (MHz)
(12.3)
where f1 = 1000 MHz, f2 = 2000 MHz and VF = Velocity Factor = 1. Thus the length to initially check is 5 cm. Next, use the following to verify the insertion phase at f1 and f2 (1000 and 2000 MHz): (360 × f × l) (12.4) v where f is the frequency (MHz), l is the length of line (cm) and v = velocity = speed of light × velocity factor, which can be reduced to the following: Phase (degrees) =
0.012 × f (MHz) × l (cm) (12.5) VF So for an airline (velocity factor is approximately 1) at 1000 MHz, the insertion phase is 60◦ for a 5 cm line; it is 120◦ at 2000 MHz. This line would be suitable as a line standard. Where the standard is fabricated in other media (microstrip for instance) the velocity factor is significant. For example, if the dielectric constant for a substrate is 10, and the corresponding ‘effective’ dielectric √ constant for microstrip is 6.5, then the ‘effective’ velocity factor equals 0.39 (1 + 6.5). Phase (degrees) approximately =
Calibration of automatic network analysers 289 Using the above a potential problem using TRL becomes evident. The lengths of airline required at low frequencies become so long that they are difficult to fabricate.
12.13 Data-based calibrations Traditionally the calibration standards used in any network analyser calibration routine have been defined in terms of the way in which their parameters vary in relation to the measurement frequency; for instance, the open circuit would be defined in terms of capacitance. Three or four frequency terms would be employed, f , f 2 , f 3 and sometimes f 4 . Open circuits would be defined in a similar manner, in terms of inductance. As correction algorithms progressed some standards were defined in terms of both capacitance and inductance. Loads were usually considered as perfect. These definitions are usually excellent providing that it is possible to define the standards using smooth curves. As processors and particularly memory have become cheaper another method of defining the calibration standards has become available, the data-based calibration. Each standard is measured across the frequency range of interest using the best equipment and techniques available. These measured values are entered into the network analyser’s database and used in the correction algorithms. At frequencies where data are not available the network analyser uses interpolation, thus if measurements are made at more frequencies on the standards, the resulting network analyser measurements will become more accurate. Electronic calibration units, where the standards are in one enclosure and a switch matrix employed to apply them to the network analyser, often use a data-based calibration routine. The accuracy available from the data-based calibration employing the electronic calibration units approaches the best available from TRL calibrations, but without needing the same level of skilled operator.
References 1 J.M. Hawkins (ed.): The Oxford Reference Dictionary. (Oxford University Press, Oxford, 1987, reprinted 1989) 2 8719ET/20ET/22ET, 8719ES/20ES/22ES Network Analysers User’s Guide, Agilent Technologies, Inc. 2000 3 HP8753A Network Analyser Operating and Programming Reference–0875390015, Hewlett-Packard Company, 1986. Now Agilent Technologies, Inc.
Chapter 13
Verification of automatic network analysers Ian Instone
13.1
Introduction
Network analysers are complex instruments that can combine many different instruments within one measurement system. With this in mind it is easy to make apparently similar measurements with a variety of different instrument settings. Each setting may enhance one particular aspect of the measurement, but this is often traded off in another area. For example, to improve repeatability we might increase the averaging or decrease the bandwidth or use a combination of both. The resulting improvement in repeatability will usually be at the expense of the considerably increased measurement time. This chapter discusses different types of verification which may be applied to network analyser measurements to enable the user to assess or confirm the most appropriate choice of settings on the network analyser for their particular measurement scenario.
13.2
Definition of verification
As with calibration, it is important to understand the interpretation of the word ‘verification’. The Oxford Reference Dictionary (1989) defines the word ‘verify’ as ‘to establish the truth or correctness of by examination or demonstration; (of an event etc.) to bear out, to fulfil (a prediction or promise)’. This dictionary definition exactly describes the process of verification as applied to automatic network analysers; the quality of measurements which the analyser is capable of making is verified by comparing them with values obtained from another source, whereas calibration characterises the network analyser prior to ‘corrected’ measurements being performed.
292 Microwave measurements
13.3
Types of verification
There are several different methods of verification so the method chosen needs to address the particular requirements of the user. In all cases the method chosen or designed should provide the user with at least acceptable confidence that the measurements being made with the network analyser meet the user’s minimum quality requirements. Verification limits are set using a combination of the measurement uncertainties and the acceptable product quality. Uncertainties should be assessed using an accepted method such as that described in EA-10/12, Guidelines on the Evaluation of Vector Network Analysers, available free from http://www. euromet.org/docs/calguides/index.html
13.3.1 Verification of error terms As described in the previous chapter, the corrected network analyser’s display is made up of the following elements: (1) (2) (3) (4)
parameters of the device under test (DUT), errors contributed by the measurement system, corrections applied to the measurements and residual errors present after correction.
Verification of the network analyser’s residual errors after correction involves measuring and quantifying the residual errors present after the error correction has been applied. This method is perhaps one of the most difficult to perform, is the most time consuming, and requires the highest skill levels, but will enable the user to determine exactly which components may require attention without any additional measurements having to be performed. Typically, this type of verification provides the greatest insight into the characteristics of the network analyser and calibration kit used.
13.3.2 Verification of measurements This verification scheme involves calibrating the network analyser (usually as part of the normal measurement process) and then measuring a known artefact(s). Appropriate acceptance limits must be set when using this method as it is often possible for one parameter showing poor performance to be masked by other parameters where performance exceeds minimum expectations. Whilst this method provides the best assessment of all the contributors combining in the uncertainty budget, the danger is that one component in the calibration kit or network analyser which is beginning to deteriorate is masked by other parameters that are still exceeding expectations. This method, however, is one of the easiest to implement, easiest to understand and quickest to perform so warrants consideration on these points alone. On a production line this method might be implemented by periodically taking a ‘sample’ DUT and re-testing it on a different network analyser or measurement system. If the measurements from both systems are compared and the results found
Verification of automatic network analysers 293 to fall within the user’s acceptable quality limits it can be assumed that both systems are making acceptable measurements. This method is often used by network analyser manufacturers and their service agents when maintaining customer’s equipment at the customer’s site.
13.4
Calibration scheme
It should be possible to perform verification of the network analyser irrespective of the calibration scheme used. The correction coefficients employed as a result of the calibration may affect the acceptance limits used for the verification but should have little or no influence on the method of verification. Ideally the calibration scheme employed will be identical to that used for measurements, and might even be exactly the same calibration. As the verification verifies the satisfactory operation of the network analyser, test port leads, adapters and calibration kit, it is essential to ensure that all of these items are used in the calibration and verification process.
13.5
Error term verification
For a full two-port measurement seven dominant error terms that could be checked are as follows: (1) (2) (3) (4) (5) (6) (7)
effective directivity, effective source match, effective load match, effective isolation, effective tracking, effective linearity and repeatability.
The term ‘effective’ as used in the list above refers to the parameter after error correction has been applied. These terms are often referred to as the residual errors, which are also contributors to the uncertainty of measurement. Methods for checking most of these terms are shown in EA-10/12.
13.5.1 Effective directivity Directivity refers to the ability of a directional device, such as a coupler or directional bridge, to separate the forward and reverse signals. Where the bridge or coupler is embedded in a network analyser the most convenient way to measure this parameter is to first reflect all of the signal using a short or open circuit (the mean between the short and open circuit is considered the most accurate in this simplistic case) and set as a reference. The short or open circuit is then replaced with a fixed termination of the correct characteristic impedance. Where the fixed termination has a good match (negligible voltage reflection coefficient) the network analyser’s display will be
294 Microwave measurements
Figure 13.1
Typical network analyser display of the voltage reflection coefficient of a fixed broadband load
predominantly composed of the effective directivity. Since the perfect termination rarely exists, we need some method of separating the network analyser’s own errors from those generated by the fixed termination. These errors tend to increase as the measurement frequency increases. Two methods of ‘signal separation’ are discussed below (Figure 13.1). 13.5.1.1 Sliding load method A sliding load can be used to separate the directivity from the terminating load. Where possible the network analyser should be set to display the measurements in ‘linear mode’. After the reference has been recorded the sliding load is connected in place of the open or short circuits. If the load element is positioned furthest away from the input connector the network analyser will display a curve representing the match of the sliding load’s load element with ripple superimposed upon the measurement. The majority of ripple is produced by the directivity either adding ‘in phase’ or ‘anti-phase’ with the load element measurement. There will also be a small error produced in this measurement contributed by the effects of imperfect source match and an imperfect sliding load element; however, this error is often so small that it is neglected. The directivity may be assessed by measuring the height of the ripples: directivity will be one-half the ripple amplitude. Sometimes the transitions in match of the sliding load make the measurement of the superimposed ripple difficult or impossible. In these cases it will be necessary to make a continuous waves (CW) measurement. The network analyser’s marker is placed at the frequency of interest. The sliding load is adjusted so that a maximum value is observed using the marker and the value noted. The sliding load is now adjusted so that a minimum value is observed using
Verification of automatic network analysers 295 the marker and the value noted. The directivity is one-half of the difference between the two marker values. The major problem in using a sliding load is that measurements on sliding loads are difficult to perform and traceability for these measurements may not be easy to obtain. 13.5.1.2 Offset load or airline method This method works in a very similar way to the sliding load method. After the reference has been recorded the airline and fixed termination are connected in place of the open or short circuits. The network analyser will display a curve representing the match of the fixed termination with ripple (from the directivity) superimposed upon the measurement. Half of the amplitude of the ripple is the directivity. This method has the same problem as the sliding load method regarding the effects of source match. Providing the fixed termination has a small reflection coefficient this problem will be kept to a minimum (Figures 13.2 and 13.3). Where the fixed termination shows a rapid transition between two values of reflection coefficient it may not be possible to make an accurate measurement of directivity. Since this method should be independent of the fixed termination used, it will be perfectly valid to select another fixed termination with a different reflection coefficient profile to provide more reliable directivity measurements at these more difficult frequencies. The calibration devices used to characterise the effective directivity term are the low-band load (at lower frequencies), and the sliding load or short airline(s) at high frequencies except in broadband load calibrations where the broadband load is used
Figure 13.2
Ripple superimposed on the fixed load response caused by the interaction of directivity and the broadband load
296 Microwave measurements
Figure 13.3
Using another broadband load with a different profile can make the ripples easier to determine
exclusively to define the directivity term. The types of measurement most affected by directivity errors are low-reflection measurements; high-reflection measurements will often appear as normal.
13.5.2 Effective source match This term refers to the impedance of the directional bridge or coupler and associated cables and adapters as they are presented to the DUT. Methods of measurement are very similar to those used to measure effective directivity. However, since we need to measure source match we must feed a reasonable amplitude signal back into the directional bridge or coupler. This task is performed best using either a short or open circuit. The short or open circuit is usually connected to the directional bridge or coupler via an airline, which provides some phase shift enabling the source match to be shown as ripple superimposed on the reflection characteristics of the short or open circuit. One problem in trying to present these data is that the loss of the airline used is often a major part of the displayed measurement. This can make it difficult to determine the ripple amplitude when the source match is fairly small. Shorter airlines will reduce the loss and will also reduce the quantity of ripples observed so a suitable compromise must be achieved. Note in the following plots that there are some ripples of very short period which can be ignored as they are probably generated by other effects within the measurement system (Figures 13.4 and 13.5). As with directivity, the peak to peak height of the ripple is twice the source match. Note also that this measured source match also contains the directivity, which at any
Verification of automatic network analysers 297
Figure 13.4
Ripple caused by the interaction of the source match and an open circuit
Figure 13.5
Ripple caused by the interaction of the source match and a short circuit
given frequency may either add to or subtract from the source match. Since we have no easy way of separating the source match and directivity, we usually consider directivity as one of the sources of uncertainty when making source match measurements. Directivity is usually much smaller than source match so this assumption causes few problems. Time-domain gating (explained below) can be used to effectively separate these interacting terms. Unfortunately, it has not been possible to provide traceability for
298 Microwave measurements
Figure 13.6
Ripple caused by the interaction of the source match and short and open circuits
any measurements in the time-domain so this function is best left to the development laboratories where it provides useful improvements in test development times. One neat trick that can be employed to provide reliable and easy to read source match measurements is to either store or plot the display with a short circuit connected, then connect the open circuit. Assuming the short and open circuits are approximately 180◦ apart in reflection phase, the resultant display will be one of two traces where the ‘peaks and troughs’ occur at approximately the same frequencies (looking similar to the envelope on an Amplitude Modulated signal). The peaks and troughs can now be read at the same frequency, producing a more accurate value of source match at a particular frequency (Figure 13.6). It is also possible to use a sliding short circuit to determine source match at any particular frequency, using a similar technique as described for the sliding load in the measurement of directivity. Unfortunately, sliding short circuits fitted with co-axial connectors are now getting harder to obtain. This technique is still useful where rectangular waveguide is employed as the transmission medium because sliding short circuits in rectangular waveguide are still supplied by several manufacturers. The calibration items used to characterise the effective source match term are the short and open circuits. A poor connection of either of these devices will affect the effective source match. Further, open circuits usually have a centre pin supported with a delicate piece of dielectric; if this dielectric fractures and the centre pin is misplaced the effect on the source match will be massive. The measurements most affected by source match errors are high-reflection measurements and transmission measurements of highly reflective devices. Poor cables can cause both the directivity
Verification of automatic network analysers 299 and source match terms to vary as the cable is flexed. The effect of this variation is that there will be errors in the measured values .
13.5.3 Effective load match Effective load match is the effective impedance of the load presented to the DUT. For a full two-port measurement the load would be represented by the ‘receiving signal port’. As there appear to be no ‘classical’ methods for measuring load match it is usually assumed that it has a similar value to the source match. Refer to Network Analyser Uncertainty Computations for Small Signal Model Extractions by Jens Vidkjær [1] for more detailed information on this subject. The measurements most affected by effective load match are all transmission and reflection magnitude measurements of low insertion loss two-port devices.
13.5.4 Effective isolation Isolation is a measure of how much signal passes from one channel to the other when both channels are terminated in their characteristic impedance. Although the error correction routines are designed to compensate for some degree of poor isolation it is good practice to maintain as ideal a value as possible. The simplest way to measure isolation is to connect the two test port cables together and set a transmission reference in each direction on the screen. Then connect reasonably well-matched terminations to the DUT ends of the test port cables and repeat the transmission measurement. The screen display will be very noisy and should consist of a combination of the network analyser noise floor and the network analyser’s isolation. Poor isolation may be caused by loose connectors within the test set or poor or worn screening throughout the measurement system. In particular, look at the test port extension cables as these are often subjected to plenty of flexing and plenty of wear and tear at the connector. Whilst connectors in poor condition will be obvious to the experienced eye, there will be few visible signs of any deteriorating screening making regular testing desirable. Where isolation is found to be a constant value at any particular frequency corrections are applied. With modern network analysers having very good isolation, often in the same area as the instrument’s noise floor, there is often a danger that the values due to the noise floor become entered into the isolation corrections causing further errors rather than correcting them. Poor isolation would affect both reflection and transmission measurements where the test channel signal is at a very low level, that is, reflection measurements and also transmission measurements where the insertion loss of the DUT is large (i.e. greater than a 50 dB attenuator).
13.5.5 Transmission and reflection tracking This correctable error includes the effects of the insertion loss of the signal separation devices, detectors (or samplers), cables, signal paths and any other items in the signal paths. Residual errors after correction may be analysed by connecting the test port cables together and examining the transmission trace. Any deviation from 0 dB may be
300 Microwave measurements due to tracking. Also, there may be an amplitude-dependent tracking error; this would be checked in the same way, but in addition the source power would be varied and the trace deviation from the 0 dB level noted. The calibration devices used to characterise transmission tracking are the transmission measurements of the ‘thru’ connection. Large variations in the tracking terms might indicate a problem in the reference or test signal path in the test set or poor connections during the calibration process. All transmission measurements are affected by transmission tracking errors. The calibration devices used to characterise reflection tracking are the short and open circuits. As with transmission tracking large variations in the tracking term might indicate a problem in the reference or test signal path in the test set or poor connections during the calibration process. All reflection measurements are affected by transmission tracking errors.
13.5.6 Effective linearity Deviation from linearity may be checked by measuring a previously calibrated stepattenuator. Providing the step-attenuator has been calibrated with a sufficiently low measurement uncertainty, and the step-attenuator has a good match in each direction, it can be assumed that any deviations noted are due to the network analyser’s deviation from ideal linearity. Effective linearity is a significant contributor in the uncertainty budget and needs to be assessed with the signal travelling in either direction. Linearity is not a term characterised using the calibration kit. Some network analysers have corrections for linearity which may be updated when a routine maintenance check is performed. All measurements are affected by linearity. 13.5.6.1 Time-domain and de-embedding Many of the higher frequency network analysers are capable of performing fast Fourier transforms (FFTs). Where implemented this process allows measurements of components within complex networks to be displayed using a process known as ‘time-domain gating’. The component under test or evaluation is mathematically de-embedded from its surrounding network and its response displayed on the screen of the network analyser. This function can be employed to provide values of directivity and source match providing a suitable reference (usually an airline in same characteristic impedance as the coupler or directional bridge) is available. Unfortunately, traceability of measurement has not been developed for this type of time-domain function, so these measurement methods are best left for routine maintenance and diagnostic tasks rather than the task of ensuring traceability of measurement. The concept of time-domain gating refers to mathematically removing a portion of the time-domain response, and then viewing the result in the frequency domain. The intent is to remove the effects of unwanted reflections, say from connectors and transitions leaving just the response of the device being measured. An experienced operator will be able to perform measurements of directivity, source match and load match much faster using time-domain gating rather than using any of the alternative methods described above.
Verification of automatic network analysers 301
13.6
Verification of measurements
This method of verification is perhaps easier to understand and provides a much easier visualisation of the general health of the network analyser, calibration kit and test port cables. The method involves calibrating the network analyser then measuring an artefact or artefacts. The measurements are then compared either with measurements performed earlier, or if it is desired to obtain traceability this way they would be compared with measurements performed on the same artefacts at a laboratory operating at a higher echelon in the traceability chain. For this method to be effective the artefacts used for the verification need to be stable with both time and temperature. For these reasons ‘simple’ devices such as fixed attenuators, fixed terminations and certain types of coupler are often chosen. Sometimes an artefact similar to that which it is desired to measure is chosen so that if an error occurs within the measuring system its effect can be seen and assessed immediately.
13.6.1 Customised verification example To improve throughput on one of the production lines it was decided to use an electronic calibration module with the network analyser testing input impedance. It was also desired to calibrate or check the e-cal module on site as the only alternative was to have it sent overseas to its manufacturer which would cause unacceptable downtime. The specification of the e-cal module is excellent so straightforward testing of it could not be performed to the desired level. It was decided that an artefact which was representative of the manufactured product could be used to access the ‘general health’ of the complete measuring system. The artefact chosen was a programmable attenuator with a short circuit connected to one port (Figure 13.7). This provides a range of mismatch that can be adjusted using software so maintaining the level of automation. It was not considered necessary to have all steps of the attenuator measured as this would provide too much information, much of which may never be looked at, hence, the following were chosen: (1) (2) (3) (4) (5)
highest mismatch, approximate upper specification of DUT, approximate centre of specification of DUT, approximate lower specification of DUT and lowest mismatch.
Figure 13.7
Artefact chosen for the comparison, an Agilent 84904K programmable step-attenuator with a type N adapter and short circuit fitted
302 Microwave measurements 8719ES and 8510C iPIMMS measurement comparison using ET54021 18 June 2004 0.095 8719ES
iPIMMS
Voltage reflection coefficient
0.090
0.085
0.080
0.075
0.070 36
2.
Hz G
Hz
38 2.
G
Hz
40 2.
G
Hz
42 2.
G
Hz
44 2.
G
Hz
46 2.
G
Hz
Hz
48 2.
G
50
Hz
G
2.
52
2.
Hz
G
54
G
2.
Measurement frequency
Figure 13.8
Plot produced from the results of a customised verification example showing all of the uncertainty bars overlapping
This list provides plenty of measurements in the range where it is essential for the network analyser to provide the most accurate measurements possible, and some supplementary measurements (highest and lowest mismatch) which could be used to provide some rudimentary diagnosis should the need arise. The attenuator was calibrated using the best and most accurate and traceable equipment possible. The attenuator was then transferred to the production line where it was measured using the network analyser and electronic-calibration system. A graphical representation of the two sets of results obtained is shown in Figure 13.8. The process is fully automated so it can be used each time the network analyser is re-calibrated. Since accurate measurements can take a long time to obtain there were only 51 points measured by the ‘accurate’ network analyser. This is adequate in this case because the attenuator is a linear resistive device so there is a high probability that linear interpolation can be used between measurement points, if necessary. The production line network analyser, however, is normally measuring active devices so measurements are made at considerably more frequencies, albeit with slightly greater uncertainties in places. In order to make this quantity of measurements within the very short times demanded by production processes they must be made faster, with the trade-off being slightly increased measurement uncertainties. Note in Figure 13.8 that the reference measurements are performed at considerably fewer frequencies. This is quite normal as ‘quality measurements’ can be expensive to perform. Sufficient measurements have been performed showing that linear interpolation between measured values is valid.
13.6.2 Manufacturer supplied verification example Many manufacturers supply verification procedures with their network analysers. The user will normally need to buy a verification kit which is often supplied with a disk containing measurements made on the component parts of the kit. Verification
Verification of automatic network analysers 303 kits and associated procedures are usually designed to provide a quick ‘health check’ on the network analyser. Testing that the network analyser (and calibration kit) meet their specification will often involve adjusting the settings on the network analyser resulting in the measurements taking far longer. The process begins with the operator performing an appropriate calibration (error correction). Test devices from the verification kit are then measured and the results compared with measurements that were made using a reference measurement system (Figures 13.9 and 13.10). If the comparison reveals that the results fall within prescribed limits the network analyser (and appropriate calibration kit) are said to be verified. This type of verification is intended as a routine ‘health check’ and is used by some manufacturers as a routine check for equipment installed at a customer’s location. To this end the software required to automate this process and therefore improve consistency is often included within the operating firmware of the network analyser.
Figure 13.9
Printed output from a typical verification program. A sheet similar to this is produced for both phase and magnitude for each S-parameter of each device tested
304 Microwave measurements
Figure 13.10
Another example from the same verification routine, this time displaying a transmission parameter
The major problem with these types of verification (manufacturer supplied and customised) is that all of the ‘errors’ and measurements are lumped together, the measured values contain both and there is no easy way to separate them. Degraded items can be offset by items still in their prime. This makes it very difficult to identify any one device in the calibration kit or network analyser which may be starting to drift into a problem state, but at least has the advantage of allowing the user to quickly estimate if their system is in a suitable state for measurements. Presentation of the results can be difficult in certain circumstances, particularly transmission phase where the phase vector often rotates through its full 360◦ and the test limit can be less than 1◦ .
References Vidkjær, J.: Network Analyser Uncertainty Computations for Small Signal Model Extractions, Technical University of Denmark, R549, Feb 1994
Chapter 14
Balanced device characterisation Bernd A. Schincke
14.1
Introduction
For decades high frequency circuits were developed using unbalanced (non-symmetrical) structures. Typical line systems, representing this kind of structure, are coaxial or coplanar line systems. Each unbalanced system consists of a signal line and a ground. The measurable signal is referenced to the ground. Balanced (or symmetrical) structures are not used that often. A typical balanced structure is a parallel line system (Lecher line), a Low Voltage Differential Signal Line (LVDS-line) or balanced amplifiers and filters. Typically such a structure consists of two lines (simply said, a ‘plus’ and a ‘minus’) and a signal can be measured between these two lines. In practice, these structures create some additional phenomena compared to unbalanced systems which must be analysed in detail. In an unbalanced system only the non-symmetrical TEM mode is present and it can be compared to the so-called common mode, which we will discuss later. In a coaxial system the inner conductor is the signal line and the outer conductor represents the ground. In addition this ground functions as a shield. Unbalanced line systems are normally connected to unbalanced circuits. Under the condition of power matching the measured voltage U1 against ground is U01 /2. We can conclude that such an unbalanced system offers very high noise immunity, it generates less radiation, the integration density is high and the losses are acceptable. If such a line is connected to, for example, a non-shielded circuit, a signal generated by an interferer (like ground noise or general electromagnetic interference) can be induced on the signal and will be present on the signal at the load. A fundamental disadvantage of an unbalanced structure is its susceptibility against an interferer (Figure 14.1). By using a balanced system (two-line-system), in an ideal case only one signal between the two lines can be measured. Here, the differential TEM mode is the only
306 Microwave measurements
Figure 14.1
Unbalanced system
Figure 14.2
Balanced system
one which is present. Analogous to the balanced line system the circuits are performed as balanced structures, too. A disadvantage by using balanced structures is that more components are needed compared with unbalanced structures. Under the condition of power matching a voltage U2 can be measured between the two lines which can be expressed by U02 /2. An important advantage is that the original signal is (theoretically) not influenced by electromagnetic radiation. A balanced system can be performed by using a transformer to transform the signal with 0◦ phase shift to the ‘upper’ line and by using a BALUN (BALanced–UNbalanced) to transform the signal with 180◦ phase shift to the ‘lower’ line. If an interferer occurs, the signals on both lines are interfered in the same way. Using the same transformer/BALUN structure at the output of the circuit the 0◦ phase shifted, interfered signal will be superimposed on the 180◦ phase shifted signal and the interference will be shortened (Figure 14.2). If a ground is present, again under the condition of power matching, the signal that can be measured between each signal line (upper and lower) and the ground is U02 /4. Between the two lines U2 = U02 /2. The signals have the same amplitude, but they are 180◦ phase shifted. This means that the needed voltage amplitudes to generate a desired power are half of the needed amplitudes working with an unbalanced structure. The advantage is that components with a lower breakdown voltage can be used. For narrow band applications especially in the higher GHz range (e.g. low noise converter (LNC)) the band-pass filtering offers sufficient interference suppression. Such a system will in the future also serve as an unbalanced system.
14.1.1 Physical background of differential structures An essential problem when working with differential structures is that we cannot regard a differential structure as a pure ‘two-line-system’. Every balanced system
Balanced device characterisation 307
Figure 14.3
Three-line-system
must be regarded together with a ground. When, for example, a twisted pair line is used in an instrument, the instrument wall is normally grounded. A multilayer board needs ground layers in order not to influence each other. Because of the ground (‘third line’) in practice such a differential structure must be regarded as a ‘three-line-system’ (Figure 14.3). In a three-line-system two different TEM modes of propagation are possible and must be analysed. On the right-hand side the (wanted) differential energy propagates through the device under test (DUT), on the left-hand side the common mode energy. Especially electromagnetic radiation and ground noise are typical common mode signals. On a board the two modes are quasi-TEM modes with different field distributions in the air and in the dielectric material. This can result in different propagation velocities and the characteristic impedances of the two modes are typically different. To perform an exact measurement and dimensional design in the RF, an S-parameter description is needed taking both modes into account. 14.1.1.1 Ideal device An ideal balanced device is characterised by ideal symmetry of, for example, the two lines. This means in detail the same electrical length, same attenuation, same dielectric, etc. In this case only the differential mode signal is transmitted and the common mode signal is suppressed. This is valid for pure differential structures (balanced input/balanced output) and for balanced to single-ended structures (e.g. balanced input/single-ended output) (Figure 14.4). 14.1.1.2 Real device Caused by asymmetries such an ideal balanced structure is normally not given. Very often it is possible to measure a common mode at the output of a DUT even though the device is powered by a pure differential mode signal. In this case a common mode signal is generated from the differential mode signal. Such a common mode signal can be described as an electromagnetic interferer. This procedure is called ‘Differential Mode to Common Mode Conversion’. If the device is powered only by a common mode signal, it is possible to measure a differential mode signal at the output. Here, from an electromagnetic interferer at the input, a differential mode signal at the output is generated which will be superimposed the original differential signal. Caused by this ‘Common Mode to Differential Mode Conversion’ the structure becomes susceptible to an EMI (Figure 14.5).
308 Microwave measurements Gain = 1 Differential-mode signal Fully balanced
Common-mode signal (EMI or ground noise) Gain = 1 Differential-mode signal
Balanced to single ended
Common-mode signal (EMI or ground noise)
Figure 14.4
Ideal device Differential to common mode conversion +
Generates EMI
Susceptible to EMI
Common-mode to differential conversion
Figure 14.5
Real device, transmission characteristic
These facts are valid for the transmission characteristic of the DUT as well as for the reflection characteristic of the DUT. We can conclude that real devices are normally non-ideal devices. Non-ideal devices convert differential mode energy into common mode energy and common mode energy into differential mode energy. This conversion can be measured at the input of a DUT (converted, reflected energy) and at the output (converted, transmitted energy). The complete description of a non-ideal device is shown in the signal-flow diagram in Figure 14.6. Using this model the balanced device is described by two separate systems, a pure common mode system and a pure differential mode system. The pure common mode S-parameters are the connection between the common mode stimulus signals and the measured common mode responses. The pure differential mode S-parameters are described by the connection between differential mode stimulus signals and measured differential responses. The conversion parameters, caused by the interaction between the two systems, are also shown in this model.
Balanced device characterisation 309
Common mode
Differential mode Common mode Differential mode Ground
Figure 14.6
14.2
Ground
Signal-flow diagram
Characterisation of balanced structures
The typical parameters to be tested are (1) (2) (3) (4)
performance in the pure differential mode, performance in the pure common mode, conversion from differential mode to common mode (in both directions) and conversion from common mode to differential mode (in both directions).
To be able to do all these measurements the unbalanced two-port model must be extended to a balanced two-port model. Such a balanced two-port model has by definition four unbalanced physical ports. To measure the pure differential mode and the pure common mode behaviour as well as the conversion parameters we must be able to generate differential mode and common mode signals and to measure the desired responses. These measurements must be done in both directions. The connection between the stimulus signals and the measured responses are described by the so-called Mixed Mode S-parameters Matrix. bDD,1 SDD,11 SDD,12 SDC,11 SDC,12 aDD,1 bDD,2 SDD,21 SDD,22 SDC,21 SDC,22 aDD,2 (14.1) bCC,1 = SCD,11 SCD,12 SCC,11 SCC,12 · aCC,1 bCC,2 SCD,21 SCD,22 SCC,21 SCC,22 aCC,2 The differential mode stimulus signals are labelled with aDD at port one and at port two and the common mode stimulus signals with aCC . The differential mode and the common mode response signals are described by bDD and bCC (Figure 14.7).
310 Microwave measurements Differential ports
bDD,1
aDD,2
Symmetrical two-port
aCC,1
bDD,2 aCC,2
Port-pair_2
Port-pair_1
aDD,1
bCC,2
bCC,1
Common ports
Figure 14.7
Balanced two-port
The S-parameters shown with the indices ‘DD’ and ‘CC’ are called selfparameters. These parameters are comparable to the unbalanced S-parameters, because by these the reflection quantity and the transmission quantity for the common mode and for the differential mode operation are described. The S-parameters shown with the indices ‘CD’ and ‘DC’ are the conversion parameters. These parameters describe the reflection behaviour and the transmission behaviour of the DUT under the condition that mode conversion happens. If possible, the conversion parameters must be as low as possible. Ideally the common mode system is completely separated from the differential mode system. Then the conversion parameters are zero. The conversion parameters of differential structures become very low, whenever the lines are symmetric. This means that each line offers the same attenuation, same electrical length, etc.
14.2.1 Balanced device characterisation using network analysis Network analysers are in general not developed to characterise balanced devices because they are unbalanced and normally only have two ports. They are working with CW (continuous wave) signals and do not generate common mode signals and differential mode signals. In addition, the hardware structure is not designed to measure the common mode and the differential mode response and characterise the common mode and the differential mode behaviour of the DUT. In addition for balanced devices, balanced calibration standards and a normalised reference impedance (Z0 ) are not available.
14.2.2 Characterisation using physical transformers By using physical transformers it is possible to transform a single-ended signal into a balanced common mode signal and using a BALUN it is possible to generate a balanced differential mode signal. Normally line impedances of 50 0002 against ground are used. In this case a common mode impedance of 25 0002 and a differential mode impedance of 100 0002 are generated (Figure 14.8). By using a four-port network analyser it is possible to connect one transformer at port 1 and one BALUN at port 3 to feed the balanced input of the balanced DUT with a common mode signal and a differential mode signal. Using both, the differential mode and the common mode response can also be measured. At port 2 of the DUT the second transformer and the second BALUN can be connected to measure the transmitted common mode and differential mode signal (Figure 14.9).
Balanced device characterisation 311 Balanced common mode signal
Balanced differential mode signal 10
25 Ω
0Ω
V2
2) (Z
) 22) (Z
2 VV
50 Ω
Figure 14.8
I) (ZZ II ( VV
I) Z I( VV
Uunsym.
50 Ω
50 Ω
50 Ω
Uunsym.
Physical transformer and BALUN
DUT balanced
Figure 14.9
BALUN setup
Using such a setup the conversion parameters can be measured as well, because it is possible to generate a differential mode stimulus signal at port 1 and to measure the differential mode and the common mode response at port 1 (reflection characteristics) and at port 2 (transmission characteristics). These measurements can be done bidirectionally. This simple test setup needs four physical ports and additional external equipment. Caused by this external equipment some disadvantages are known which make it impossible to use this configuration in the range of super high frequencies (SHF range) and partly in the VHF range (very high frequencies). An important disadvantage is that the calibration plane is different from the measurement plane because of the unavailability of balanced calibration standards. A calibration can be performed at the single-ended ports on the basis of coaxial calibration tools. The measurement results after such a calibration are results of the DUT including the characteristics of the used transformers and BALUNs. Especially, the poor RF performance of a normal BALUN degrades the measurement accuracy. In addition the RF performance is responsible for the limited frequency range. These problems can be compensated by using the so-called Virtual Ideal Transformers.
312 Microwave measurements 16 measured unbalanced S-parameters
Description of virtual ideal transformers
Calculated mixed mode S-parameters
Figure 14.10
Modal decomposition method, principle Test fixture Port 1
a b
Port 3
DUT
Port 4
Port 2
a1 a2 a3 a4 Figure 14.11
S11 S12 S13 S14 =
S21 S22 S23 S24 S31 S32 S33 S34 S41 S42 S43 S44
a b
b4 .
b3 b2
(14.2)
b1
Unbalanced measurement
14.2.3 Modal decomposition method The principle is to measure 16 unbalanced S-parameters and to calculate with the help of (virtual) ideal transformers, the Mixed Mode S-parameters. The whole theory and procedure are given by Bockelman and Eisenstadt [1] (Figure 14.10). First, measure the 16 unbalanced S-parameters of the balanced two-port model using a four-port analyser (Figure 14.11). As S-parameters can be converted into all other parameters it is possible to convert the S-parameters into Z-parameters which connect – according to Ohm’s law – voltages with currents (Figure 14.12). [V ] = [Z] · [I ]
(14.3)
The next step is to express the unbalanced measured currents and voltages by balanced currents and voltages. This connection can be shown for two coupled lines (14.5) using the Kirschoff laws. The principle is shown only for the balanced port 1. For the balanced port 2 it can be demonstrated in the same way. The current at the physical port 1 can be expressed by the sum of the differential mode current at the balanced port 1 and half of the common mode current at the balanced port 1. Respectively the current at the physical port 4 can be expressed
Balanced device characterisation 313 I1 Port 1
V1
Port 2
V2 V3
I2
I4
V3
Port 3
V4
Port 4
Z11 Z12 Z13 Z14 =
V4 Figure 14.12
DUT
V2
V1
I3
Z21 Z22 Z23 Z24 Z31 Z32 Z33 Z34 Z41 Z42 Z43 Z44
I1 .
I2
(14.4)
I3 I4
Conversion S-parameters → Z-parameters
by the sum of the negative differential mode current and half of the common mode current (14.5). Port 1: 1 I1 = Idiff .1 + Icom.1 2 1 I4 = Idiff .1 + Icom.1 2 1 (I1 − I4 ) 2 = I1 + I4
Idiff .1 = Icom.1
(14.5)
(14.6)
Using this connection the differential mode and the common mode currents at the balanced (or logical) port 1 and the balanced (or logical) port 2 can be expressed by the measured (unbalanced) currents (Figure 14.13). The voltage at the physical port 1 can be expressed by the sum of the differential mode voltage at the balanced port 1 and the voltage U4 at the unbalanced port 4. Respectively, twice the common mode voltage at the balanced port 1 can be expressed by the sum of U1 and U4 (Figure 14.14). Port 1: U1 = Udiff .1 + U4 2.Ucom.1 = U1 + U4 Udiff .1 = U1 − U4 1 Ucom.1 = (U1 + U4 ) 2
(14.7)
(14.8)
314 Microwave measurements 2
I2
I3
P_2
P_3 U3
U2
−Idiff 2
Idiff 2
½ Icom2
½ Icom1 −Idiff 1 Idiff 1 P_4
P_1 I4
I1
U4
U1
1
Figure 14.13
Nodal → modal, currents at port 1
I2
2
P_2
P_3 Udiff 2
Ucom 2
Udiff 1
Ucom1 P_4
P_1 I4
I1
U4
U1
1
Figure 14.14
I3
Nodal → modal, voltages at port 1
U2
U3
Balanced device characterisation 315 To give a total description according to the (14.5) and (14.7) the following matrixes can be used: 1 0 0 1 2 Idiff .1 1 I1 I2 0 0 −1 2 Icom.1 · = (14.9) I I3 1 0 0 diff .2 1 I4 2 Icom.2 1 −1 0 0 2 I = Q · Im
(14.10)
U1 U2 U3 U4
1 1 0 0 2 Udiff .1 1 0 0 − 2 1 Ucom.1 = · U 1 0 0 diff .2 1 2 Ucom.2 1 − 1 0 0 2
(14.11)
U = P · Um
(14.12)
At this point the calculation can be done using the following procedure. As the mixed mode voltages and currents are directly connected to the measured unbalanced voltages and currents it is possible to show the measured quantities by the mixed mode quantities virtually linked to ‘ideal transformers’ (Q, P-matrix). The quotient Um /Im is equal to the mixed mode impedances Zm . The last step is to convert the mixed mode impedance matrix into the mixed mode S-parameters matrix. V = [P] · Vm I = [Q] · Im V = [Z] · I V = [Z] · [Q] · Im [P] · Vm = [Z] · [Q] · Im Vm = [P −1 ] · [Z] · [Q] · Im Zm = [P −1 ] · [Z] · [Q] → Sm Calculation 1: calculation of Sm using Z-parameter.
316 Microwave measurements Another possibility to explain the calculation of the mixed mode S-parameters is to proceed directly using the wave quantities. Then the differential/common currents and voltages must be expressed according to (14.6) and (14.8) 1 1 0 0 − Idiff .1 I1 2 2 1 1 Idiff .2 0 − I2 0 · = (14.13) 2 2 I I3 com.1 0 0 1 1 Icom.2 I4 0 1 1 0 Im = Mi · I
1
(14.14) 0
0 −1 Udiff .2 = 1 U 0 com.1 2 Ucom.2 1 0 2 Udiff .1
0 1 0 1 2
−1 U1 0 U2 1 · U 3 2 U4 0
Um = Mu · U
(14.15)
(14.16)
Wave quantities are normalised to the root square of the impedance. By unbalanced system the reference impedance is normally 50 0002. 0007 Ui ii = Ii Z0 ; ui = √ (14.17) Z0 Because of the differential mode impedance normally being twice the reference impedance and the common mode impedance normally being half of the reference impedance according to Bockelman and Eisenstadt [1] the normalisation shown in the following equation is common (Figure 14.15). Form 2 (Bockelmann a.o.) idiff .i = Idiff .i · icom.i
√
2Z0 ;
→ Zdiff =2Z0 Z0 = Icom.i · ; 2 Z0 → Zcom = 2
Udiff .i udiff .i = √ 2Z0 Ucom.i ucom.i = √ Z0 /2
(14.18)
The calculation of the mixed mode S-parameters is based on the ratio between the measured wave quantities. Using a normalisation according to (14.17), the measured
Balanced device characterisation 317 ad2 ac2
P_2
bd2 bc2
P_3 P_2
P_1 P_4
P_1
ad1
ac1
Figure 14.15
bd1
bc1
Balanced two-port description
mixed mode response can be shown by mixed mode S-parameters multiplied with a mixed mode stimulus signal: bm = Sm · am ui = ai + bi ;
ii = ai − bi
1 (ui − ii ) 2 1 ai = (ui + ii ) 2 bi =
Using the Mi and the Mu matrix, it is possible to calculate the mixed mode wave quantities from the single-ended wave quantities and the measured (unbalanced) S-parameters. The ratio between the mixed mode stimulus and response wave quantities describes the mixed mode S-parameters. Using the normalisation according to (14.18) it can be shown that Mu = Mi 1 (um − im ) = 2 1 am = (um + im ) = 2 M · S · a = Sm · M · a bm =
1 M (u − i) = 2 1 M (u + i) = 2
1 1 M ·b= M ·S ·a 2 2 1 M ·a 2
318 Microwave measurements Port Port33 Port Port 11
Port Port 22 Port44 Port
Logical ports
DUT Port 1
Figure 14.16
Physical ports
Port 2
Port configuration
Smode res.;mode stim.;port res.;port stim. Figure 14.17
Naming convention
Sm = M · S · M −1 S = M −1 · Sm · M Calculation 2: calculation using form 2. Important for all calculations is that the port numbering must be known because two single-ended physical ports are combined to a logical (balanced) port 1 and the other two single-ended physical ports are combined to a logical (balanced) port 2 (Figure 14.16). Especially, the calculations which are based on form 2 are referred to differential mode impedance which is twice the single-ended impedance and a common mode impedance which is half of the single-ended impedance.
14.2.4 Mixed-mode-S-parameter-matrix The resulting S-parameters matrix, called mixed mode S-parameters matrix, contains S-parameters describing the reflection and the transmission characteristics of a DUT using differential and common mode stimulus signals and measuring differential and common mode responses. The naming convention is related to the naming convention of the S-parameters. The first letter shows the TEM mode of the measured signal (response) and the second letter the TEM mode of the stimulus signal (Figure 14.17). The first number names the logical port where the response is measured and the second number names the logical port where the generator is working. The mixed mode S-parameters matrix describes in the upper left quadrant (or ‘DD-quadrant’) the fundamental performance of the DUT in pure differential mode operation and the lower right quadrant (or ‘CC-quadrant’) in pure common mode operation. Each of the four S-parameters represents reflection coefficients at logical port 1 and port 2 and the forward/reverse transmission coefficients between the logical ports (Figure 14.18).
Balanced device characterisation 319
Figure 14.18
Figure 14.19
Sdd11
Sdd12
Sdc11
Sdc12
Sdd21
Sdd22
Sdc21
Sdc22
Scd11
Scd12
Scc11
Scc12
Scd21
Scd22
Scc21
Scc22
Pure differential and pure common modes
Sdd11
Sdd12
Sdc11
Sdc12
Sdd21
Sdd22
Sdc21
Sdc22
Scd11
Scd12
Scc11
Scc12
Scd21
Scd22
Scc21
Scc22
Mode conversion parameter
The upper right and the lower left quadrant provide the information about the conversion parameter. In the upper right quadrant (or ‘DC-quadrant’) the conversion of a common mode stimulus signal to a differential mode response is described. A conversion of a differential mode stimulus signal to a common mode response is described in the lower left quadrant (or CD-quadrant). It is obvious that these reflection and transmission parameters are equal to zero in the case of ideal symmetry (Figure 14.19). As the DC-quadrant shows the part of differential mode energy generated from a common mode stimulus signal, this quadrant describes directly the susceptibility to an EMI. However, the CD-quadrant describes the amount of produced common mode energy from a differential mode stimulus signal. Therefore the information of this quadrant is related to the generation of EMI.
14.2.5 Characterisation of single-ended to balanced devices Such a typical three-port device is a surface acoustic wave (SAW)-filter. The mixed mode S-parameters of a three-port device can also be calculated from the unbalanced measured S-parameters using the same theory (Figure 14.20).
320 Microwave measurements Single-ended
Port 1 (unbalanced)
Figure 14.20
Figure 14.21
Differential-mode common-mode DUT
Port 2 (balanced)
Three-port device
Sss11
Ssd12
Ssc12
Sds21
Sdd22
Sdc22
Scs21
Scd22
Scc22
Nine-parameter mixed mode matrix
The difference to a fully balanced DUT is the single-ended input and the balanced output. A structure containing a balanced input and a single-ended output is also possible. Here the resulting mixed mode S-parameters matrix is a nine S-parameters matrix. At the single-ended port only the normal reflection coefficient can be measured (labelled with Sss ). The mode conversion parameters in the transmission paths describe the mode conversion from the single-ended signal into a common mode signal and into a differential mode signal in the forward and in the reverse direction. At the logical port 2 the reflection coefficients in the pure common mode and the pure differential mode operation can be measured, as well as the mode conversion parameters of the reflected energy at port 2 (Figure 14.21).
14.2.6 Typical measurements The measurement parameters directly give some information about the differential and common mode insertion loss and the differential and common mode return loss. By using external hardware or network analysers providing more than four ports it is also possible to make Near End Crosstalk (NEXT) and Far End Crosstalk (FEXT) measurements. Other very popular quality parameters are the amplitude imbalance and the phase imbalance because this information is directly related to the symmetry of the structure and therefore to the mode conversion characteristic of the DUT. The imbalance parameters can be calculated using (14.19). Using the unbalanced MAG-information it is possible to show the amplitude imbalance and using
Balanced device characterisation 321
Port b Port a Port c Logical port 1
Figure 14.22
Logical port 2
Imbalance and CMRR measurement
the unbalanced phase measurements it is possible to show the phase imbalance (Figure 14.22). IMB =
Sba Sca
(14.19)
The common mode rejection ratio (CMRR) is the relation between the Sds21 parameter and the Scs21 parameter and provides information about the rejected common mode energy . CMRR =
Sds21 Scs21
(14.20)
Modern network analysers with powerful Math-functions are able to calculate these results immediately and show the results in an additional trace.
14.3
Measurement examples
14.3.1 Example 1: Differential through connection This simple example shows the influence of the symmetry on the conversion parameters, and thus on the pure differential and pure common mode parameters. Two coaxial lines connected at physical port 1 and physical port 2 of the analyser are combined to a logical port 1. The other two coaxial lines are connected at physical port 2 and physical port 4 of the analyser and combined to a logical port 2. The two logical ports are directly connected (through connection). To avoid measurement errors caused by different lengths or different attenuations of the coaxial lines, a coaxial full four-port calibration is recommended (Figure 14.23). The diagrams in Figure 14.24 show all the 16 mixed mode S-parameters. The traces 1, 2, 5 and 6 show the results under pure differential mode operation. We see that the DUT is well matched at both ports and that the differential mode energy does transmit the DUT with negligible losses. The traces 3, 4, 7, 8, 9, 10, 13 and 14 display the conversion parameters. It is evident that the mode conversion from differential mode energy to common mode energy and the conversion from common mode energy to differential mode energy are very low.
322 Microwave measurements
Port 3
Port 1
Port 4
Port 2
SMA
Logical port 1
Logical port 2 Reference planes
Figure 14.23
Test setup, example 1
The pure common mode behaviour of the DUT is shown in the traces 11, 12, 15 and 16. To show the influence of the symmetry on the structure of a balanced device, we will change the symmetry in two different ways. (1) Change of the electrical length of one part (line) of the balanced device by implementing an additional small piece of line between ports 2 and 3. (2) Creation of two different attenuations, by implementing a 3 dB attenuator between ports 2 and 3 and by implementing a 6 dB attenuator between ports 1 and 4. It is essential to use two different attenuators because, otherwise, the electrical length will be changed significantly. First, change of the electrical length between the ports (Figure 14.25). As we are using a very small piece of line, the influence in the lower frequency range is lower to the mode conversion than in the higher frequency range. This happens due to the relation between the dimension of the additional line and the wave length (Figure 14.26). As expected, the mode conversion, especially in the higher frequency range, becomes higher. This is shown in the lower two diagrams. For comparison with the ideal results, these are traced. Another point of interest is that the converted energy (differential to common mode) will no longer be transmitted as differential mode energy. In the higher frequency range the transmitted differential mode energy seems to be attenuated. The next exercise is to use different attenuations in the two parts of the balanced device (Figure 14.27). Because of the attenuator being a broadband working device, the influence of the symmetry change in this way will be the same during the whole frequency range. Compared with the ideal (traced) results the mode conversion becomes higher during the whole frequency range. The transmitted differential mode energy is once again attenuated, because a part of the differential mode energy is converted into common mode energy. In other words, an EMI is produced from the differential mode energy at the input (Figure 14.28).
Figure 14.24
0 dBrr Stop
8 GHz
Ch1
Start
0 dBrr Stop
0 dBrr Stop
Ch1
Sdd11
8 GHz
Ch1
−70
−50
−30
0 −10
Sdd21
100 Trc15
8 GHz
dB Mag 10 dB/Ref
Pwr
Sdd22
Pwr
Ch1
100 Trc11
8 GHz
−70
−50
−30
0 −10
Sdd21
60 Trc7
Start
8 GHz
Ch1
−70
−50
−30
0 −10
−2
2
−5
5
0 dBrr Stop
−1
0.5 1
1
8 GHz
Ch1
−70
−50
−30
0 −10
Sdd12
Pwr
0 dBrr Stop
8 GHz
Ch1
Sdd22
Sdd12
Start
0
0 dBrr Stop
Pwr
−0.5
0.2
−2
2
−5
5
0 dBrr Stop
−1
0.5 1
1
120
8 GHz
120
8 GHz 10 dB/Ref
0 dBrr Stop dB Mag
Pwr
80
8 GHz
10 dB/Ref
dB Mag 10 dB/Ref
Pwr
dB Mag
40
8 GHz
10 dB/Ref
0 dBrr Stop
dB Mag
Pwr
0.5
Sdd22
Start
Sdd12
Start
Sdd22
Start
Sdd22
70 Trc8
dB Mag 10 dB/Ref 110 Trc15
Pwr
−0.5
0.2
Sdd21
Start
0
0.5
0 dBrr Stop
10 dB/Ref
dB Mag 10 dB/Ref 110 Trc12
Pwr
dB Mag
Ch1
−70
−50
−30
0 −10
Sdd12
30 Trc4
8 GHz
10 dB/Ref
0 dBrr Stop
dB Mag
Pwr
Sdd11
Start
Sdd21
Start
Sdd11
Measurement of mixed mode S-parameters acc. to example 1
Pwr
−70
−70
Start
−50
−50
Ch1
−30
Trc14
−2
−5
5
0 dBrr Stop
−1
0.5 1
2
dB Mag 10 dB/Ref
Pwr
−0.5
0.2
Sdd12
Start
−30
90
Ch1
0 −10
Ref 1 U
8 GHz
0 −10
Smith
0 dBrr Stop
Sdd22
Sdd21
Pwr
Sdd21
Trc13
Start
−70
−70
Ch1
−50
0
1
10 dB/Ref
Ch1
−70
−50
−30
0 −10
Sdd11
20 Trc3
8 GHz
10 dB/Ref
0 dBrr Stop
dB Mag
Pwr
dB Mag
0.5
Sdd22
Start
Sdd12
Trc10
−30
90
Ch1
Sdd12
Start
Sdd22
Trc6
−50
Ref 1 U
8 GHz
50
Ch1
−30
Smith
0 dBrr Stop
Ref 1 U
8 GHz
−70
−50
−30
0 −10
Sdd12
Trc2
0 −10
Sdd11
Trc9
Pwr
Smith
0 dBrr Stop
−2
−5
5
C1a
Sdd11 0 −10
Start
Ch1
−70
−50
−30
0 −10
Sdd21
Sdd21
Trc5
Pwr
−1
2
Ref 1 U
0.2 0.5 1
1
Smith
−0.5
Start
0
0.5
Sdd11
Ch1
Sdd11
Trc1
Balanced device characterisation 323
324 Microwave measurements
Port 3
Port 1
Port 4
Port 2
SMA
Logical port 1
Logical port 2 Add. line
Figure 14.25
Trc1 Sdd11 Smith
Change of electrical length
Ref 1 U
Cal
1
1
Sdd11
2
0.5
Sdd21 dB Mag 10 dB / Ref 0 dB Trc5 Mem14[Trc5] Sdd21 dB Mag 10 dB / Ref 0 dB Sdd21
Cal
5
10 0 5
0
0.2
0.5
1
2
−10 10 −20 20
5
30 −30 −40 40 −5
0.5 −0.5
50 −50 −60 60
−2
70 −70
−1 Ch1 Start 300 kHz
Pwr 0 dBm
Sdc21 dB Mag 10 dB / Ref 0 dB Mem15[Trc7] Sdc21 dB Mag 10 dB / Ref 0 dB Trc7
Stop 8 GHz Cal
7
Sdc21 10
Ch1 Start 300 kHz
0
0
10 −10
10 −10
20 −20
20 −20
30 −30
30 −30
−40 40
−40 40
50 −50
50 −50
−60 60
−60 60
−70 70
70 −70
Ch1 Start 300 kHz
Figure 14.26
Pwr 0 dBm
Stop 8 GHz
Pwr 0 dBm
S Trc13 cd21 dB Mag 10 dB / Ref 0 dB Mem16[Trc13] Scd21 dB Mag 10 dB / Ref 0 dB S cd21 10
Ch1 Start 300 kHz
Mode conversion with additional line
Pwr 0 dBm
Stop 8 GHz Cal
13
Stop 8 GHz
Balanced device characterisation 325
Port 3
Port 1
Port 4
Port 2
SMA 6-dB 3-dB Logical port 1
Logical port 2 Attenuators
Figure 14.27
Trc1 Sdd11 Smith
Change of the attenuation
Ref 1 U
Cal
1
1
Sdd11 0.5
2
Sdd21 dB Mag 10 dB / Ref 0 dB Trc5 Mem14[Trc5] Sdd21 dB Mag 10 dB / Ref 0 dB Sdd21
Cal
5
10 0 5
0
0.2
0.5
1
2
−10 −20
5
−30 −40 −5
−0.5 0.5
−50 −60
−2
−70
−1 Ch1 Start 300 kHz
Pwr 0 dBm
Sdc21 dB Mag10 dB / Ref 0 dB Trc7 Mem15[Trc7] Sdc21 dB Mag10 dB / Ref 0 dB S dc21 10
Stop 8 GHz Cal
7
Ch1 Start 300 kHz
0
−10
−10
−20
−20
−30
−30
−40
−40
−50
−50
−60
−60
−70
−70
Figure 14.28
Pwr 0 dBm
Stop 8 GHz Cal
13
10
0
Ch1 Start 300 kHz
Pwr 0 dBm
Scd21 dB Mag 10 dB / Ref 0 dB Trc13 Mem16[Trc13] Scd21 dB Mag10 dB / Ref 0 dB Scd21
Stop 8 GHz
Ch1 Start 300 kHz
Mode conversion by different attenuation
Pwr 0 dBm
Stop 8 GHz
326 Microwave measurements Trc1 Sds21 dB Mag 5 dB / Ref 0 dB
Trc2 Ssd12 dB Mag 5 dB / Ref 0 dB
1
S
sd12
0
−5 −10 −15 −20 −25 −30 −35 −40 Ch1 Center 1.85 GHz SdS21 T dB Mag 10 dB / Ref 0 dB rc3
Pwr 0 dBm Trc5
SCS21
Span 195 MHz 2
dB Mag 10 dB / Ref 0 dB
SCS21
10
0 −10 −20 −30 −40 −50 −60 −70 Ch1 Center 1.85 GHz
Figure 14.29
Pwr 0 dBm
Span 195 MHz
Transmission behaviour of the SAW-filter
14.3.2 Example 2: SAW-filter measurement A SAW-filter is a typical three-port device with one single-ended input and a balanced output. When measuring a SAW-filter it is of importance that most of the single-ended input energy is converted into differential mode energy. It is not intended to receive common mode energy. This type of energy must be rejected because otherwise an interferer is produced from the single-ended signal (Figure 14.29). To calculate the CMRR we can use (14.20) and using the User Defined Math Editor the result can be shown directly (Figure 14.30).
14.4
(De)Embedding for balanced device characterisation
By working with single-ended 50 0002 systems, the differential mode impedance is 100 0002 and the common mode impedance is 25 0002. These impedance values are not the normalised reference values. A SAW-filter, for example, provides differential output impedances different from 100 0002 (e.g. 150–240 0002 or other), but the calculation routine works with 25 and 100 0002. By working with such a real device a mismatching happens. This mismatching can be reduced by using physical matching networks. Disadvantages of physical matching networks are the poor reproducibility, their being normally restricted to lower frequencies and the possibility to only use them in the narrow band. Another disadvantage is that using physical networks the user cannot operate as flexibly as possible.
Balanced device characterisation 327 CMRR Scs21 dB Mag 7.5 dB / Ref 15 dB Math
3 of 3 (Max)
Scs21 45.0
37.5
30.0
22.5
15.0
7.5
0.0 −7.5 −15.0
Ch1 Center1.85 GHz
Figure 14.30
Pwr 0 dBm
CMRR of a SAW-filter
P1
P2
Physical ports
Impedance transformer
−R
R
Figure 14.31
Span 195 MHz
L
C
P3
100 to 150 Ω
Matching network parallel L
L
R
−R
C
Virtual matching
The use of virtual (theoretically) matching networks provides a high range of flexibility with no frequency restriction. Using these virtual networks both embedding and de-embedding are possible.
328 Microwave measurements To provide the impedance transformation from 100 to 150 0002 a virtual transformer must be embedded. In general, ‘Embedding’ is used to implement virtual additional components and circuits and to show the S-parameters with the influence of these virtual networks. The de-embedding functionality can be used to remove virtually an influence caused by the hardware, for example, the characteristics of a test fixture when it is possible to give a complete S-parameters description of the fixture. When, for example, a DUT with 150 0002 output impedance is placed in a test fixture with an RC-characteristic the structure can be matched using a virtual network shown in Figure 14.31. Virtual embedding and de-embedding are possible for single-ended and for balanced structures at all used physical and logical ports. It is possible to use predefined structures and vary the parameters of the given lumped elements or to import the S-parameters to describe the networks.
Further Reading 1 Bockelman, D. E., and Eisenstadt, W. R.: ‘Combined differential and common mode scattering parameters: theory and simulation’, IEEE Transactions on Microwave Theory and Techniques, 1995;43(70): 1530–9 2 Simon, J.: Measuring balanced components with vector network analyzer ZVB, Rohde and Schwarz Application Note 1EZ53, September 2004 3 Heuermann H.: 7.10.2003, Grundlagen der Hoch- und Höchstfrequenztechnik, Umdruckversion 1.1, Fachhochschule Aachen (script from studies at university) 4 Concepts in Balanced Device Measurements, Multiport and Balanced Device Measurement Application Note AN1373-2, Agilent Technologies 5 Martius S.: January 2002, Nodale und Modale Streumatrizen (Dreileiteranordnungen), Lehrstuhl für Höchstfrequenztechnik Universität Erlangen-Nürnberg (script from studies at university)
Chapter 15
RF power measurement James Miall
15.1
Introduction
This is a brief introduction to guided-wave power measurements in the approximate range of a few MHz to several hundreds of GHz, some devices that can be used to measure RF power and the techniques for calibrating these devices.
15.2
Theory
15.2.1 Basic theory The instantaneous incident power due to an electromagnetic field can be written as [1] 0001 1 P= E0002t × H0002t dS 2 0002 t and H 0002 t are the electric and magnetic fields at a time t, and S is the surface where E over which the power is being measured. In terms of voltage (V ) and current (I ) in a transmission line, power can be written as Pinstantaneous = V (t) × I (t) Paverage = VRMS × IRMS × cos(φ) where φ is the phase angle between the voltage and current waveforms. In many situations V (t) and I (t) are sinusoids and in this case the instantaneous power will vary at twice the frequency of the sinusoid. However, these are not particularly useful definitions at RF and microwave frequencies because the instantaneous voltage, current and field distributions are not easily measured. At RFs and above power becomes the only convenient measure of signal strength.
330 Microwave measurements In practice RF and microwave power is usually measured using substitution techniques based on its heating effect, or by rectification. The unit of power is Watt (W), where 1 W = 1kg m2 s−3 Power ratios are often more conveniently expressed in decibels where given Power bel = log10 (Power Ratio) and 1 decibel =
1 bel 10
the power ratio in decibels is therefore 0002 0003 Power 1 Power dB = 10 × log10 Power 2 A power in dBm is defined as the ratio with respect to 1 mW, that is 0003 0002 Power Power dBm = log10 1 mW That is, 0 dBm corresponds to 1 mW, 20 dBm to 100 mW and −50 dBm to 10 nW. Often ‘power’ refers to CW power, that is, the average power produced by a constant sinusoid waveform at a single frequency. It should be assumed that these notes are dealing with this case unless otherwise specified. Discussion of non-CW power occurs in section 15.9. In general, in power measurements, a source of power will be connected via a transmission line to a load (Figure 15.1). Both the source and the load will reflect some of the incident electromagnetic field and therefore the power delivered into the load will be dependent on the reflection coefficients of both devices. If we define, at the connection to the load, the forward voltage wave (a), reflected voltage wave (b), reflection coefficient of the load 0004, incident power (Pi ), reflected power (Pr ) and the power delivered to the load (Pd ) then we can write the
a
b Γ
Generator
Pi
Figure 15.1
10.05 mW
Pr
Pd
Incident, reflected and delivered power from source to load in a general power measurement situation
RF power measurement 331 following relations: Pi =
|a|2 Z0
|b|2 Z0 |b| |0004| = |a| Pr =
|0004|2 =
|b|2 |a|2
Pr = Pi |0004|2 Pd = Pi − Pr Pd = Pi − Pi |0004|2 Pd = Pi (1 − |0004|2 ) The power delivered to the load is never greater than the incident power. Until now this treatment has ignored the power source. Any generator can be thought of as an idealised source with available power Pa and an internal impedance Z0 (cf. the DC case) (Figure 15.2). The power dissipated into a load with impedance Z is PZ . The Z0 -available power, PZo , is the power available to a load with impedance Z0 . The maximum power that can be dissipated in a load occurs when the load has the complex conjugate impedance of the source internal impedance. Pd = Pa
(1 − |0004G |2 )(1 − |0004L |2 ) |1 − 0004G 0004L |2
PZo = Pa (1 − |0004G |2 ) PZo = Pd
|1 − 0004G 0004L |2 1 − |0004L |2
As expected if 0004L = 0 the power delivered to the load is the Z0 -available power, PZo . In general we can measure Pi or Pd with a power sensor but often we wish to know PZo , the power available to a perfectly matched load, which can be found, for example, by using (15.1). A more comprehensive description of the relationship between powers in different points in microwave circuits can be found in Reference 22. PZ0 = Pi |1 − 0004G 0004L |2
(15.1)
No power sensor is a perfect indicator of the delivered power. There will always be losses within the sensor and systematic errors within the measurement process that will mean that the measured power is not the same as the power delivered (Figure 15.2).
332 Microwave measurements
10.05 mW Generator
ΓG
ΓL
Pa Pz
o
Figure 15.2
Effect of generator match
The Effective Efficiency (ηe ) of a power sensor can be defined as the ratio of the measured power to the RF absorbed power ηe =
Pmeas Pd
and the calibration factor (K) as the ratio of the measured power to the RF incident power K=
Pmeas Pi
(15.2)
so the two definitions are related by K = ηe (1 − |0004L |2 ) In a power sensor calibration certificate, K would usually be quoted for each frequency (either relative to absolute power or often relative to the figure at 50 MHz).
15.2.2 Mismatch uncertainty By combining equations (15.1) and (15.2) we can write Pmeas |1 − 0004G 0004L |2 K and if our power meter supplies a reading Prdg , corrected for the sensor calibration factor, as is often the case, then PZo =
PZo = Prdg |1 − 0004G 0004L |2 this has a maximum and minimum given by PZo = Prdg (1 ± |0004G ||0004L |)2 for small 0004 this can be expanded as PZo ≈ Prdg (1 ± 2|0004G ||0004L |) PZo ≈ Prdg ± Prdg 2|0004G ||0004L | or in other words the approximate mismatch [3] uncertainty when making a power measurement where only the magnitudes of the source and load reflection coefficients are known is 200|0004G ||0004L |%. The mismatch uncertainty has a U -shaped distribution [4].
RF power measurement 333
15.3
Power sensors
There are a great variety of different techniques for measuring RF and microwave power. All the different sensor types have advantages and disadvantages. Several of the more common sensor types have been covered in earlier chapters and these will only be mentioned briefly along with a short introduction to some more unusual sensor types.
15.3.1 Thermocouples and other thermoelectric sensors •
Coaxial and waveguide sensors easily available on the market: − Coaxial: DC to 50 GHz − Waveguide: 8–110 GHz (limited supply outside these frequencies) • Power range: 1 µW to 100 mW (50 dB range) • Advantages (+) and disadvantages (−): + Good long-term stability + Reasonably linear + Generally lower VRC than thermistor mounts + Easily integrated into automatic systems − Often require a reference source − Only measure average power
15.3.2 Diode sensors • • •
Coaxial sensors easily available in range: 0.1 MHz to 50 GHz Power range: 1 nW to 100 mW (90 dB) Advantages (+) and disadvantages (−): + Good long-term stability + Reasonably linear at low levels + Generally lower VRC than thermistor mounts + Easily integrated into automatic systems + Fast response allowing envelope power to be tracked + High dynamic range − Require a reference source − Poor linearity at higher levels − Can be inaccurate for modulated and distorted signals
15.3.3 Thermistors and other bolometers •
Coaxial and Waveguide mounts available on the market: − Coaxial: 1 MHz to 18 GHz − Waveguide: 2.6–200 GHz • Operate with DC substitution (closed-loop operation) • Advantages (+) and Disadvantages (−): + Very good long-term stability + Fundamentally very linear
334 Microwave measurements − − − − − −
Power range: 10 µW to 10 mW (30 dB range) High VRC at high frequencies (especially waveguide) Older technology Slow response time Only measure average power Poor dynamic range
Fundamentally, if the requirement is for a fast, high dynamic range sensor then a diode sensor should be used. For slightly higher accuracy over a smaller power range then a thermocouple sensor should be used. Thermistor sensors are generally only used in situations where very high linearity and stability are needed, such as a calibration laboratory.
15.3.4 Calorimeters Calorimeters measure the heat produced by incident microwave radiation. They are typically constructed from a thermally insulating section of waveguide, a load and a temperature sensor such as a thermopile. They are in most cases the most accurate sensors available and so are used in national standards and some other calibration laboratories. Their main disadvantage is their extremely long time constant (often 20+ minutes) so they are not suitable for use in many measurement situations. 15.3.4.1 Twin load calorimeters Twin load calorimeters [5] consist of two identical loads at the end of thermally insulating RF line sections within a thermally insulating container (see Figure 15.3). The temperature difference between the two loads is measured with temperature sensors. RF power can be applied to one side of the calorimeter and DC power to the other. When the temperature difference between the two sides is zero the RF and DC powers can be considered equivalent. 15.3.4.2 Microcalorimeters Microcalorimeters [6] are used to calibrate thermistor type sensors. These sensors operate in a bridge circuit such that the power dissipated in the sensor should be constant whether or not RF power is applied. The microcalorimeter measures the small temperature change caused by the extra losses in the input line of the sensor in the RF case. A microcalorimeter consists of a thin-walled line section connected to the thermistor sensor being calibrated (see Figure 15.4). A thermopile measures the temperature difference between the thermistor and a dummy sensor or temperature reference. By measuring the temperature change due to the RF loss in the sensor and the input line, the efficiency of the sensor can be calculated. 15.3.4.3 Flow calorimeters Flow calorimeters [7] are suitable for higher power measurements than the other calorimeters mentioned so far. They contain a quartz tube carrying flowing water
RF power measurement 335 Copper blocks
50 Ω loads
Thin wall lines
Figure 15.3
A coaxial twin dry-load calorimeter
Figure 15.4
Waveguide calorimeters for WG27 and WG16
Resistance thermometer
336 Microwave measurements which is positioned at an angle across a waveguide. The power into the waveguide can be calculated by measuring the temperature rise of the water and the flow rate. The RF heating is compared to DC heating by means of heating wires within the quartz tube that provide an identical temperature distribution.
15.3.5 Force and field based sensors There are several unusual types of power sensor such as the torque vane [8] and electron beam sensors [9] that have existed previously but are not found in a commercially available form today. With improved fabrication techniques and component quality some of these designs may form the basis of future generations of power sensors. In the torque vane sensor a conductor vane is hung in a waveguide. In the presence of electromagnetic fields a torque will be produced on the vane and if this torque can be measured then the power level can be determined. A commercial version of this type of sensor has been produced in the past. The electron beam power sensor operates by measuring the field strength in a cavity of known geometry necessary to just stop a beam of electrons of known energy. From this the RF power can be calculated. Other novel power sensors include atomic fountain based power sensors, which have been the subject of recent research [10,11] and Hall Effect sensors [12] which measure the voltage across the faces of a piece of semiconductor in the presence of an RF magnetic field. 15.3.5.1 MEMS MEMS is an abbreviation of Micro Electro-Mechanical Systems and typically refers to a moving system fabricated on a silicon wafer with measurements made using electrical methods. MEMS interest has greatly increased over recent years as the cost of wafer production, a spin-off from the semiconductor industry, has decreased. MEMS-based power sensors offer the possibility of easily measuring the very small forces produced by the strength of electromagnetic field associated with a power level in the mW range or lower. Some recent MEMS power sensor designs [13,14] have been based on variations on the theme of capacitively measuring the deflection of a thin bridge caused by power passing along a coplanar waveguide structure beneath it.
15.3.6 Acoustic meter This type of quasi-optic sensor [15] is designed for use from mm wave up to optical frequencies. Pulse-modulated incident power is absorbed in a thin metal film supported by a mylar substrate within a closed cell. This generates a sound wave within the gas of the cell at the modulation frequency, which is picked up by a microphone. A DC current pulse of opposite phase is then applied until there is no microphone response, at which point the microwave and DC power can be said to be equal.
RF power measurement 337
0.965 mW
Ref
Standard power meter
0.000 mW
Ref
Generator Unknown power meter
Figure 15.5
15.4
A ‘simple’ power measurement made by exchanging power sensors
Power measurements and calibration
15.4.1 Direct power measurement In a direct power measurement such as the one shown in Figure 15.5 the calibration factor of the device under test (CFDUT ) in terms of the calibration factor of the standard sensor is given by CFDUT = CFstd
|1 − 0004Src 0004Std |2 PDUT |1 − 0004Src 0004DUT |2 PStd
(15.3)
where Px is the power measured by device x, 0004x is the reflection coefficient of device x and Src refers to the generator or source.
15.4.2 Uncertainty budgets Table 15.1 is an example uncertainty budget for a power measurement made by connecting a calibrated power sensor (such as a thermocouple) on to a badly matched source, where neither reflection coefficient is known. The numbers are for illustration only but are typical of real uncertainties in certain situations. There are several ways to improve this measurement and lower the uncertainties such as: (1) Measuring the complex voltage reflection coefficient (VRC) of the source and load and performing a full mismatch correction. (2) Evaluating the connector repeatability by doing several repeat connections using torque spanners.
338 Microwave measurements Table 15.1
Uncertainty budget for basic power measurement without mismatch correction
Source of uncertainty
Calibration factor Drift in calibration factor Reference source (including mismatch) Mismatch VRC magnitude of sensor: 0.03 VRC magnitude of source: 0.20 Power meter Repeatability
Divisor
Uncertainty contribution
Standard uncertainty
√2 3 √2 2
1.0 0.2 0.7 1.2
0.500 0.116 0.350 0.857
2 1
0.2 0.1
0.100 0.100
Combined standard uncertainty Expanded uncertainty (k = 2)
1.07 2.14
(3) Referencing the power sensor to a better characterised (with known output port match, for example) 50 MHz reference source than the one on the power meter.
15.5
Calibration and transfer standards
Calibration of a power sensor involves comparing it against another power sensor of known calibration factor. Rather than just connecting the two sensors in turn to a source this is generally done using a transfer standard. Usually this would take the form of a power splitter (or coupler) with a power sensor permanently attached to one arm of the splitter. The use of a transfer standard has many advantages: it allows the ratio of the instantaneous powers to be taken; the transfer standard can be measured against the standard, which may be a slow device, and then the device under test can be measured more rapidly against the transfer standard; the full S-parameters of the coupler (or splitter) do not need to be known; and the repeatability of the transfer standard can be evaluated over time.
15.5.1 Ratio measurements Many power meters have an internal reference source with an RF connector on the front panel for calibrating or checking the operation of the power sensor. These sources produce a known power level (generally 1 mW) at a single frequency (generally 50 MHz or DC). The sensor should be referenced to this known power level when it is first turned on and periodically after that. Often when calibrating this type of sensor a calibration of the response of the sensor at the calibration frequency compared to the reference frequency is required, such as the following
RF power measurement 339 definition: Cal Factor = Reference Cal Factor ×
Incident Power at 50 MHz Incident Power at Cal Freq
When calibrating this type of sensor on a splitter based transfer standard against a calibrated standard sensor the calibration factor of the DUT (CFDUT ) is given by CFDUT = CFStd
RStd50 RDUTRF MStdRF MDUT50 RStdRF RDUT50 MStd50 MDUTRF
where CFStd is the calibration factor of the standard sensor, RStd50 is the ratio of the power indicated on the standard sensor to the power indicated on the transfer standard at 50 MHz, MDUTRF is the mismatch factor for the DUT at the RF calibration frequency. MDUTRF = |1 − S0004DUT |2 where S, the equivalent output port match (here at port 2 of the splitter), is given by S = S22 −S21 S32 /S31 . The other definitions follow the same logic. Note the similarity of this equation to (5.3).
15.6
Power splitters
Couplers and splitters can both be used to make the power ratio measurements necessary to calibrate a power sensor (Figure 15.6) [11]. Two resistor power splitters (not to be confused with three resistor power dividers) are well-matched devices that are extremely useful for coaxial calibrations
1.000 mW
Ref
Reference power meter
Generator 1.005 mW
Figure 15.6
Calibration using a power splitter
Ref
340 Microwave measurements
Two resistor power splitter
50 Ω resistors
Figure 15.7
A two resistor splitter
(Figure 15.7 and Table 15.2). When used in a leveling loop the voltage at the centre of the T is held constant and a device on the other arm of the splitter sees an ideal source with a 50 characteristic impedance.
15.6.1 Typical power splitter properties • • • • • • •
Wide frequency range of operation 7 mm DC to 18 GHz 3.5 mm DC to 26.5 or 33 GHz 2.4 mm DC to 50 GHz Reasonably good output match Good long-term stability Limited power capability (6 dB loss: Max. input ≈ 0.5 W)
15.6.2 Measurement of splitter output match Knowledge of the splitter output port source match is necessary in order to perform a full mismatch correction: there are several ways to measure this. The easiest is probably to measure the S-parameters of a reasonably high value attenuator and attach this on to one arm of the splitter. The match of the attenuator and splitter together will be approximately that of the attenuator on its own. This method has the disadvantage of significantly reducing the output power which is often a particular problem at higher
RF power measurement 341 Table 15.2
Example uncertainty budget for measurement of the calibration factor of a power sensor wrt 50 MHz using a power splitter based transfer standard
Source of uncertainty Calibration factor Drift in calibration factor Ratio 1 Ratio 2 Ratio 3 Ratio 4 Drift in transfer standard Mismatch Std at 50 MHz Mismatch DUT at 50 MHz Mismatch Std at 18 GHz Mismatch DUT at 18 GHz Repeatability of standard Repeatability of DUT
Divisor
Uncertainty contribution
Standard uncertainty
√2 √3 √3 √3 √3 √3 3 1 1 1 1 1 1
0.60 0.20 0.10 0.10 0.10 0.10 0.20 0.04 0.08 0.15 0.20 0.10 0.10
0.300 0.116 0.058 0.058 0.058 0.058 0.116 0.029 0.057 0.150 0.200 0.100 0.100
Combined standard uncertainty Expanded uncertainty (k = 2)
0.50 1.00
frequencies where broadband, higher power sources are not so readily available. Another method is to measure all the S-parameters of the splitter with a load (or other known impedance) attached to the other ports in turn. The equivalent output port match can then be calculated from these values [16]. A third method, known as the ‘direct method’ [17,18], involves performing a one-port calibration on one arm of the splitter using a network analyser connected to the other two ports (Figure 15.8).
15.6.3 The direct method of measuring splitter output If for a setup similar to Figure 15.8, the uncalibrated S-parameter data (S11,raw and S21,raw ) from the ANA is extracted, for any item connected to the splitter port, and the ratio x taken of the two S-parameters x=
S11,raw S21,raw
then following the procedure below, the splitter output match can be calculated. Three devices of known VRC such as Short (0004SC ), Open (0004OC ) and Load (0004L ) can be connected to the splitter port in turn. The three ratios for the Load, Open and Short can be defined as being A, B and C, respectively, and the three one-port error terms defined as Directivity EDF , Source Match ESF and Reflection Tracking ERF .
342 Microwave measurements
VNA
L
ΓL
Figure 15.8
S
O
ΓSC
ΓOC
Measurement of splitter output match using the direct method
The equations relating all these can be written in matrix form as 1 A0004L 0004L EDF A 1 B0004OC 0004OC ESF = B 1 C0004SC 0004SC E C where E = ERF − EDF ESF . These can be solved by finding the inverse of the square matrix (or by any other matrix equation solving technique). Writing the solutions out in full gives ESF =
A(0004SC − 0004OC ) + B(0004L − 0004SC ) + C(0004OC − 0004L ) A0004L (0004SC − 0004OC ) + B0004OC (0004L − 0004SC ) + C0004SC (0004OC − 0004L )
EDF =
A(C − B)0004OC 0004SC + B(A − C)0004L − 0004SC + C(B − A)0004OC 0004L A0004L (0004SC − 0004OC ) + B0004OC (0004L − 0004SC ) + C0004SC (0004OC − 0004L )
E=
A(B0004OC − C0004SC ) + B(C0004SC − A0004L ) + C(A0004L − B0004OC ) A0004L (0004SC − 0004OC ) + B0004OC (0004L − 0004SC ) + C0004SC (0004OC − 0004L )
RF power measurement 343 Once ESF , ERF and EDF are calculated the values can be checked against a reference device of known VRC by performing a ‘normal’ one-port VRC measurement using (15.4). x − EDF ERF + ESF (x − EDF ) x − EDF = E + ESF x
S11 =
(15.4)
where x is, as above, the ratio of the two uncalibrated S-parameters for the known device. ESF , the splitter output match, has now been established.
15.7
Couplers and reflectometers
Calibration of waveguide sensors and higher power calibrations in coaxial line are often done using couplers. If the DUT and coupler S-parameters are already known then a calibration can occur in a manner similar to using a power splitter. If the coupler or DUT S-parameters are not known then two couplers and power sensors can be combined (Figure 15.9) to form a basic reflectometer that gives an indication of the forward and reverse powers and hence the DUT VRC. The directivity of the couplers will limit the accuracy of any calibrations made using this method. Calibrations at higher power levels than those at which calibrated standards exist can be performed using multiple, well-matched, high coupling factor couplers with power sensors on the sidearm and by varying the power level at each stage of the calibration process over the linear range of the sidearm power sensors.
15.7.1 Reflectometers If the transfer instrument is a Reflectometer such as a VNA, six-port or multistate reflectometer, the DUT reflection coefficient can be determined at the same
Prefl
Pinc
Pd
Standard sensor
Prefl
Figure 15.9
Unknown sensor
Calibration of a waveguide power sensor using two couplers
344 Microwave measurements Sliding short
Pref
Pinc Standard sensor
DUT
Impedance standards
Figure 15.10
Multistate reflectometer
time as taking the necessary power ratios to calibrate the device allowing mismatch corrections to be made. The multistate refiectometer [19] (Figure 15.10) consists of two couplers with power sensors to measure the forward and reverse powers and a sliding short circuit which alters the ‘state’ of the system. By measuring the power ratio between the forward and reverse coupler arms in several states for several known impedances the system properties (such as coupler directivity) can be found. For each state k the ratio of the powers on the forward and reverse arms of the couplers is given by dk 0004 + ek 2 Pref = Pinc ck 0004 + 1 where ck , dk and ek are state-dependent complex constants and 0004 is the reflection coefficient of any device attached to the output port. At NPL multistate reflectometers using three states and four known impedances are used for waveguide calibrations between 8.2 and 110 GHz.
15.8
Pulsed power
The topic of non-CW power measurements is extremely large and cannot be covered adequately in the space available here. The notes here present a brief introduction. In a CW signal, such as the one illustrated in Figure 15.11 the instantaneous power will cycle at twice the frequency of the voltage or current. The power reported by a sensor with much longer time constant than the RF frequency will remain constant at the average power. In a case such as the one shown in Figure 15.12 a slowly varying signal is then modulated onto a much higher RF frequency. Here, there are three obvious definitions of power: the instantaneous power, the average power and the envelope power
RF power measurement 345 1
0.5
V(t ) I(t ) PInstant
†
0
200
400
600
800
1000
1200
PAverage −0.5 −1
Figure 15.11
1.023×103
t
Voltage, current and instantaneous and average power
1
0.8
PInstant
†
0.6
PEnvelope
†
PAverage
0.4
PEP 0.2
3.425×10−11 0
200
400
600
t
Figure 15.12
800
1000
1200 1.023×103
Modulated RF – instantaneous, average and envelope power
averaged over each RF cycle. A slow-response power sensor will still measure the average power but a faster diode-based power sensor may be able to follow the envelope and provide details about the power–time template. A sensor with a very fast response, such as an oscilloscope, may be able to trace the RF frequency, and the envelope can then be extracted by various methods providing even greater details of the pulse shape.
346 Microwave measurements Peak envelope power Overshoot 4dB −6dB
Pulse average power
1dB −1dB Average power
−30dB Pulse width
Power off noise floor
−70dB Risetime
Figure 15.13
Falltime
GSM pulse specifications
Perhaps the simplest pulsed measurement involves measuring the average power of a repetitive pulsed signal and multiplying by the duty cycle to arrive at a ‘pulse’ power. However pulses are never exactly square, or of constant power and so this method tells us relatively little about the pulse. The GSM Pulse specification for envelope power shown in Figure 15.13 is typical of the usual pulsed measurements that are required – peak envelope power, pulse average power, average power and pulse risetime and falltime. The calibration factor of a diode power sensor capable of performing measurements on fast pulses will not, in general, be the same as its CW calibration factor. These sensors do not measure true RMS power and factors such as sensor impulse response time, recovery time or nonlinearity will lead to errors.
15.9
Conclusion
These notes have briefly covered the techniques and instruments needed to make a variety of common power measurements and power sensor calibrations. A more detailed guide to power measurements across a wide range of topics is the book by Alan Fantom [20] and this is recommended as a good starting point for those who wish to learn more about this area.
15.10 Acknowledgements The author would like to thank Geoff Orford and Alan Wallace who both previously worked in the Power Measurement area at NPL and RSRE and contributed greatly to previous versions of these notes and viewfoils.
RF power measurement 347
References 1 Ramo, S., Whinnery, J. F., and van Duzer, T.: Fields and Waves in Communication Electronics (Wiley, New York, 1965). 2 Kerns, D. M., and Beatty, R. W.: Basic theory of waveguide junctions and introductory microwave network analysis (Pergamon Press, London, 1967) 3 Warner, F. L.: Microwave Attenuation Measurements, (Peter Peregrinus, London, 1977) 4 ‘The expression of uncertainty and confidence measurements’, United Kingdom, Accreditation Service (UKAS) document M3003, London 1997 5 Fantom, A.: ‘Improved coaxial calorimetric RF power meter for use a primary standard’, Proc. Inst. Electr. Eng., 1979;126(9):849–54 6 Macpherson, A. C. and Kerns, D. M.: ‘A microwave microcalorimeter’, Review of Scientific Instruments, 1955; 26(1):27–33 7 Abbott, N. P., Reeves, C. J., and Orford, G. R.: ‘A new waveguide flow calorimeter for levels of 1–20 w’, IEEE Trans. Instrum. Meas. Inst. Electr. Eng., 1974; IM-23(4):414–20 8 Cullen, A. L. and Stephenson, L. M. A.: Torque operated wattmeter for 3 cm microwaves, Proc. Inst. Electr. Eng., 1952;99(4):112–20 9 Oldfield, L. C., and Ide, J. P.: A fundamental microwave power standard, IEEE Trans. Instrum. Meas., 1987;IM-36(2):443–9 10 Paulesse, D., Rowell, N., and Michaud, A.: Realization of an atomic microwave power standard, Digest of Conference on Precision Electromagnetic Measurements, Ottawa, Canada, 2002; pp. 194–5 11 Donley, E. A., Crowley, T. P., Heavens, T. P., and Riddle, B. F.: ‘A quantum-based microwave power measurement performed with a miniature atomic fountain’, Proceedings of the 2003 IEEE International Frequency Control Symposium, Tampabay, FL, 2003; pp. 135–7 12 Barlow, H., and Katoaka, S.: The Hall Effect and its application to power measurement at 10 G c/s, Proc. Inst. Electr. Eng., Part B, 1958;105:53–60 13 Fernandez, L. J., Visser, E., Sese, J., et al.: ‘Development of a capacitive MEMS RF power sensor without dissipative losses: towards a new philosophy of RF power sensing’, Digest of Conference on Precision Electromagnetic Measurements, London, UK, 2004; pp. 117–18 14 Alastalo, A.Kyynanainen, J., Sepa, H. et al.: ‘Wideband microwave power sensor based on MEMS technology’, Digest of Conference on Precision Electromagnetic Measurements, London, UK, 2004; pp. 115–16 15 NPL News, Spring 1990, no. 369, p. 12 16 Tippett, J. C., and Speciale, R. A.: ‘A rigorous technique for measuring the scattering matrix of a multiport device with a 2-port network analyser’, IEEE Transaction on Microwave Theory and Techniques, 1982;MTT-30: 661–6 17 Juroshek, J.: ‘A direct calibration method for measuring equivalent source mismatch’, Microwave Journal, 1997;40:106–18
348 Microwave measurements 18 Rodriguez, M.: ‘A semi-automated approach to the direct calibration method for measurement of equivalent source match’, ARMMS Conference, Bracknell, UK, April 1999, pp. 35–42. 19 Oldfield, L. C., Ide, J. P., and Griffin, E. J.: A multistate reflectometer, IEEE Trans. Instrum. Meas, 1985;IM-34(2):198–201 20 Fantom, A.: ‘Radio frequency and microwave power measurement’, Electrical Measurement Series no. 7’, (Peter Peregrinus, London, 1990) 21 Johnson, R. A.: Understanding microwave power splitters, Microwave Journal, Dec 1975, pp. 49–51, 56 22 Engen, G. F.: Power equation: a new concept in the description and evaluation of microwave systems, IEEE Transactions on Instrumentation and Measurement, 1971;IM-20(1):49–57
Chapter 16
Spectrum analyser measurements and applications Doug Skinner
Spectrum analyser is a measuring instrument, which is used to display many different kinds of signal. This chapter is an introduction to the spectrum analyser and covers the most important parts of the analyser performance that need to be understood. This overview of spectrum analysers is split into four parts. Part 1: Introduction. Describes the basics of signal analysis and compares the oscilloscope time-domain display with the spectrum analyser frequency-domain display and some basic spectrum analyser measurements are also described. Part 2: How the spectrum analyser works. Provides an explanation of how a basic spectrum analyser works. It includes a description of the importance and significance of the main operator controls and how they are used to ensure a clear understanding of the display and to reduce or prevent mistakes. Part 3: The important specification points of a spectrum analyser. Describes the important specification points that need to be known and understood in order to select the correct instrument for a particular measurement. Some sources of errors and measurement uncertainties are also covered in this section. Part 4: Spectrum analyser measurements. Discusses some of the common measurements that are made using a spectrum analyser and the measurements reviewed include harmonic and intermodulation measurements as well as the measurement of modulated and pulsed signals.
16.1
Part 1: Introduction
16.1.1 Signal analysis using a spectrum analyser Before making any measurements using a spectrum analyser the user should prepare the spectrum analyser for use by carrying out any pre-calibration procedure (Auto Cal)
350 Microwave measurements Amplitude
Frequency
Time
Figure 16.1
Three-dimensional graph
recommended by the manufacturer. Some spectrum analysers include a RESET button to return the analyser to the initial set of conditions if the user has problems in interpreting the display. The next step is to consider the type of input signal and power level that are to be applied to the spectrum analyser to avoid overloading or damaging the input circuitry. The final step is to interpret and understand the displayed results.
16.1.2 Measurement domains Suppose that there is a requirement to analyse a signal that consists of a sine wave with a second harmonic component. Consider the three-dimensional graph shown in Figure 16.1. It can be seen that the graph has three mutually perpendicular axes that are calibrated in terms of time, amplitude and frequency. The objective of the signal analysis is to display the components of such a signal and there is a choice to view the signal in terms of Amplitude against Time or as Amplitude against Frequency.
16.1.3 The oscilloscope display The display when viewed as an Amplitude against Frequency display is shown in Figure 16.2 and is recognisable as a typical oscilloscope display and it is known as a time-domain display. In this situation only a single combined waveform is shown on the display. This is the waveform in the Figure shown as a solid line, but there are in
Spectrum analyser measurements and applications 351 Combined waveform
Amplitude
Fundamental
Second harmonic
Time
Figure 16.2
Oscilloscope amplitude against time display
fact at least two sinusoids present as shown by the two thin lines. The oscilloscope time-domain display does not separate out the individual frequency components and its shape changes depending on the relative amplitudes and phase of the sinusoids present.
16.1.4 The spectrum analyser display The spectrum analyser display of Amplitude against Frequency is shown in Figure 16.3 and is known as a frequency-domain display. In this case, it reveals the two separate frequency components of the applied signal, the fundamental and the harmonic. The fundamental frequency is represented on the display by the first single vertical line. The shorter vertical line that can be clearly seen to the right of the fundamental represents the second harmonic. How the Amplitude against Frequency display is achieved using the spectrum analyser is explained later in this chapter.
16.1.5 Analysing an amplitude-modulated signal 16.1.5.1 Amplitude modulation – Oscilloscope The first analysis example is to look at the relatively simple amplitude-modulated signal as displayed on an oscilloscope. Figure 16.4 shows the familiar oscilloscope display of an amplitude-modulated signal. It can be seen that the high-frequency carrier has a low-frequency signal superimposed upon it. The modulation envelope can also be seen on the display. It is possible to measure the modulation frequency (f mod) and modulation depth from
Amplitude
352 Microwave measurements
Frequency
Figure 16.3
Spectrum analyser amplitude against frequency display % Modulation =
Emax − Emin Emax + Emin
× 100
Emin
Emax
Amplitude
Figure 16.4
1
Time
Fmod
The oscilloscope display
the display but it is difficult to obtain any further information over and above modulation depth and modulation frequency. Consequently, the oscilloscope is not widely used to analyse radio frequency (RF) and microwave signals because of the limitations described.
Spectrum analyser measurements and applications 353
Figure 16.5
The spectrum analyser display
16.1.5.2 Amplitude modulation – spectrum analyser Figure 16.5 shows an amplitude-modulated signal as displayed by a spectrum analyser. The carrier, upper and lower side frequencies and noise can all be clearly seen. Note that the analysis of the amplitude-modulated waveform clearly demonstrates the superior analytical powers of the spectrum analyser. Spectrum analyser display of Amplitude against Frequency is more useful because the harmonics, spurious signals, sidebands and noise can be observed. One further advantage of a spectrum analyser is its high sensitivity, which means that it can measure very low-level signals down to less than 0.1 µV because it is selective rather than broadband. It can also display low-level signals at the same time as high-level signals because logarithmic amplitude scales are used. An oscilloscope, which generally has a linear vertical scale, does not have this capability. Many other measurements can also be made on many different and complex signals using a spectrum analyser as will be described later in Part 4. It should be emphasised at this stage that the interpretation of some spectrum analyser displays of complex waveforms requires careful study.
354 Microwave measurements
16.2
Part 2: How the spectrum analyser works
16.2.1 Basic spectrum analyser block diagram A greatly simplified block diagram of a basic swept-tuned heterodyne spectrum analyser is shown in Figure 16.6. In practice, the implementation is considerably more complex as there are many more frequency conversion stages. The input signal is applied to the input mixer through an input attenuator, which adjusts the sensitivity and optimises the signal level at the mixer to prevent overload or distortion. An input low-pass filter is also included at this stage to avoid intermediate frequency (IF) feed-through and to reject the upper image frequency. The mixer converts the input signal to a fixed IF, at which point a range of Gaussian band-pass filters or digital filters are switched in to change the selectivity or resolution. To give a vertical scale, calibrated in dB, the signal at the IF stage is passed through a logarithmic amplifier. The signal is then applied to a detector and passes through selected video filters before being applied to the vertical scale of the display. The horizontal input of the spectrum analyser display (frequency) is achieved by using a variable amplitude ramp generator, or saw-tooth generator, which is also applied to a voltage-controlled oscillator that feeds the mixer. As the ramp voltage is increased, the receiver tunes to a progressively higher frequency and the trace on the display moves from left to right. Using this technique, an Amplitude against Frequency display is shown on the spectrum analyser.
16.2.2 Microwave spectrum analyser with harmonic mixer The basic block diagram of Figure 16.6 is generally only used for spectrum analysers covering up to around 4 GHz. For a 4 GHz instrument the first local oscillator would have to cover from approximately 5 to 9 GHz but the local oscillator for a 26.5 GHz spectrum analyser would have to cover approximately 30–56.5 GHz. This is a major engineering challenge especially as the oscillator needs to be at a high level and have good voltage frequency linearity, low-noise, low-level spurious signals and an output Mixer RF input
RF attenuator
Preselector
IF amplifier
IF attenuator
Resolution filters
Log amp
Detector Video filter
Local oscillator Reference oscillator Sweep generator
Figure 16.6
Block diagram of a basic spectrum analyser
Display
Spectrum analyser measurements and applications 355 level that is adequately independent of frequency. Furthermore, the design has to be implemented at an economical price. An alternative more practical approach, used in most microwave spectrum analysers, is to use a harmonic mixer. This concept is shown in Figure 16.7. The fundamental frequency of the local oscillator is used for the lower frequencies and higher harmonics are used to cover the higher frequencies. A separate harmonic multiplier is not actually used in practice; the mixer is designed to mix with harmonics of the local oscillator.
16.2.3 The problem of multiple responses The system described in Figure 16.7 will operate to high microwave frequencies but there is a major limitation. The type of analyser shown in the previous diagram has a fundamental flaw: one signal at the input generates multiple responses such that one signal has many other signals associated with it, as shown in Figure 16.8 which is obviously incorrect.
Mixer IF output
RF input
X1
X2
X3
X4
Local oscillator
Figure 16.7
Microwave spectrum analyser with harmonic mixer Fundamental
Figure 16.8
2nd Harmonic
3rd Harmonic
Multiple responses for a single input frequency
356 Microwave measurements RF input
Mixer IF output
YIG filter
X1 X1
X2 X2
X3 X3
X4 X4
Local oscillator
Figure 16.9
Microwave spectrum analyser with a tracking preselector
Not only does this one signal mix with each of the harmonics of the local oscillator to produce multiple responses but additional responses are also generated at the image frequencies. Some of the earlier microwave spectrum analysers used this technique but the limitations are so severe that it is very rarely, if ever, used today.
16.2.4 Microwave spectrum analyser with a tracking preselector The diagram in Figure 16.9 shows how adding a band-pass filter at the input of the spectrum analyser can refine the harmonic mixer technique. This is known as a tracking preselector and the microwave spectrum analyser uses a YIG (Yttrium Iron Garnet) swept band-pass filter for the tracking filter and is usually referred to as a preselector.
16.2.5 Effect of the preselector The effect of using a preselector is shown in Figure 16.10. The swept band-pass filter selects only the wanted signal so that all the unwanted signals are rejected to make the measurement valid. A quality instrument has a preselector with high out of band rejection and the ability to track closely the input tuned frequency. Certain earlier spectrum analysers required the preselector to be ‘peaked’ before a measurement was made to ensure that the preselector is tuned correctly but this is not necessary with the latest and more complex instruments.
16.2.6 Microwave spectrum analyser block diagram In practice, modern microwave spectrum analysers are usually a combination of a fundamental frequency analyser and a harmonic analyser. The fundamental frequency
Spectrum analyser measurements and applications 357
Figure 16.10
Effect of the preselector
‘Harmonic’ mode
Input
To 502.6 MHz IF
4.5–9 GHz 4.9 GHz
‘Fundamental’ mode 4.2 GHz 4.4 GHz
Figure 16.11
100 Hz to 4.2 GHz spectrum analyser
method of operation is used at the lower frequencies but at the higher frequencies the multiplication technique, with a preselector, is used. Figure 16.11 shows the architecture of a typical 100 Hz to 4.2 GHz spectrum analyser. In the fundamental mode the input signal is mixed with a local oscillator covering from 4.5 to 9 GHz. The IF is then downconverted to a 502.6 MHz signal by a fixed 4.4 GHz local oscillator. To cover the higher frequencies the change over switch operates to bring the swept harmonic mixer into play and the 4.5–9 GHz local oscillator is used to downconvert the signal to the IF of 502.6 MHz. Microwave spectrum analysers that use a harmonic mixer have a characteristic ‘stepped’ noise floor as illustrated in the display in Figure 16.12. The rise in the noise
358 Microwave measurements occurs at the frequency break points where the higher harmonics of the local oscillator are used. From Figure 16.12 it can be seen that the instrument is approximately 10 dB less sensitive at 22 GHz compared with the sensitivity at 2 GHz.
16.2.7 Spectrum analyser with tracking generator Spectrum analysers are made even more useful by the addition of a tracking generator. A tracking generator is a swept signal whose instantaneous frequency is always the same as the frequency to which the spectrum analyser is tuned. Many spectrum analysers incorporate tracking generators to increase the applications of the instrument to include wide dynamic range swept frequency response measurements. The use of
10 dB/ division
Start 2 GHz
Figure 16.12
Stop 22 GHz
Noise floor display Mixer
RF input
RF attenuator
IF amplifier
Preselector
IF attenuator
Resolution filters
Log amp
Detector Video filter
Local oscillator Reference oscillator
Sweep generator Display
Tracking generator output
Fixed oscillator Mixer Tracking generator
Figure 16.13
A spectrum analyser with tracking generator
Spectrum analyser measurements and applications 359 a tracking generator means that it is not always necessary to have an external signal source when making some measurements. Figure 16.13 shows how a tracking generator facility can be added to a spectrum analyser. The output signal synchronously tracks the input tuned frequency of the instrument with the advantage that the dynamic range is better than would be obtained if a broadband detector was used. A dynamic range of over 110 dB can be achieved with a spectrum analyser using a tracking generator.
16.3
Part 3: Spectrum analyser important specification points
Spectrum analysers are complex items of test equipment and they can easily be misused. At worst, a wrong result can be obtained; at best, the operator may not be getting the best performance from the instrument. The latest spectrum analysers have many automatic functions, but incorrect results are still possible. When using a spectrum analyser it is important that the operator understands the function of the basic controls of the instrument in order to be able to use it effectively and to avoid incorrect results. The spectrum analyser block diagram (Figure 16.14) is repeated here to show how the controls change the instrument functions. There are four main controls on a spectrum analyser and they are (1) (2) (3) (4)
RF Attenuator and IF gain, sweep speed, resolution bandwidth and video bandwidth.
The reason for highlighting the four controls listed above is that they are probably the most commonly misunderstood and abused. Incorrect settings of these controls can cause serious measurement errors, so it is important to realise their significance. The frequency and amplitude are also important controls, but they are more easily understood and less likely to cause problems. Mixer RF input
RF attenuator
Preselector
IF amplifier
IF attenuator
Resolution filters
Log amp
Detector Video filter
Local oscillator Reference oscillator Sweep generator
Figure 16.14
Spectrum analyser controls
Display
360 Microwave measurements Mixer To detector
RF input
Attenuator
Resolution filter
IF amplifier
Local oscillator
Figure 16.15
Input attenuator and IF gain controls
16.3.1 The input attenuator and IF gain controls The block diagram Figure 16.15 shows how the sensitivity of a spectrum analyser can be changed. To increase the sensitivity of the spectrum analyser the operator has two options, either the input attenuation can be reduced or the IF gain can be increased, but if the wrong option is chosen then the measurement may become invalid. It is essential to arrange the correct signal power input level to the mixer to ensure correct operation. If the input attenuation is reduced too much then the input mixer could be overloaded with the result that unwanted distortion products are generated within the spectrum analyser. If the IF gain is increased then the risk of overloading the input mixer is removed but the noise level could rise to an unacceptable level with the result that some signals of interest could be masked in the noise. A further problem that could arise is the introduction of distortion or intermodulation in the IF stages. Many spectrum analysers automatically select the optimum RF attenuation and IF gain settings once the reference level at the top of display has been selected. Under certain circumstances, however, it may be an advantage to override the automatic selection to select a mode of operation with either lower noise or lower intermodulation.
16.3.2 Sweep speed control The spectrum analyser sweep speed must be swept sufficiently slowly to allow the signal level in the narrow resolution filters to settle to a stable value. Figure 16.16 shows two different analyser responses to the same signal and the effects produced when sweeping too fast are clearly shown. First, the amplitude of the displayed signal is reduced because the filter does not have sufficient time to respond to the signal
Spectrum analyser measurements and applications 361
Correct sweep speed
Figure 16.16
Sweep speed too fast
Shows the effect of sweeping too fast
and second the maximum is moved to the right due to the delay in the response. This effect is sometimes referred to as ‘ringing’. The Sweep bandwidth factor is given by the following relationship: Sweep ∝
Span Resolution bandwidth2
(16.1)
We can see that for a given Span (total frequency scale across the screen) if the resolution bandwidth is changed then the sweep speed will change. For most spectrum analysers this is carried out automatically and modern instruments incorporate software control to ensure that the correct sweep speed is achieved. But under certain conditions, where high resolution is required, the sweep speed may need to be as slow as 100 seconds and then some form of digital storage is essential to ensure that a visible display is achieved. Manual adjustment of the sweep speed is sometimes provided on some instruments to override the automatic selection. Sweeping faster than the optimum value can be useful to carry out a rapid uncalibrated search for spurious signals or to study the effects of rapidly changing transient signals. However, the operator must be aware of the display errors that can be caused. Sweeping slower than the optimum sweep can be used, for example, when sweeping a filter with very steep skirts by using the Tracking Generator.
16.3.3 Resolution bandwidth Resolution filters are a very important part of the spectrum analyser operation and they need to be carefully used. Resolution bandwidth is the bandwidth of the IF filter that determines the selectivity of a spectrum analyser. It is basically the ability of the analyser to separate closely spaced signals. A wide resolution bandwidth is required for wide sweeps whilst a narrow filter is used for narrow sweeps. Figure 16.17 shows three displays of an amplitude-modulated signal, they illustrate why it is necessary to be able to change resolution bandwidth.
362 Microwave measurements
WideResolution resolution filter Wide Filter
Required Required Display display
Figure 16.17
Using a wide resolution bandwidth
The wide resolution bandwidth is effectively a plot of the response of the resolution filter of the spectrum analyser. As the resolution filter is swept across the frequency scale of the spectrum analyser, any signal that is within the pass-band of the filter will result in a response on the display. Figure 16.17 shows that if the signal that is being measured is a carrier with two side frequencies when the resolution bandwidth (shown dotted) is too wide it is not possible to display the signal correctly. We can see frequency response of the instrument’s filter is swept by the local oscillator and the side frequencies are not seen in this situation. The detail of the response on the display is clearly dependent upon the bandwidth of the resolution filter and speed that it is moved across the display. However, by using progressively narrower resolution filter bandwidths as shown in Figure 16.18, the display can resolve the side frequencies. However, the penalty for high resolution is that a slower sweep speed needs to be used. Most spectrum analysers have a number of resolution bandwidth filters. The wide resolution bandwidth filters are only normally used when the display needs to be updated rapidly.
16.3.4 Shape factor of the resolution filter Figure 16.19 shows two types of filter in use as resolution filters in spectrum analysers and they have defined filter shapes. 60 dB Bandwidth 3 dB Bandwidth The shape factor is defined as the ratio of the 60 dB bandwidth to the 3 dB bandwidth. The first type of filter is the Gaussian filter and it has a shape factor of 11:1 for high quality to 15:1 for a lower quality filter. The second type of resolution filter is a digital Shape Factor =
Spectrum analyser measurements and applications 363 (a)
Narrower resolution Resolutionbandwidth Bandwidth
(b)
Narrowest resolution bandwidth
Figure 16.18
(a) Using a narrower resolution and (b) the narrowest resolution
filter that has a shape factor of 5:1. The digital filter is particularly useful where a narrow resolution filter is needed, say from 1 Hz to 30 Hz. This minimum resolution bandwidth of a spectrum analyser is a key measure of the ability to measure low-level signals adjacent to high-level signals. Many spectrum analysers have a combination of Gaussian and digital filters included in their design. A measurement that illustrates the importance of minimum resolution bandwidth is the determination of low-level signal such as a 50 Hz side frequency (hum sidebands) close to a large signal. For example in Figure 16.20, the upper trace is achieved by using a 10 Hz resolution bandwidth and only one signal is discernible. The lower trace, which uses a 3 Hz resolution bandwidth, clearly shows the low-level signals. For example, if the sidebands are 70 dB down then a 10 Hz resolution bandwidth filter with a shape factor of 11:1 could not resolve the side frequencies because if the
364 Microwave measurements 3 dB
Digital filter
Gaussian filter
60 dB
Figure 16.19
Resolution bandwidth filter shape factor
10 Hz Filter filter 10Hz
3 Hz Filter filter 3Hz 3Hz Filter
100 Hz span (10 Hz/div)
Figure 16.20
Resolution bandwidth change
3 dB bandwidth is 10 Hz then the 60 dB bandwidth is 110 Hz. A signal 60 dB down and 55 Hz away could just be discerned but a signal 70 dB down and 50 Hz away would not be resolved. By using a 3 Hz filter with a shape factor of 11:1 a signal 16.5 Hz away can be resolved if it is less than 60 dB down; it follows that a signal 70 dB down and 50 Hz away can be easily measured. Digital filters are now common in spectrum analyser and they have a shape factor of 5:1 enabling close-in signals to be resolved and measured.
Spectrum analyser measurements and applications 365
Mixer RF input
To display IF amplifier Resolution filter
Local oscillator
Figure 16.21
Detector
Video bandwidth switch
Video bandwidths
16.3.5 Video bandwidth controls The previous section explained that spectrum analysers are often used to measure very low-level signals that may be almost indiscernible from the system noise. Using a narrower resolution bandwidth filter will reduce the average displayed value of the noise. However, to make the signals even easier to view it is often necessary to smooth out the random fluctuation of noise so that a coherent signal can be more clearly viewed. The traditional way to smooth the noise is to use a low-pass video filter after the detector as shown in Figure 16.21 In order to achieve the noise smoothing it is necessary to sweep more slowly because the time constant of the filter is reduced as the bandwidth of the filter is reduced. Modern instruments couple the video bandwidth controls to the sweep speed control so that the instrument automatically selects a slower sweep speed if the video bandwidth is reduced. Conversely, a lower frequency video bandwidth is automatically selected if the sweep speed is increased. A useful general rule is to set the video bandwidth to be one-tenth of the resolution bandwidth being used. 16.3.5.1 Video averaging An alternative method of noise averaging that has become increasingly popular on software-controlled instruments is to use multiple sweep video averaging. Successive sweeps are averaged so that the amplitudes of coherent signals are unchanged whilst the levels of varying noisy signals are averaged out. The effect of using video averaging is to see the noise level slowly fall. Any low-level coherent signals that have been obscured by noise may become visible. Clearly, it is most important that an operator is aware of the difference between the video bandwidth controls and the resolution bandwidth controls and not to confuse
366 Microwave measurements their different functions. Additional critical aspects of the performance of a spectrum analyser are noise, dynamic range, accuracy and local oscillator phase noise.
16.3.6 Measuring low-level signals – noise The problem when measuring low-level signals is that even a component such as passive resistor generates noise due to thermal effects. The noise voltage generated is given by the equation: V 2 = 4KTBR where K is the Boltzmann’s constant (1.374 × 10−23 J ◦ K−1 ), T is the temperature in K (absolute temperature), B is the bandwidth of the system (Hz) and R is the resistor value (generally 50 0003 for most measurements). Using the figures given above results in a value for V 2 of 8.927 × 10−10 V EMF and converting this to dBm gives a value of −174 dBm. If a spectrum analyser has a typical noise figure of 20 dB then with a 1 Hz resolution bandwidth, the lowest level signal that could be discerned would be 20 dB higher in amplitude than the noise of −174 dBm of a passive termination. This means that with a 1 Hz filter, a spectrum analyser with a 20 dB noise floor could theoretically measure −174 + 20 = −154 dBm. An analyser with the same noise Figure but with a minimum resolution bandwidth of 3 Hz could discern a signal at −149 dBm and with a 1 kHz resolution bandwidth could only measure down to −119 dBm, which is 30 dB worse (Figure 16.22). The use of a pre-amplifier at the input of a spectrum analyser can assist to measure lower amplitude signals.
16.3.7 Dynamic range A useful definition of the dynamic range is that it is the ratio of the largest to the smallest signal simultaneously present at the input of the spectrum analyser that Resolution bandwidth
Figure 16.22
Noise floor
10 kHz
−110 dBm
1 kHz
−120 dBm
100 Hz
−130 dBm
10 Hz
−140 dBm
3 Hz 1 Hz
−145 dBm −150 dBm
Shows how the noise floor drops as the resolution bandwidth is reduced
Spectrum analyser measurements and applications 367 permits the measurement of the smaller signal taking into account the uncertainty of the measurement. The dynamic range is usually quoted in dB. Note that uncertainty of measurement is included in the definition so we need to consider, how the internally generated distortion and noise affect the measurement that we make. For a constant local oscillator level the mixer output is linearly related to the input signal level and for all practical purposes this is true provided that the input signal is more than 20 dB below the local oscillator drive level. The input signal at the mixer determines the dynamic range. The level of signal we need for a particular measurement can be calculated using data from the manufacturer’s specification for the analyser and in some cases the manufacturer’s data sheets include graphs showing the information. 16.3.7.1 Intermodulation and distortion A spectrum analyser can introduce intermodulation and cause distortion on a measurement; certain measurements cannot be made if the instrument itself generates excessive distortion. The distortion is normally described by its order and is noted by its relationship to the signal frequency, therefore second harmonic distortion is known as second order and the third harmonic distortion is known as third-order. Let us consider the second-order distortion first. Suppose that the information from the manufacturer’s specification gives the following data that the second harmonic distortion is 75 dB down on the fundamental for a signal level of −40 dBm at the mixer input. We can plot the data on the graph in Figure 16.23. This means we can measure distortion down to 75 dB. The value can be plotted on a graph of Distortion (dBc) against the mixer input level. Now if the mixer level is changed to −50 dBm we know that distortion changes by 10 dB to −85 dBm. Now if 0 −10 −20
Distortion dBc
−30 − 40 −50 −60 −70 −80 −90 −100 −110 −60
Figure 16.23
−50
−40
−30
−20 −10 0 Mixer level dBm
Second-order distortion
10
20
30
368 Microwave measurements 0 −10 −20
Third-order slope = 2
Distortion dBc
−30 −40
Secondorder slope = 1
−50 −60 −70 −80 −90 −100 −110 −60
Figure 16.24
−50 −40 −30 −20 −10 0 Mixer level dBm
10
20
30
Third-order distortion added
the signal level at the mixer changes to −50 dBm then the internal distortion and the measurement range changes from −75 dBc to −85 dBc. From mathematical analysis of the mixer, it is known that for the second-order distortion the two points are on a line whose slope is 1 so we can draw a line on the graph giving the second-order performance for any level at the input to the mixer. Similarly, we can now construct a line for the third-order distortion. The manufacturer’s data sheet gives −85 dBc for a level of −30 dBm at the mixer input and this value is plotted on the graph in Figure 16.24. If the difference between the two values changes by 20 dB the internal distortion is changed to −105 dBc. Again from mathematical analysis of the mixer these two points are on a line of slope 2 giving the third-order performance for any level at the input to the mixer. 16.3.7.2 Noise There is a further effect on the dynamic range and that is the noise floor of the spectrum analyser. Remember that the definition of the dynamic range is the ratio of the largest to the smallest signal that can be measured on the display. So the noise level places a limit on the smaller signal. The dynamic range is relative to the noise and becomes the signal-to-noise ratio where the signal is the fundamental we require to measure. To plot the noise on a dynamic range chart we take the data from the manufacturer’s data sheet, which gives −110 dBm for a 10 kHz resolution bandwidth. If our signal level at the mixer is −40 dBm it is 70 dB above the average noise. Now for every dB we lose at the mixer input we lose 1 dB of signal-to-noise ratio so the noise curve is a straight line having a slope of −1 and this can be drawn on the graph as shown in Figure 16.25.
Spectrum analyser measurements and applications 369 0 −10 −20 −30
dBc
−40 −50 −60 −70 −80
No
ise
10
kH z
BW
A B
−90 −100 −110 −60 −50 −40 −30 −20 −10 0 Mixer level dbm
Figure 16.25
10
20
30
Dynamic range versus distortion and noise
Figure 16.25 shows two intercepts marked A and B. A is the second-order maximum dynamic range and B is the third-order maximum range. Therefore, the best dynamic range for the second-order distortion is therefore A = 72.5 dB and for the third-order distortion it is B = 81.7 dB. Practically, the intersection of the noise and distortion graph is not sharply defined because the noise adds to the continuous wave (CW) like distortion and reduces the dynamic range by a further 2 dB. The plot for other resolution bandwidths can be added to the graph as required and shows that by reducing the resolution bandwidth the dynamic range can be improved. The two points A and B in Figure 16.26 show the second and third dynamic range improvement by changing the resolution bandwidth from 10 kHz to 1 kHz. Unfortunately, there is no one to one change between the lowered noise floor and the improvement in the dynamic range. And for the second order the change is one-half of the change in the noise floor and for the third-order distortion two-thirds of the change in the noise floor. 16.3.7.3 Spectrum analyser local oscillator phase noise The final item affecting the dynamic range is the local oscillator phase noise on the spectrum analyser and this affects only the third-order distortion measurements. For example, if a two-tone third-order distortion measurement was being made on an amplifier and the test tones were separated by 10 kHz, the third-order distortion components are also separated by 10 kHz. Now, suppose we choose the resolution bandwidth of the spectrum analyser to be 1 kHz allowing for a 10 dB decrease in
370 Microwave measurements 0 −10 −20 −30
dBc
−40 −50 −60 −70
No ise 10 No kH ise zB 1k W Hz BW
Second-order Second order Dynamic dynamicrange range improvement improvement
−80
Third-order dynamicrange range Third order Dynamic improvement improvement
−90 −100 −110 −60
Figure 16.26
−50
−40
−30
−20 −10 0 Mixer level dbm
10
20
30
Reducing resolution bandwidth improves dynamic range
the noise curve then the maximum dynamic range is approximately 88 dB. But if the phase noise at a 10 kHz offset is only −80 dBc then this value becomes the limit of the dynamic range. 16.3.7.4 Selecting the optimum conditions Figure 16.27 combines the graphs given in the two previous illustrations. From this combined graph the optimum dynamic range can be determined. The signal-to-noise ratio improves as the input mixer level is increased. An example illustrates the use of the graph. To determine the optimum dynamic range available to measure third-order intermodulation products the ‘1 kHz bandwidth (BW)’ line is followed; at −34 dBm mixer level the signal-to-noise ratio is almost 90 dB. No further improvement is possible because as the mixer level is increased further the level of the third-order intermodulation products increases. At a mixer level of −30 dBm, the dynamic range is reduced to 80 dB. In addition to the three key aspects highlighted above, other points are also covered in this section, such as sideband noise, residual responses, residual FM and input overload, where experience shows that these areas are also frequently misunderstood. 16.3.7.5 Sideband noise Three specification points affect the ability of a spectrum analyser to measure lowlevel signals close to high-level signals. Two of the points have already been described; they are minimum resolution bandwidth and resolution filter shape factor. The third point is the sideband noise of the local oscillators in the instrument.
Spectrum analyser measurements and applications 371 −50
−60
dBc
−70 Phase noise @ 10 kHz offset
−80
−90 Dynamic range reduction due to phase noise
−100
−110 −60
Figure 16.27
−50
−40
−30
−20 −10 0 Mixer level dBm
10
20
30
Phase noise limit
Phase noise
Figure 16.28
Local oscillator noise sidebands
Figure 16.28 shows the sideband noise of the instrument’s local oscillator superimposed on the resolution bandwidth response. Measurement of low-level signals close to a carrier can be impaired if sideband noise is too high. When developing spectrum analysers designers endeavour to keep the local oscillator phase noise as low as possible. 16.3.7.6 Checking for internal distortion Some spectrum analysers have an ‘Intermodulation Identify’ key (Figure 16.29) to automate and simplify the self-test procedure. In the latest spectrum analysers the
372 Microwave measurements Intermodulation Identify button (may be soft key)
Mixer RF attenuator
Figure 16.29
IF amplifier
Intermodulation distortion identification button
intermodulation key may be a ‘soft key’ and is included as a part of the software functions that appear on the display. However, when the key is pressed additional input attenuation is introduced and the IF amplification is simultaneously increased by an equal amount. If signal levels seen on the display do not move then the measurement is valid. This is a useful, quick and effective way to check for a possible mixer overload situation. If this feature is not available then a useful way to check for any internal overload is to introduce temporarily additional RF attenuation. If a further 10 dB of attenuation is introduced, then all the signals on the screen should drop by 10 dB. If the level changes by a different amount then this indicates that the spectrum analyser is being overloaded and distortion is present.
16.3.8 Amplitude accuracy A good amplitude accuracy specification is essential for accurate and repeatable measurements, but there can be considerable measurement uncertainty if the input match is poor.
16.3.9 Effect of input VSWR The input match, generally expressed as VSWR, reflection coefficient or Return Loss, is a measure of the proportion of the signal incident at the input that is reflected back. Amplitude measurement uncertainty deteriorates; as the match becomes worse, the effect is aggravated more if the source match is poor. The graph of Figure 16.30 shows a convenient plot to give an estimate of the uncertainty limits for a variety of source and load values. The uncertainties rise considerably as the matches become worse. For example, Figure 16.30 shows the mismatch uncertainty for a source VSWR of 2.0:1 and the spectrum analyser input VSWR of 1.5:1 gives a mismatch uncertainty of 1.2 dB.
Spectrum analyser measurements and applications 373
1.5 2:1 1.5:1
Mismatch error limit dB
1.0
1.2:1
0.5 2:1
4:1
3:1
0 dB
Source VSWR −0.5
1.2:1
−1.0
1.5:1 2:1
−1.5 Instrument input VSWR
Figure 16.30
Input mismatch uncertainty
16.3.10 Sideband noise characteristics Figure 16.31 shows the typical sideband noise performance of a quality spectrum analyser. The Figure shows how the sideband noise can reduce close-in resolution as well as reducing dynamic range even for measurements 200 kHz away from the carrier.
16.3.11 Residual responses In an earlier section, the problem of spurious responses was highlighted. A spectrum analyser can display a signal on the screen although no signal is present at the input. Instrument designers endeavour to eliminate this undesirable phenomenon but these residual responses are known to be present in all instruments to a greater or lesser extent. Residual responses occur because within a spectrum analyser there are a number of local oscillator frequencies and their harmonics which can mix with each other to produce signals which can fall within the IF bandwidth and will appear as false signals. Active RF and microwave systems frequently generate non-harmonically related signals that need to be identified and measured. Tracking down and then reducing the level of unwanted spurious signals is a very common application of a spectrum analyser. Inexperienced spectrum analyser users can have problems with such a measurement if they are unaware of the limitations of the instrument. The problem of internally generated harmonically related distortion products has been described but a spectrum
374 Microwave measurements −30
10 Hz
100 Hz
1 kHz
10 kHz
100 kHz
1 MHz Resolution bandwidths
−40 −50
3 Hz
−60 −70 −80 −90 −100 −110 −120 −130 −140
10 Hz Noise dBc/1Hz
Figure 16.31
100 Hz
1 kHz 10 kHz 100 kHz Frequency offset from carrier
1 MHz
10 MHz
Sideband noise graph
analyser itself can have spurious responses. It is essential to ensure that a signal visible on the screen is not generated within the spectrum analyser. The internally spurious signals generated can either be caused by residual responses that are an inherent limitation of the design or caused inadvertently by the operator if the instrument is overloaded. Image responses and multiple responses are also encountered in microwave spectrum analysers if a preselector is not used. Residual responses (see Figure 16.32) can create significant measurement problems so it is important to purchase an instrument with a very good specification. Residual responses of a quality instrument are typically less than −120 dBm to −110 dBm. Some instruments can have inferior specifications or in some cases, the residual responses are not even quoted at all. To be absolutely certain that a signal is not being internally generated it may sometimes be necessary to replace the signal being analysed with a known pure signal and to investigate the difference.
16.3.12 Residual FM An important specification point is residual FM. If the local oscillator in the spectrum analyser has appreciable FM on it then close to carrier measurements cannot be made. Residual FM on a quality instrument will vary from around 1 Hz to 10 Hz depending on frequency range. Figure 16.33 shows how poor residual FM can invalidate close-in measurements.
Spectrum analyser measurements and applications 375
Figure 16.32
Residual responses
Poor quality
Figure 16.33
High quality
Residual FM
16.3.13 Uncertainty contributions A spectrum analyser is a very complex device with many elements, which can change with frequency, temperature and time. Each element contributes towards the inaccuracy or uncertainty of a measurement. Figure 16.34 shows a simplified block diagram of a typical instrument with uncertainty contributions added. These figures are taken from the specification of an instrument in present widespread use. For a given measurement, all the uncertainties may not necessary apply, but the accuracy of such an instrument is poor. The problem can be worse when it is realised that with many instruments it is necessary to adjust front panel presets to obtain such accuracy. This relies on the diligence and skill of the operator and is therefore not reliable. Some spectrum analysers use an automatic self-calibration process and at the touch of a button on the front panel or a soft key the instrument runs through a self-calibration
376 Microwave measurements Input mismatch ± 0.13 dB
RF attenuator RF input
± 0 to 0.8 dB
Mixer
IF amplifier
± 0.3 to 1.0 dB Resolution filters
± 0.1dB Detector
Log amp
Mixer and input filter flatness ± 0.1dB ± 0.2 to 0.8 dB Frequency response ± 0.4 to 2 dB
Display
Temperature drift 0.05 dB/deg C.
Internal calibrator
± 0.07 to 1.2 dB ± 0.25 to 0.4 dB
Figure 16.34
Uncertainty contributions
routine. A typical self-calibration routine includes setting up the amplitude and frequency of each of the resolution filters, measuring and correcting for the attenuation of each of the input attenuator steps. Instruments that have a built-in tracking generator can also correct for the frequency response of the system by sweeping through the entire frequency range whilst routing the amplitude levelled tracking generator into the input. The advantage of automatic self-calibration is that total level accuracy is improved dramatically and the specification is valid for all levels and frequencies and for any span or resolution bandwidth. For engineers who need to produce uncertainty budgets a useful approach is to list all the contributions to the uncertainty of measurement and then to include only those that affect a particular measurement in a final budget as shown in Figure 16.35.
16.3.14 Display detection mode Modern spectrum analysers use digital methods for acquiring and manipulating the data to display. The input data at the input of the spectrum analyser is placed in to segments sometimes called bins and the bins are digitally sampled for further processing and then displayed. The point in the bin where the data are sampled will clearly affect the displayed information. Spectrum analysers may have a number of selectable detector modes and the mode of detector chosen will determine how the input signal is displayed. Table 16.1 shows the advantages and disadvantages of the various detector modes.
16.4
Spectrum analyser applications
Spectrum analysers are used to make a very wide range of measurements. It is not possible to cover all the possible applications but the more common measurements are included in this section.
Figure 16.35
Table 16.1
✓
✓
✓
✓ ✓ ✓ ✓ ✓ ✓ ✓
Adjacent channel power ratio
Channel power ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
✓ ✓ ✓
Phase noise close to carrier
✓
3rd order intercept
3rd order inter modulation products
✓
Phase noise far from carrier
✓ ✓ ✓ ✓ ✓ ✓ ✓
Power versus time for TDMA signals
Absolute level Frequency response RF attenuation IF gain Linearity error Bandwidth switching Resolution Bandwidth Sampling Mismatch
Harmonic distortion
CW signal
Spectrum analyser measurements and applications 377
✓
✓ ✓ ✓
✓
✓
✓
Typical uncertainty contributions for some spectrum analyser measurements Detector modes
Detector mode
Method
Advantages
Disadvantages
Peak
Detects the highest point in the bin
Good for analysing sinusoidal waveforms
Over responds to noise
Sample
Detects the last point in the bin whatever the power
Good for noise measurement
Not good for CW signals with narrow bandwidths and will miss signals that do not appear at the same point in the bin
Negative peak
Detects the lowest power level in the bin
Good for AM/FM demodulation and can distinguish between random and impulse noise
Does not improve the analyser sensitivity although the noise floor will appear to fall
Rosenfell
Dynamically classifies the data as either noise or signal
Gives an improved display of random noise compared with peak detection and avoids the missed signal problem of sample detection
Only used in the high performance spectrum analysers
378 Microwave measurements
Figure 16.36
Harmonic distortion
16.4.1 Measurement of harmonic distortion A spectrum analyser can be used to measure the amplitudes of the fundamental and even very low-level harmonics. Sometimes, however, it is necessary to quote not only the level of the harmonic distortion products but also to give the total harmonic distortion. The total harmonic distortion as shown in Figure 16.36 can be calculated by measuring the amplitudes of all the harmonics and then take the square root of the sum of the squares.
16.4.2 Example of a tracking generator measurement The display shown in Figure 16.37 is a typical tracking generator measurement, the analysis of a 10.7 MHz band-pass filter over a wide dynamic range. The display shows two different traces simultaneously. The upper trace shows the overall response of the filter over a dynamic range in excess of 80 dB. The other trace shows the ripple on the pass-band of the filter displayed with a resolution of 0.5 dB per division.
16.4.3 Zero span The principal function of a spectrum analyser is to sweep through a selected part of the frequency spectrum. In certain circumstances, however, it may be necessary to analyse the characteristics of just one fixed portion of the spectrum. The zero span mode is used for such applications. In this mode, the local oscillator of the instrument is no longer swept; the oscillator is held at a fixed frequency so that the signal of interest can be studied. If sweeping ceases one would expect to merely see a dot or
Spectrum analyser measurements and applications 379 −34.7
Atten 00 dB 50 Ω TG-10.0 dBm
−36.32
−54.7
−36.82
−64.7
−37.32
−74.7
−37.82
−84.7
−38.32
−94.7
−38.82
−104.7
−39.32
−114.7
−39.82
−124.7
−40.32
−134.7 Ref 10.70000 MHz Inc 5.00 kHz
Figure 16.37
−35.82
−44.7
5.00 kHz/Div 200 ms /Div
−40.82 Res bw 300 Hz Vid bw 350 Hz
Measurement of a 10.7 MHz band-pass filter
line on the display, which moves up and down according to the change in amplitude of the signal to which the instrument is tuned. This would provide a certain amount of information, but much more information is obtained if a time base sweeps the spot horizontally in a manner similar to the technique used in oscilloscopes. By sweeping the spot horizontally the display will show amplitude versus time variations of the signal to which the instrument is tuned.
16.4.4 The use of zero span There are many applications of zero span mode but one of the most obvious is to demodulate an amplitude-modulated carrier as shown in Figure 16.38. Another common use is to measure response times, one example is the measurement of transmitter decay time at switch off; this can be a critical measurement since it may determine how quickly an adjacent sensitive receiver can be enabled. Synthesiser switching times and overshoots can also be evaluated using the zero span mode. The time base of modern sophisticated instruments is derived from the reference oscillator. This ensures the very best accuracy when timing measurements are made. Some instruments only have an inaccurate time base, so it is a wise precaution to check the specification of the instrument before making a measurement.
16.4.5 Meter Mode In addition to the zero span mode some instruments incorporate a ‘Meter Mode’. This is used for applications where a spectrum display needs to be retained whilst still monitoring the changing amplitude of a part of the spectrum. A typical application of ‘Meter Mode’ is shown in Figure 16.39. The amplitude of the FM carrier is continuously updated in real time whilst the rest of the display is saved. Any part of the display, selected by the movable marker, can be updated
380 Microwave measurements A Volts 5.00
AM Demodulation Atten 60 dB 50 Ω TG off
4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 Ref 2.010914 MHz Inc 0 Hz
Figure 16.38
Zero span res bw 30 kHz 200µs /div
AM demodulation
A dBm
FM 1kHz mod. freq 2.4 kHz deviation Atten 40 dB 50 Ω TG off
0.0 −10.0 −20.0 −30.0 −40.0 −50.0 −60.0 −70.0 −80.0 −90.0 −100.0
Figure 16.39
Meter−35.47dBm Ref 150.000000MHz Inc 500 Hz
150.000000 MHz 500 Hz/div
Res bw 100 Hz 200 ms/div Vid bw 1kHz
Meter Mode
and monitored. This method is very useful when measuring carrier deviation by the Bessel Disappearing Carrier Technique.
16.4.6 Intermodulation measurement Measuring the harmonic distortion caused by a device is not a very discriminating measurement. A more searching method is to use two or more test signals and to
Spectrum analyser measurements and applications 381 Signal generator F1 Device under test Spectrum analyzer Signal generator F2
Figure 16.40
Combiner
Two-tone test set up
measure the intermodulation products that are generated at the output of the device under test. By using more than one test signal the device receives signals that are closer to the more complex signals that are generally encountered in practical systems. Two separate signal generators and a combiner are needed as shown in Figure 16.40. There are also special signal sources developed that contain two or more sources in order to provide the best possible signals for this test. Another problem is that any non-linearity in the output amplifiers of the signal generators can produce intermodulation. Further problems can arise if the automatic level control (ALC) detector at the output of one signal generator also detects the signal from the other signal generator. It is for these two reasons that it is good practice to insert an attenuator between the signal generator output and the combiner. This may not be practical in some circumstances, because the signal level may be too low. For higher frequency measurements, an isolator is recommended to improve the measurement integrity.
16.4.7 Intermodulation analysis A typical spectrum analyser display of a two-tone intermodulation test is shown in Figure 16.41. Annotation has been added to explain the origin of the intermodulation products. Signal generator 1 has a fundamental frequency of F1 and signal generator 2 has a fundamental frequency of F2 . Non-linearity in the device under test will cause harmonic distortion products of frequency 2F1 , 2F2 , 3F1 , 3F2 , etc. to be generated. Spectrum analyser will record these harmonic distortion products but the significance of the intermodulation test is that the non-linearity causes the harmonic products to mix together to generate additional signals. Numerous intermodulation products can be generated but the two most commonly encountered ones are known as the third-order and fifth-order products. Third-order products have frequencies of 2F1 − F2 and 2F2 − F1 Fifth-order products have frequencies of 3F1 − 2F2 and 3F2 − 2F1
382 Microwave measurements F2
F1
2F2–F1
2F1–F2
3F2–2F1
3F1–2F2
Figure 16.41
Intermodulation display +30 Output level (dBm)
Intercept point
+20 +10 0
Fundamental
−10 −20 −30 −40
3rd order products
−50 −60 −70 −70
−60
−50
−40
−30
−20
−10
0
Input level (dBm)
Figure 16.42
Intermodulation intercept
Even order products such as F1 + F2 and F2 – F1 are also seen but are less significant since the intermodulation products are widely separated from the two frequencies (F1 and F2 ) and they can generally be readily rejected. High-performance spectrum analysers have an intermodulation distortion of typically −95 dBc or better with a signal level of −30 to −40 dBm at the input mixer to allow for the measurement of low levels of distortion.
16.4.8 Intermodulation intercept point The amplitudes of intermodulation products change according to the amplitudes of the test signals applied; therefore, it is necessary to specify the level of the test signals. It can be difficult to compare the performance of different devices if they were measured at different levels. The solution is to use the concept of an intermodulation intercept point. An intercept point is the theoretical point at which the amplitudes of the intermodulation products equal the amplitudes of the test signals, the illustration shows the concept. There are two lines on the graph in Figure 16.42.
Spectrum analyser measurements and applications 383 +25
+30
+20
+20
0
0
+15
+10
5
10
+10
0
10
20
+5
−10 10
15
30
0
−20
20
40
−5
−30
25
50
−10
−40
30
60
−20
−50
35
70
−30
−60
40
80
−40
−70 Signal level (dBm)
45
90
Intercept point (dBm)
Figure 16.43
2nd Order
3rd Order
Intermodulation products dB down
Nomograph to determine intercept
The fundamental line shows a linear relationship between the input and output signals, the line has been extrapolated beyond the output level of +5 dBm since at such levels the response becomes non-linear. Input and output signal levels have also been plotted for the third-order products and the line is extrapolated. The two lines meet at the intermodulation intercept point. The slope of the intermodulation product lines is equal to their order, that is, the second-order lines have a slope of 2:1, the third-order lines have a slope of 3:1. Practically, this means that if the level of the test signal is reduced by 10 dB then the third-order product will theoretically drop by 30 dB, provided that the device is operating in a linear mode.
16.4.9 Nomograph to determine intermodulation products using intercept point method The nomograph in Figure 16.43 gives a rapid but not very accurate means of determining the intercept point. A straight edge is used to join the two known values so that the unknown can be determined.
16.4.10 Amplitude modulation Figure 16.44 shows an idealised spectrum analyser display of an amplitude-modulated signal. The carrier frequency is Fc ; the frequency of the modulating signal is Fm . Three separate frequency components are seen The carrier frequency
Fc
Lower side frequency Fc − Fm Upper side frequency
Fc + F m
The modulation depth in per cent is given by the following formula: Per cent modulation = 2 ×
side frequency amplitude carrier amplitude
× 100 (measured on a linear scale)
384 Microwave measurements
Carrier frequency Fc Upper side frequency Fc + Fm
Lower side frequency Fc–Fm
Figure 16.44
Amplitude modulation measurement
The amplitude of the carrier always remains constant as the modulation depth changes but the sideband amplitudes will change in proportion to the modulation depth. The frequency separation between the carrier and either sideband changes as the modulation frequency changes. When the modulation depth is 100 per cent half of the power is in the sidebands and each sideband frequency amplitude will be 6 dB less than that of the carrier. For lower modulation depths, the sideband amplitude is proportionately less. To measure modulation depth it is thus necessary to measure the amplitude difference between the carrier and the sidebands.
16.4.11 AM spectrum with modulation distortion In practice, there will be harmonics of the modulation frequency also present at Fc ± nF m . Figure 16.45 shows distortion produced at Fc ± 2Fm .
16.4.12 Frequency modulation An FM spectrum theoretically has an infinite number of sidebands, which are symmetrical about the carrier and separated by the modulation frequency. The FM spectrum display shown in Figure 16.46 is thus considerably more complex than an AM spectrum display. Sideband and carrier amplitudes are determined by the unmodulated carrier amplitude and the modulation index (β) which is expressed as Modulation index, β =
Frequency deviation Modulation frequency
In practice, although there are an infinite number of sidebands the amplitudes of the higher frequency ones rapidly reduce to near zero and can be neglected.
Spectrum analyser measurements and applications 385
Additional spectrum caused by distortion Fc−2F
Fc−Fm
Fc
Figure 16.45
Modulation distortion
Figure 16.46
Frequency modulation spectrum
Fc+ Fm
Fc+ 2F
16.4.13 FM measurement using the Bessel zero method With frequency modulation the carrier amplitude is not constant; it varies according to the modulation index and will become zero at times. The sideband amplitudes also become zero at specific values of modulation index. Modulation indices at which the carrier or sidebands have zero amplitude can be calculated. Tables are available
386 Microwave measurements
Figure 16.47
Bessel null
IF filter response
Detected FM
Figure 16.48
FM demodulation
listing the zeros, or Bessel nulls as they are more commonly called. Bessel zeros (see Figure 16.47) are used for accurate calibration of signal generators and modulation meters.
16.4.14 FM demodulation If zero span mode is used on a spectrum analyser no information should be seen if frequency modulation is applied since zero span shows amplitude variation with time. However, if the spectrum analyser is de-tuned by a small amount then the demodulated signal will be seen. This occurs because the slope of the resolution filter acts as a slope detector as shown diagrammatically in Figure 16.48. Accurate measurements are not possible but this does provide a convenient method to view a demodulated signal. It should be noted that the technique might be invalid
Spectrum analyser measurements and applications 387 if significant spurious AM is present in addition to the FM. Some spectrum analysers can measure FM directly. The demodulated FM signal is displayed on a graticule that is vertically calibrated in FM deviation; the horizontal scale is calibrated in time as for the zero span. The illustration shows the technique used.
16.4.15 FM demodulation display Some spectrum analysers incorporate a function that demodulates the FM signal and displays deviation vertically against time horizontally. A typical FM demodulation screen display from a spectrum analyser is shown in Figure 16.49. The peak-to-peak FM deviation can be readily measured from the vertical scale.
16.4.16 Modulation asymmetry – combined AM and FM Simultaneous amplitude and frequency modulation is usually an undesired effect rather than a deliberate form of modulation. It usually results when amplitude modulation is being generated. What happens is that the carrier oscillator frequency is pulled by the modulating signal and hence introduces a small amount of FM together with the desired AM. The result is that AM together with narrowband FM is present at the same modulating frequency producing a combined spectrum. The AM spectrum consists of the carrier and two sidebands but the FM spectrum will consist of a carrier and an infinite number of sidebands but it must be remembered that the amplitude of the FM sidebands falls off very quickly outside of the peak deviation ±0005F. A dev FM 1.0 kHz mod. freq. 3 kHz deviation Atten 40 dB 50 Ω TG off 1kHz/div
Ref 150.000000 MHz Inc 0 Hz
Figure 16.49
FM demod Res bw 10 kHz 500 ps/div
Peak-to-peak FM deviation display
388 Microwave measurements
Figure 16.50
AM and FM asymmetry
For narrowband FM where 0005F is considerably less than the modulating frequency f , the higher-order sidebands fall off so rapidly that only the first sideband need be considered. The narrowband FM spectrum differs from AM in that one side band is 180◦ out of phase with respect to the other sideband. So the resulting spectrum when seen on the spectrum analyser as in Figure 16.50 will be a spectrum where one sideband is larger than the other and it clearly shows the presence of FM on AM. Where the difference in the amplitudes is less than 20 per cent the modulation depth can be calculated by taking the mean of the two-sideband amplitudes to represent the amplitudes of the sidebands due to the AM alone.
16.4.17 Spectrum of a square wave Pulsed RF waveforms are most commonly encountered in radar systems both at IF and at microwave frequencies. To understand the analysis of pulsed RF it is first necessary to study the spectrum of a square wave. Figure 16.51 shows the idealised oscilloscope display of a train of rectangular pulses of pulse repetition frequency, F, and pulse width, t. The corresponding spectrum analyser display in the illustration shows that the individual spectral lines are spaced by the pulse repetition frequency 1/t. The spectrum analyser display also shows that the amplitudes of the individual spectral lines rise and fall in a regular way; the pulse envelope of the spectral lines follows a curve of the form represented by the expression y = sin x/x. The first zero of the sin x/x envelope occurs at a frequency equal to 1/t. Subsequent zeros occur at multiples of 1/t. Each of the rising and falling patterns is referred to as a lobe. In theory, the lobes continue to infinity but in practice the amplitudes of the lobes soon become negligible as the frequency rises.
Spectrum analyser measurements and applications 389
Spectrum analyser
1/t
F
F = Pulse repetition frequency (PRF)=1/T t = Pulse width Oscilloscope T=1/F
t
Figure 16.51
Spectrum of a square wave
16.4.18 Pulse modulation Figure 16.52 shows a typical spectrum analyser display of a pulse-modulated carrier. The spectral line, which can be seen at the centre of the display, is the RF carrier. The individual spectral lines, which are symmetrical about the carrier, are separated by a frequency equal to 1/T as for the basic pulse train; refer back to Figure 16.45 for clarification. The sin x/x zeros again occur at multiples of 1/t. The display is only theoretically symmetrical about the carrier since in some practical radar systems, where there are imperfections, the display may be asymmetrical.
16.4.19 Varying the pulse modulation conditions Pulsed RF can be confusing since the spectrum analyser display depends on both the pulse repetition frequency and the period of the modulating signal. The illustration helps to clarify the situation by showing how the characteristics of a pulse-modulated spectrum change according to the changes in the pulse width and pulse repetition frequency. The upper portion of each of the four displays shows the oscilloscope representation of the modulating waveform; the lower portion of each of the four displays is the spectrum analyser representation of the pulsed RF signal. The Display 1 (top left) of Figure 16.53 is an arbitrary starting point. In Display 2 (top right) of Figure 16.53 the pulse width of the modulating signal is increased whilst the pulse repetition frequency is the same. Increasing the pulse width reduces the value of 1/t so the first zero is at a lower frequency; the lobes are thus narrower. In Display 3 (bottom left) of Figure 16.53 the pulse width is the same as for Display 1 but this time the pulse repetition frequency is lower. Spectral lines are spaced
390 Microwave measurements PRF
1/T
Spectrum analyser
f =1/t Oscilloscope
t
T
Figure 16.52
Pulse modulation
1
2
Pulse wider than 1 narrower lobes PRF and line density same
Narrow pulse wide lobes High PRF low line density
3
PRF lower than 1 higher line density Pulse width and lobes same
Figure 16.53
Varying pulse modulation
4
PRF and line density same as 3 Wider pulse narrower lobes
Spectrum analyser measurements and applications 391 Line mode BW < 0.3 × PRF
1. Line spacing constant in frequency 2. Displayed amplitude independent of resolution bandwidth 3. Line spacing independent of sweep time
Figure 16.54
Envelope display or pulse mode BW >1.7 × PRF
1. Pulse spacing independent of frequency span 2. Displayed amplitude changes with resolution bandwidth 3. Pulse spacing changes with sweep time
Line and pulse mode
according to 1/T so the line density is increased as the pulse repetition frequency is decreased. The Display 4 (bottom right) of Figure 16.53 again shows that a wider pulse causes narrower lobes.
16.4.20 ‘Line’ and ‘Pulse’ modes Pulsed RF spectrum analysis is complicated because the display changes according to the resolution bandwidth selected; if it is significantly higher than the pulse repetition frequency then individual spectral lines will not be resolved. Figure 16.54 shows the frequency response of the resolution filter superimposed over a train of pulses. On the left the resolution bandwidth is shown to be less than the pulse repetition frequency so individual spectral lines are resolved; this is known as ‘line mode’. On the right the resolution bandwidth is greater than the pulse repetition frequency so individual spectral lines are not resolved; this is known as ‘pulse mode’. In the pulse mode, the display seen is not a true frequency-domain display; it is a combination of a time and frequency display. The lines are displayed when a pulse occurs irrespective of the instantaneous tuned frequency of the instrument. The display is in fact a time-domain display of the spectrum envelope. One can rapidly determine that a pulse mode display is occurring by changing the scan time or sweep time; the pulse line spacing will change. The line spacing will not change when the span is changed, as one would expect for a normal spectrum analyser display. A further characteristic of a pulse display is that the displayed amplitude increases as the bandwidth increases. A ‘rule of thumb’ to apply for line mode is to use a resolution bandwidth of less than 0.3 × pulse repetition frequency. For pulse mode, the resolution bandwidth should be greater than 1.7×pulse repetition frequency.
392 Microwave measurements
LO out
IF in
Mixer
RF in (up to 300 GHz)
Figure 16.55
Extending the frequency range
16.4.21 Extending the range of microwave spectrum analysers Most RF spectrum analysers have ‘Local Oscillator Output’ and ‘IF Input’ connectors on the front panel to allow the frequency range to be extended higher with the use of external millimetric mixers. Although this can be useful for a ‘quick look see’ the measurements can be misleading due to poor amplitude accuracy and multiple responses. This feature shown in Figure 16.55 should be used with extreme caution!
16.4.22 EMC measurements The spectrum analyser can be used to make EMC measurements and in some cases additional types of detector are included such as Peak, Average, RMS and Quasi Peak detectors. The spectrum analyser is a very useful instrument to use as a diagnostic tool for EMC measurements. Figure 16.56 shows a plot from a spectrum analyser used for a conducted measurement measured in a semi-lined screened room. The test was made to comply with the European EMC Standards EN 55011 and EN55022 limits.
16.4.23 Overloading a spectrum analyser Applying AC or DC signals of greater than approximately 0.5 W (+27 dBm) can permanently damage the input of a spectrum analyser. The input attenuator and mixer can be destroyed resulting in costly repair and loss of use of the spectrum analyser.
Spectrum analyser measurements and applications 393
Figure 16.56
Spectrum analyser EMC display
Two techniques to protect against overload are incorporated in modern spectrum analysers. In VHF and UHF instruments, a coaxial relay is generally incorporated in the input. Protection to 50 W is possible on VHF instruments. Microwave instruments can be switched to AC input so that DC voltages up to 50 V can be safely applied.
16.5
Conclusion
The above paragraphs show how useful the spectrum analyser is in design and calibration and there are many more fields of measurements and applications where it can be used. The purpose of this chapter is to act as an introduction to the types and applications of spectrum analysers. Finally, remember what you see is not necessarily what you have got! There is a trend to develop multifunction RF and microwave instruments and they often include a spectrum analyser.
Further reading 1 Hewlett Packard: Spectrum Analyser Basics, Application note 150, Publication number 5952-0292, November 1989 2 Hewlett Packard: 8 Hints to Better Spectrum Analyser Measurements, Publication number 5965-6854-E, December 1996
394 Microwave measurements 3 Hewlett Packard: Amplitude and Frequency Modulation, Application note 150-1, Publication number 5954-9130, January 1989 4 Witte, R. A.: Spectrum and Network Measurements (Prentice Hall Inc., Englewood Cliffs, NJ, 1993) 5 Rauscher, C.: Fundamentals of Spectrum Analysis, 2nd edn (Rhode and Schwarz GMBH, Munich, 2002)
Chapter 17
Measurement of frequency stability and phase noise David Owen
An ideal frequency source generates only one output signal with no instability in its output frequency. In reality, however, all signal sources exhibit some uncertainty in their instantaneous output frequency. The uncertainty can be expressed in a number of different ways. The method of expressing the uncertainty is likely to depend upon the intended application as well as the performance of the signal source, and in many cases a source may be characterised in more than one way. High-accuracy frequency sources, such as crystal oscillators and rubidium or caesium frequency standards, are principally measured in terms of their long- and short-term frequency stability by directly measuring the source with a frequency counter. Aging rate is used to express the long-term change of the frequency of the source period of many hours (or more) over a while the short-term stability is a measure of the random fluctuation of the source over a period of the order of seconds. Provided a frequency counter with enough frequency resolution and a frequency standard with adequate performance are used as a reference, the measurement of stability presents no serious problems. Adjustable sources tend to have their frequency stability measured in other ways. For communication systems the most common method of expressing the frequency uncertainty is either as residual phase or frequency modulation or as phase noise. Residual modulation is typically measured by demodulating the carrier and filtering the base band signal through a band-pass filter and measuring the signal in terms of peak, average or RMS radians or Hertz deviation. Phase noise is the most generic method of expressing frequency instability. The carrier frequency instability is expressed by deriving the average carrier frequency and then measuring the power at various offsets from the carrier frequency in a defined bandwidth. The result is then expressed as a logarithmic ratio compared with the total carrier power. The power ratio is usually normalised to be the equivalent signal power
396 Microwave measurements present in a measurement bandwidth of 1 Hz. For some applications (e.g. specifying adjacent channel power on a transmitter) it can be expressed in other bandwidths (in the case of adjacent channel power the receiver bandwidth). The various ways of expressing frequency stability are all measurements of the same physical characteristics but are specified in terms of a critical characteristic of their application. The most useful general measurement, however, is the phase noise characteristics since other measurements can be derived from a phase noise plot. For communication systems the most important offset frequencies are those around 1 kHz, since this strongly influences the residual FM and therefore the ultimate signal–to-noise ratio, offsets between 10 and 25 kHz. At the higher frequency offsets phase noise affects transmitted adjacent channel power and adjacent channel selectivity measurements on narrow band receivers. Phase noise characteristics are important for digital as well as analogue communication systems. The 1 kHz phase noise characteristics of oscillators in transmitters using time-domain multiple access (TDMA) or time-domain duplex (TDD) techniques often determine the residual phase or frequency jitter within a single burst of the carrier frequency. As wider bandwidth systems are adopted phase noise at larger offsets will become increasingly specified, but in general the toughest target is likely to remain the 1 kHz offset performance. The sensitivity to the noise in the 1 kHz offset region on digital modulation systems arises because the signal is split into blocks of information, typically with a duration of 1–20 ms, for the purpose of encoding speech or adding error correction. The details of this are beyond the scope of this chapter. The blocks of information usually have within them a sequence of digital bits that are used to extrapolate the phase and frequency reference of the transmitted signal over the entire block. Having obtained this phase reference the digital data can be derived. This phase or frequency estimation process means that phase noise at low carrier frequency offsets is removed whereas noise at frequencies corresponding to the data block length can directly lead to an increase in measured modulation error. The longer the length of the data block used the more susceptible the system is to lower frequency noise. The measurement of phase noise is likely to continue to be an important activity in the design of communication systems.
17.1
Measuring phase noise
The performance of frequency sources varies considerably and consequently making measurements can be complex. Different methods can be used according to the expected performance and the controls available to set up a measurement (Figure 17.1). The phase noise performance of oscillators can vary greatly according to the type of oscillator and the complexity (and hence cost) of the design.
Measurement of frequency stability and phase noise 397 SSB Noise dBc/Hz −60 1 GHz VCO −100
100 MHz VCXO
−140 −180 10 Hz 100 Hz
1 kHz 10 kHz 100 kHz 1 MHz Offset frequency
Figure 17.1
Phase noise of a voltage controlled crystal oscillator compared to a typical 1 GHz VCO
A crystal oscillator can exhibit a phase noise of −170 dBc Hz−1 at a 20 kHz offset from a carrier of 100 MHz. A well-designed voltage controlled oscillator covering a frequency range of onequarter of an octave at 1 GHz will produce a phase noise of −115 dBc Hz−1 at a 20 kHz offset frequency. A typical microwave yttrium iron gasnet (YIG) oscillator could have a significantly worse performance and have the added complication of including large amounts of low-frequency uncertainty caused by disturbance of its magnetic tuning field from mains transformers, switch mode power supplies and display drive circuits. Measuring such widely divergent oscillators causes considerable measurement problems and it is not surprising that none of the techniques solves all the problems. Four basic measurement techniques are described based on spectrum analysers, delay line discriminators, quadrature technique and FM discriminators. All of these methods can be used to successfully measure the characteristics of a signal source and each has their advantages and disadvantages. The methods of all measurements rely on a similar basic principle (Figure 17.2). The signal to be measured is frequency converted to a baseband or IF and then passed through a device which extracts either phase or frequency information from the carrier. A frequency selective measuring device is then used to measure the noise as a function of offset frequency. A calibration system is used to scale the results into meaningful units.
17.2
Spectrum analysers
Since spectrum analysers measure the RF signal power in a specific bandwidth they can clearly be used to measure phase noise. Most modern analysers include software functions which will convert a measured signal level from its measured value (in the
398 Microwave measurements
Ref osc.
(except delay line discriminator)
Device to translate to phase/frequency
Frequency selective measuring device
Source under test Calibration system (software and hardware)
Figure 17.2
Principle of all phase noise measurements SSB noise dB/Hz 0 −20 Limited by filter bandwidth
−40 −60
Limited by LO noise
−80 −100 −120
Figure 17.3
10Hz
10kHz 10MHz Offset frequency
Limitations of phase noise measurements with a low/medium cost spectrum analyser
spectrum analyser filter bandwidth) to the equivalent noise signal in a 1 Hz bandwidth provided the noise can be treated as Gaussian. By measuring the total carrier power (on a wide filter setting) and then measuring the noise signal normalised to a 1 Hz bandwidth, a phase noise measurement can be derived. In practice, the performance of simple spectrum analyser measurements is very limited (Figure 17.3). Typical spectrum analyser noise performance is not adequate to measure noise at offset frequencies much beyond 1 kHz and the minimum filter resolution bandwidth of 3 or 10 Hz limits measurements to offset frequencies above 50 Hz. Those spectrum analysers which perform narrow band measurements using digital techniques can generally perform better close to carrier measurements than analogue versions and, with the right software, provide more reliable conversion of measurement results to phase noise.
Measurement of frequency stability and phase noise 399 The performance at larger offsets is limited by the performance of the synthesisers used to convert the input frequency signal to the spectrum analyser measuring frequency and the relatively poor noise figure of a spectrum analyser front end converter. The noise figure arises because the spectrum analyser usually has to be optimised to obtain the best linear operating range to its maintained intermodulation and spurious specification.
17.3
Use of preselecting filter with spectrum analysers
For some applications, the noise floor and synthesiser noise limitations of spectrum analysers can be partially overcome by the use of band-pass filters. A typical measurement will require the use of second reference RF or microwave source and a mixer to convert the signal to an intermediate frequency (IF). The signal from the mixer is then passed through a band-pass filter and amplifier before being measured by the spectrum analyser. Typically, the band-pass filter is a commercial inductor/capacitor, crystal or ceramic IF filter commonly used in radio receivers. Alternatively the filter can be a band stop filter to reject the IF, but such filters are not as commonly available (Figure 17.4). Some care needs to be taken in making measurements in this way. Suitable filters with narrow bandwidths are rarely designed for 50 0001 systems and often have severe changes of impedance with frequency. The mixer has to be buffered from this impedance variation to avoid errors due to reflected signals re-mixing. The filters can also exhibit non-linear behaviour at both low levels (particularly crystals) and high levels (as crystal or ceramic devices exceed their linear power ratings). These problems, combined with frequency response unflatness in the pass band, can make the measurement accuracy unreliable unless precautions are taken. It also has to be
Source under test
Mixer
Low pass filter
LNA
Reference source
Figure 17.4
Using a spectrum analyser with preselection
Xtal band pass filter
400 Microwave measurements remembered that both the phase and the amplitude components of noise are being measured. The technique is also restricted to measurements at offsets of typically greater than (typically) 10 kHz since it relies on the filter having to reject a significant proportion of the carrier signal at the IF. The improvement in performance using this method occurs because the signal from the local oscillators inside the spectrum analyser no longer mixes with the carrier frequency of the signal being measured because it is rejected by the band-pass or band stop filter. The spectrum analyser local oscillator noise no longer dominates the measurement and the ratio of the signal to be measured to the total power at the input of the spectrum analyser is much lower, which considerably lowers the dynamic range required of the spectrum analyser.
17.4
Delay line discriminator
A broadband FM discriminator can be constructed by taking the RF signal to be measured and splitting it into two paths (Figure 17.5). One path is fed directly into a mixer and the second path is passed through a delay line and the output is mixed with the non-delayed signal. The delay line includes a variable phase shifter or a mechanically adjustable transmission line so that the phase of the two signals applied to the mixer can be set for phase quadrature. The bandwidth of the discriminator is a classic sin x/x response with the first null at a frequency equivalent to the time delay between the two RF paths. The conversion sensitivity of the discriminator is dependent on the RF level applied, the conversion loss of the mixer and the time delay of the delay line. The longer the delay line the greater the sensitivity of the measurement but the more restricted is its measurement bandwidth. The great advantage of this technique is that it does not require the use of a second RF source to convert the frequency of the source to be measured to a fixed IF (or base band signal). This removes one potential source of error, that is, an additional source
Source under test
Splitter
Mixer
Delay line
Figure 17.5
Delay line discriminator
LNA
Measurement of frequency stability and phase noise 401 of noise. Also, since the method is based on the use of a frequency discriminator it is not too prone to being overloaded by low-frequency sources of phase noise (e.g. power supply related signals). It does have the practical disadvantage of not being easily automated. It needs to be calibrated which can be troublesome. The sensitivity of the system is dependent on the applied RF signal levels. The normal method of calibration is to adjust the time delay to find the peak positive and negative voltage that can be obtained from the mixer. From this the sensitivity can be deduced if it is assumed that the mixer is behaving in a linear fashion. At microwave frequencies the insertion loss of the delay line can result in the sensitivity of the measurement being limited. Commercial products are available based on the use of this measurement method.In general, this method is not capable of measuring high-performance oscillators over a significant bandwidth but is capable of measuring typical free running YIG and RF voltage–controlled oscillator (VCO) sources.
17.5
Quadrature technique
In the quadrature system, two oscillators at identical frequencies are used (Figure 17.6). Typically, one of the oscillators will be the source being tested and the other will be a reference source whose performance is known to be better than the source under test. The oscillator outputs are combined in a mixer and the resulting output signal is filtered and amplified by a low noise amplifier (LNA). A fast Fourier transform (FFT) analyser or a spectrum analyser typically measures the output from the mixer.
OSC 1
Mixer
OSC 2
Figure 17.6
Low pass filter
LNA
FFT analyser
or Spectrum analyser
Quadrature method shown with a feedback loop to maintain phase quadrature at the mixer
402 Microwave measurements In order to provide a valid measurement the phase of the two oscillators has to be set so that they are in phase quadrature at the mixer input. The mixer output will then be close to 0 V and the mixer will behave as a phase detector. Setting the sources to be in phase quadrature is not always very easy. If both frequency sources are synthesisers with good long-term stability, then there is usually not a great problem – the phase adjustment controls can be used to set the signals in quadrature. However, in the more typical applications where measurements are undertaken under less than ideal conditions, a feedback system has to be used to maintain phase quadrature. The feedback system forms a phase locked loop which drives one of the oscillators to correct for departures from quadrature. The use of phase locked loop to maintain phase quadrature does imply some knowledge of the tuning characteristics of one of the oscillators and the mixer drive levels since the bandwidth of the phase locked loop is affected by both of these parameters. In practice for many sources the availability of a low noise signal generator with a high-performance DC coupled FM capability, such as the IFR 2040 series, can considerably simplify the measurement system. If the peak phase excursion of the noise exceeds 0.1 radians, the mixer phase detector response becomes non-linear and degrades the measurement accuracy. Since the peak phase excursion is caused primarily by low-frequency noise then under these conditions, the phase locked loop bandwidth has to be widened in order to restrict the peak phase excursion. In order to carry out a measurement, the quadrature system has to be calibrated since the sensitivity of the measurement is dependent on the insertion loss and drive level used for the mixer. If the local oscillator (LO) input level required for the mixer is substantially greater than the RF port drive, a calibration assessment can be obtained by offsetting the frequency of one of the sources by a small amount. A low-frequency sine wave is produced at the output of the mixer whose amplitude can be measured to determine the sensitivity of the mixer. If both ports of the mixer are driven at a high level to give the maximum sensitivity then the waveform from the mixer will be more like a triangle waveform than a sinusoid and the mixer sensitivity should be more linear with errors in phase quadrature present. However, the slope of the triangle wave is more difficult to measure accurately than in the case where a sine wave is produced. A further complication in the calibration process can arise if the drive signals are not well matched to the source impedance. Whichever port of the mixer is driven hard, the mixer tends to convert the signal to a square wave and reflections can cause re-mixing and slope perturbations in the output. An alternative, and often more reliable method of calibration, is to use a signal generator as one of the sources and to set a known amount of phase or frequency modulation. Measuring the resulting output can provide the required calibration information. The phase modulation applied has to have a modulation index of less than 0.1 radians to avoid mixer overload, and a modulation frequency significantly in excess of the phase locked loop bandwidth used for setting up phase quadrature.
Measurement of frequency stability and phase noise 403 This in itself can be another source of error in the measurement since the phase locked loop is used to set up phase quadrature. The loop tends to remove low-frequency phase noise that is present on the source under test. The errors introduced by the phase-locked loop must either be set so that they are below the frequency offset of interest or they have to be corrected for by measuring the loop characteristics and then mathematically correcting the measurement result. There is a further practical problem that needs to be assessed. If there is a lack of isolation between the two RF sources then, as their frequencies are brought close together, there will be a tendency for them to become injection locked. If one of the oscillators is a VCO then this is certain to happen and will need to be characterised. Under these conditions it is advisable to ensure that the deliberate phase locked loop bandwidth exceeds the injection locked bandwidth. Even then the loop must be characterised if accurate measurements are to be made on the source (Figure 17.7). The phase locked loop response can be measured by injecting a calibration signal into the loop. The calibration signal can be swept signal (e.g. the tracking generator output of a spectrum analyser or the modulation oscillator of a signal generator) or a noise source (often available on an FFT analyser). Outside the loop bandwidth the analyser measures the amplitude of the calibration signal but inside the loop bandwidth the phase-locked loop (PLL) reduces the level of calibration signal measured. From the frequency response plotted on the analyser, a correction plot can be deduced and applied to correct the phase noise measurement results. Care needs to be taken when interpreting results that include high correction factors: the software may display the answers to a high degree of precision not reflected in the real accuracy of the numbers. Commercial systems are available from a number of vendors based on the use of the Quadrature Technique.
Calibration signal
OSC 1
Mixer
Low pass filter
+
LNA
or Spectrum analyser
OSC 2
Figure 17.7
FFT analyser
Method for calibrating the effects of phase locked loop
404 Microwave measurements
17.6
FM discriminator method
This method uses a mixer and a reference source to convert the signal to an IF where it is demodulated by an FM discriminator (Figure 17.8). In principle any FM discriminator, including a discriminator of the type found in a modulation analyser, can be used. However, the noise performance of the discriminator is likely to have a critical effect on the ability to make a phase noise measurement. A proprietary FM discriminator phase noise measuring system is used at IFR Ltd (now part of AeroFlex) to measure high-performance signal generators based on a high performance. A 1.5 MHz discriminator is shown in Figure 17.8. This system is used to aid the design of the oscillator systems deployed in the company’s signal generators. The discriminator is based on the use of a splitter, a band-pass filter and a mixer acting as a phase detector. The band-pass filter uses a coupled resonator design that ensures that at the centre frequency of operation, the phase shift through the filter is 90◦ so the inputs to the phase detector are in quadrature. In the practical implementation two band-pass filters are available, one allowing a measurement bandwidth of up to 20 kHz and the other allowing measurements to 100 kHz offset. In principle, the system behaves in a way similar to the delay line discriminator method but it does have some substantial advantages. In particular, since the discriminator operates at an IF, a limiter can be used to control the amplitude of the signal into the discriminator and hence the conversion gain of the discriminator is independent of RF input level. Operation at an IF also allows the FM discriminator to be implemented using a different type of phase detector operating at much higher signal levels. The design used in the IFR version uses two transformer coupled full wave rectifiers operating at very high signal levels to increase the signal-to-noise ratio. As with the Delay Line Discriminator, it is important to remember that FM noise is being measured rather than phase noise. Conversion between the two measurements
OSC 1
Limiter
LNA
FFT analyser
FM discriminator
Mixer
Low pass filter
300Hz to 3 kHz voltmeter
OSC 2
Figure 17.8
20kHz tuned voltmeter
Method of measurement using an FM discriminator
Measurement of frequency stability and phase noise 405 is relatively straightforward (by differentiation of the spectrum measurements) and some FFT analysers are available which can mathematically convert the measurement result automatically. Calibration of the system is very straightforward since the system sensitivity is independent of the input drive level to the frequency conversion mixer. Once a system has been constructed, the calibration factors are constants that can be allowed for by periodic (six monthly) calibration checks. Calibration is typically performed by making one of the sources a signal generator with calibrated amounts of FM or phase modulation. The system used at IFR Ltd includes a meter to measure the residual FM of a signal source in a 300 Hz to 3 kHz bandwidth (a common signal generator specification parameter) and a tuned voltmeter to measure phase noise at 20 kHz offset to give a fast measurement of these two signal generator parameters. The performance of an FM discriminator system is limited by the noise figure of the amplifiers and limiters which recover the signal from the output of the mixer and by the performance of the discriminator itself. In the case of the system described previously the discriminator consists largely of passive components, which exhibit very good noise characteristics, and very high signal levels can be used to maximise the Hz V−1 at the output of the discriminator. Performance tends to be controlled by the slope of the discriminator and it is for this reason that two band-pass filters are used to allow a compromise between sensitivity and measurement bandwidth. A high-performance FM discriminator is capable of measuring very low levels of phase noise. The above system is capable of measuring residual phase noise of −170 dBc Hz−1 at 20 kHz offset and residual FM of 0.003 Hz in a 300 Hz to 3 kHz bandwidth. The FM discriminator system also has some disadvantages. The need to have sources at different frequencies can be inconvenient. The mixing process can also generate intermodulation products that can give a false indication of there being spurious signals present. With a 1.5 MHz IF, however, this is unlikely to be a problem for carrier frequencies above 50 MHz. A less obvious problem is that if a source exhibits a flat noise profile from the offset frequency being measured to the image frequency (approximately 3 MHz offset for a 1.5 MHz IF) then the image frequency noise will be added to the noise at the required offset. Most signal sources, however, tend to exhibit better noise performance at the image frequency than at the closer offset frequencies. The substitution of a single-sideband (SSB) mixer for the double balanced mixer can eliminate this problem.
17.7
Measurement uncertainty issues
The measurement methods for measuring phase noise are often subject to large error bands. There are a number of basic problems that lead to difficulties. For this reason it is difficult to obtain truly traceable measurement results, and indeed improving the traceability of phase noise is a subject being actively pursued by the National Physics Laboratory and other standards organisations.
406 Microwave measurements Some of the issues are as follows: •
• •
• •
Removal of the carrier signal means the reference value has been removed and needs to be reinstated by the calibration system • inherent to quadrature and delay line methods (but important to its performance) • implies software correction (hard to prove under all conditions, hard to assign unique values, susceptible to changing levels, increases test time) Reliance on phase coherence at a mixer • more calibration and software problems for PLL effects • restricts the type of on device that can be tested The spectrum or FFT analysers are subject to significant errors • filter BW correction numbers • absolute level errors • inherent frequency response • absolute level errors • scale shape errors • detector response to noise like signals (noise is a power measurement) • display formatting algorithms (especially FFT analysers) • input attenuator accuracy and VSWR • reference level accuracy • IF switched gain errors • amplitude display non-linearities (not to be confused with display distortion) LO residual phase noise Injection locking defects
These errors make it difficult to assign a traceability figure to phase noise measurements. Often measurements of the same device will lead to differing answers, even when measured on the same system. It is not uncommon for instance to see ‘stitching’ errors in the results where the test system changes settings to measure noise at different offset frequencies.
17.8
Future method of measurements
There are, however, other techniques that may be developed in the future which could offer other solutions. A promising area is the use of direct Analogue to Digital conversion of IF from a mixer. Current levels of performance are limited by A to D linearity, quantisation error and aperture dither, the resulting noise tending to restrict the usefulness of this measurement technique to offset frequencies of a few kHz. However, improvements in converters are being steadily made.
17.9
Summary
From the above discussion it can be seen that no measurement scheme for phase noise can be said to offer a complete solution in all applications. Of the methods discussed
Measurement of frequency stability and phase noise 407 Table 17.1
Advantages and disadvantages of the various methods described
Method
Advantages
Disadvantages
Spectrum analyser
Simple to use Simple to get a result
Delay line discriminator
Requires no additional RF source Can measure drifting RF sources
Quadrature technique
Reference oscillator is at the same frequency Large dynamic range Measurements can be made at small and large offsets
FM discriminator
Large dynamic range Does not require frequent calibration Very accurate and hard to make errors Can measure drifting sources easily Tolerates LF noise
Poor dynamic range Cannot measure close to carrier noise Difficult to measure sources with frequency drift Requires frequent calibration Restricted dynamic range Restricted bandwidth Difficult to automate Requires direct manipulation of microwave sources Requires calibration of every measurement Requires the use of PLL and prior knowledge of the source Takes a long time to make accurate measurements Easy to make errors Requires a frequency offset source Limited frequency offset range Frequency conversion can make the results pessimistic due to image signals
the most reliable technique is the FM Discriminator Method, since it is the most ‘fail safe’ technique. The quadrature technique is the most widely used since it offers better overall capability (and the greatest number of commercial solutions) but requires much more care (and time) to undertake a measurement. The spectrum analyser based techniques are often the most convenient to undertake since the equipment is likely to be readily available in most laboratories. Table 17.1 shows the advantages and disadvantages of the various methods described in a summary.
Chapter 18
Measurement of the dielectric properties of materials at RF and microwave frequencies Bob Clarke
18.1
Introduction
In all RF and microwave (RF and MW) applications electromagnetic (EM) fields interact with materials, that is, with solids, liquids or gases. Viewed on a macroscopic scale, all materials will allow EM-fields to pass into them to some extent: even good conductors and superconductors. Therefore, in one sense, all materials may be said to be dielectrics: the word ‘dielectric’ is a contraction of ‘dia-electric’, which means that electric fields can (to some extent) pass through them. In designing RF and MW components for applications, therefore, we need to understand just how electric and magnetic fields propagate into and through materials. We also need to know how they behave (reflect, transmit, scatter, etc.) when they meet interfaces between different materials, for example, between air and an insulator or between a crystal and a metal. To achieve this understanding we need to be able to measure the dielectric and magnetic properties of the materials. The characterisation of the EM properties of materials is a very broad topic and we can only touch on the most general points in this overview. A wide variety of important functional or active materials are used in RF and MW applications. They include semiconductors, superconductors, chemically active media and non-linear media in general. Studies of such materials require special detailed consideration and they are generally regarded as specialist topics in their own right. We will not be considering such materials here, we will rather be concerned with materials that respond linearly to low-field strength electric fields and it is this subset of materials (which excludes semiconductors, superconductors and so on in their active functional roles) to which the term ‘dielectric’ is usually applied on a day-to-day basis. Good conductors such as metals are usually excluded from this class too, though virtually everything we will be saying about dielectrics at RF and MW frequencies applies to
410 Microwave measurements metals too – they can be regarded as dielectrics with very high conductivity. Even with this restricted definition ‘dielectrics’ nevertheless make up a very wide and important class of materials for RF and MW applications. They are variously used to transmit, absorb, reflect, focus, scatter or contain EM-fields and waves. Bear in mind also that in many applications – radar, RF and MW processing (e.g. in microwave ovens), also in biomedical studies and treatments – the materials that are being detected, studied or treated are themselves dielectrics, so we need to understand their EM properties too. At RF and MW frequencies, with wavelengths in the centimetre to millimetre range, we are normally dealing with macroscopic components – that is, to say that the linear scale of the components that we are concerned with is much greater than the molecular scale – this is true even in modern ‘micro’-devices such as RF MEMs (microelectromechanical devices). It is for this reason that we are normally concerned with parameters that characterise the materials on a macroscopic scale in our practical studies and uses of dielectrics. Of course, on a microscopic scale there are complex EM interactions between atoms, electrons, holes and molecules – and for full understanding of the theory of dielectrics we must also study dielectrics on this scale. However, in the practical realm of RF and MW activities we wish to deal with parameters that capture the macroscopic consequences of all of the microscopic phenomena in the material. The most important of these parameters are the complex permittivity, ε∗ , and the complex magnetic permeability, µ∗ . This chapter is mainly concerned with the characterisation of dielectric materials at RF and MW frequencies. There are a number of existing publications that deal with this topic in depth that are well worth consulting. The most recent is the Good Practice Guide from NPL [1] (on which this chapter is based), which deals with the topic comprehensively. The long-standing ‘bible’ of dielectric metrology is the book by von Hippel [2]. It has deservedly stood the test of time and remains one of the most useful treatises on RF and MW dielectric measurement ever written. It covers background theory in greater depth than Reference [1], though the measurement technology described in it is now rather dated. A number of reviews (e.g. [3] and [4]) and book with details on measurement (e.g. [5]), and conference proceedings (e.g. [6]) also provide a useful background to this discipline. However, before we take up the topic of measurement, we must turn first to the dielectric theory behind the parameters, ε∗ and µ∗ – the parameters that we wish to measure.
18.2
Dielectrics – basic parameters
Introductory theoretical treatments on dielectrics can be found in most standard textbooks on electromagnetism and in books on dielectrics (e.g. see [1,5,7–12]). The quantity with which we are most concerned here is the relative permittivity, ε ∗ . This can be converted to the absolute permittivity if we multiply it by the permittivity of free-space, ε0 = 8.8542 × 10−12 F m−1 . Note that absolute permittivities in the SI system have units of farads per metre, whereas relative permittivities are dimensionless quantities. In the practical world we are usually concerned with
Measurement of the dielectric properties of materials 411 relative permittivities. As it is a complex quantity, ε ∗ has two components: ε∗ = ε0005 − jε 00050005
(18.1)
√ where j = −1. If we assume that our dielectric material is placed between planeparallel electrodes to form a capacitor, as in Figure 18.1, ε 0005 , the real part of the permittivity, characterises the capacitative part of the admittance, Y , of the capacitor and ε 00050005 characterises the conductive or lossy part of the admittance. In all materials, ε0005 and ε00050005 depend on ambient parameters such as the temperature, relative humidity, as well as the frequency, so neither ε∗ nor ε 0005 should be given the name ‘dielectric constant’ – they are not constant (the only true dielectric constant is ε0 ). The properties of the capacitor in Figure 18.1 can be captured in simple equivalent circuits, such as those shown in Figure 18.2a and b, in which the resistive and conductive components R and G represent the dielectric loss of the specimen. It is usually better to use the parallel equivalent circuit of Figure 2b for dielectric materials because C and G are proportional to ε0005 and ε 00050005 , respectively. In some circumstances it is better or more conventional to quote the loss tangent, tan δ, to quantify the conductive or lossy part of the complex permittivity, rather than ε 00050005 : tan δ =
ε00050005 ε0005
(18.2)
Dielectric specimen
Electrodes
Figure 18.1
A dielectric specimen in a plane-parallel-electrode admittance cell
(a)
(b)
R
G
C C
Figure 18.2
Simple series (a) and parallel (b) equivalent circuits of the dielectric specimen in the admittance cell of Figure 18.1. R and G take account of the dielectric loss in the specimen. R is the equivalent series resistance and G is the equivalent parallel conductance of the dielectric
412 Microwave measurements For small losses it is often convenient instead to refer to the loss angle, δ, measured in radians, which is the arctangent of tan δ. As δ ≈ tan δ for small angles, they can be numerically equivalent for most practical measurements. The advantage of using loss angle is that one can use the convenient unit ‘microradian’ (µrad) to quantify small losses [similarly, ‘milliradian’ (mrad) can be used for medium losses]. As implied in Section 18.1, we may encounter many different types of dielectric material in our work and they will display a wide range of properties. ε0005 , for example, can vary from 1.0 for air, 2–3 for typical low to medium loss polymers, 5–100 for typical electroceramics, 80 for water, 5 to >1000 for biological tissues and up to >2000 for ferroelectrics. The loss tangent, tan δ, may be as low as 3 × 10−5 for crystals such as quartz and sapphire at room temperature (or as low as 10−7 at cryogenic temperatures). Typical low-loss polymers have tan δ in the range 10−4 − 10−3 , while absorbing materials like radiation absorbing materials (RAM) and bodily tissues can have tan δ > 0.1 or even >1. With such a wide range of dielectric properties and an equally wide range of physical properties (as dielectrics can be solids, liquids, powders, malleable, hard, etc.) it is not surprising that many different dielectric measurement techniques have been developed over the years. It is good practice in dielectric measurement, if we wish to reduce our measurement uncertainties to match the technique to the material. In this overview, for convenience, we refer to materials with tan δ less than 3 × 10−4 as low-loss, above 3 × 10−2 as ‘high-loss’ and those with tan δ in between these two values as ‘medium loss’. The magnetic parameter that corresponds to the dielectric parameter ε∗ is the complex relative magnetic permeability, µ∗ , which may be defined and treated by analogy with ε ∗ µ∗ = µ0005 − jµ00050005
(18.3)
In many materials for all practical purposes µ∗ ≈ (1.0 − j0.0) and we can refer to these as ‘non-magnetic materials’ or just simply as ‘Dielectrics’. If µ∗ differs significantly from (1.0 − j0.0) we have a magnetic material and we need to take account of its magnetic properties in our measurements. There is an important difference between dielectric and magnetic responses in most materials. The dielectric response to small signals is typically linear while the magnetic response can be non-linear even for small signals, so that µ∗ is a function of signal strength – one well-known manifestation of this non-linearity is magnetic hysteresis. At sufficiently high fieldstrengths all dielectric materials will also respond non-linearly to applied fields (e.g. see [2,13]). However, we will restrict our discussion here to the normal, low signal and linear regime. As we move up in frequency through to the millimetre-wave region of the spectrum and up through THz frequencies, it becomes more convenient to characterise dielectrics in terms of quasi-optical or optical parameters such as the complex refractive index: n∗ = n − jk [14]. This quantity is related to ε∗ and µ∗ by n∗ = n − jk =
0001 ε ∗ µ∗
(18.4)
Measurement of the dielectric properties of materials 413 For non-magnetic materials, 2
ε∗ = n∗ = (n − jk)2 ,
so ε0005 = n2 − k 2 and ε 00050005 = 2nk
(18.5)
Rather than using k to quantify the loss, it is more conventional in optical and quasioptical systems to employ the power absorption coefficient, αp , αp =
4π fk c
(18.6)
where f is the frequency and c is the speed of light and αp is the power absorption coefficient per unit length of signals transmitted through the medium. αp is conventionally measured in the units nepers per metre (Np m−1 ). As 1 Np = 8.69 dB, the power attenuation of a signal passing through the dielectric may also be expressed in decibels as 8.69 × αp dB m−1 . We can express the loss tangent of the material in terms of the (quasi-)optical parameters n and αp as follows: tan δ =
8π fncαp ((4π fn)2 − cαp )2
(18.7)
which for low-loss materials having αp << 4π fn/c reduces to tan δ ∼ = cαp /2π fn.
18.3
Basic dielectric measurement theory
As most dielectric measurements make use of cells to contain the dielectric, and as we can regard the cell as an RF and MW component, many dielectric measurement techniques, viewed at the instrumental level, are similar to other S-parameter measurement techniques that are covered in-depth in other chapters and also in textbooks on RF and MW measurements (e.g. [15–17]). A more comprehensive version of the treatment given here can be found in the Good Practice Guide [1]. Dielectric measurement methods and measurement cells largely fall into two broad classes: (1) Those in which the dielectric properties are measured as an impedance, Z, as in Figure 18.2a, or more commonly, as an admittance, Y , as in Figure 18.2b. These may collectively be called lumped-impedance methods and are generally used at low frequencies (LF) and in the RF region of the spectrum up to 1 GHz. (2) Those in which the dielectric is considered to be interacting with travelling and standing electromagnetic waves – these may collectively be called ‘Wave Methods’. Both lumped-impedance and wave techniques can be used in resonators. Resonators are measurement cells with resonating EM-fields inside them that are used to obtain high sensitivity for measuring the loss of low-loss dielectrics (see below).
414 Microwave measurements
18.3.1 Lumped-impedance methods In these methods we use an impedance/admittance analyser or bridge to perform the measurements on the cell. If we carry out a measurement in the cell of Figure 18.1, we usually measure the cell admittance Y = G + jB, where G is the equivalent parallel conductance and B is the equivalent parallel susceptance, both measured in units of siemens. The equivalent circuit for a lossy dielectric is shown in Figure 18.2b, where C is related to B by B = ω C, where ω = 2π f and f is the frequency in hertz. The cell shown in Figure 18.1 is commonly called an admittance cell because one determines ε∗ by measuring its admittance. In lumped-impedance analysis one therefore treats continuous dielectric media, and specimens thereof, in terms of lumped equivalentcircuits, that is, circuits containing discrete components: inductors, capacitors and resistors. This is perfectly acceptable as long as their physical dimensions are very small compared with the wavelength, λ, of the radiation. It is this requirement that limits the usefulness of lumped-impedance methods as one moves up through the spectrum.
18.3.2 Wave methods Measurements at MW frequencies usually differ from electrical measurements at lower frequencies because they are conceived of differently: they deal with waves rather than with impedances and admittances. Wave methods may be travellingwave or standing-wave (resonant) methods and they may employ a guided-wave or a free-field propagation medium. Coaxial, metal and dielectric waveguide, microstrip, co-planar waveguide and optical-fibre transmission lines are examples of guidedwave media while propagation between antennas in air uses a free-field medium. In guided-wave travelling-wave methods the properties of the measurement cell are measured in terms of Scattering Parameters or ‘S-parameters’ (e.g. see [16] and Figure 18.3). It is good practice in such measurements to ensure that as much of the measurement system as possible is matched to the transmission-line characteristic impedance, Z0 , because mismatches produce reflections and multiple reflections that can seriously reduce the accuracy of measurement. The reflection coefficient, , from an impedance Z that terminates a transmission-line of characteristic impedance Z0 [18] is given by =
Z − Z0 Z + Z0
(18.8)
so reflections are only absent if Z = Z0 . In fact, the propagation of EM waves through any uniform isotropic medium, or any uniform transmission-line containing such a medium, is governed by two parameters: the characteristic impedance, Z0 , and the complex propagation constant, γ , of the medium [10]. Both are functions of the complex permittivity, ε∗ , and permeability, µ∗ , of the medium. The propagation constant governs both the wavelength and attenuation of waves moving through the medium: 0001 γ = α + jβ = 2π f ε0 ε ∗ µ0 µ∗
Measurement of the dielectric properties of materials 415 or, because c= √
γ =
1 ε0 µ 0
2π f
√ √ ∗ ∗ ε µ 2π ε ∗ µ∗ = c λ0
(18.9)
where c is the speed of light in free-space and λ0 is the free-space wavelength, α is called the attenuation constant and β is the phase constant. For low-loss dielectrics in which it is assumed that α ≈ 0, β is sometimes itself called the propagation constant. In non-magnetic materials, µ∗ = (1.0 − j0.0) and γ =
2π √ ∗ 2π f √ ∗ ε = ε c λ0
In a low-loss dielectric α is small (α << β) and we find √ √ λ0 2π ε 0005 π ε 0005 tan δ π fn tan δ λ ≈ √ ,β ≈ and α ≈ or α ≈ λ0 λ0 c ε0005
(18.10)
(18.11)
so tan δ ≈ cα/π fn and referring back to (18.18), we find α = αp /2. This relationship actually follows more fundamentally from the definitions of α and αp . First is the exponential coefficient for decay of field-strength as the wave propagates through the medium, the second describes the decay of power, so the relationship α = αp /2 is valid even if α is not small. The measurement of propagation or transmission parameters, such as β, γ and λ, provides a means for deriving dielectric parameters. Many dielectric measurement methods are based on this principle. The same is true of the measurement of reflection parameters, , S11 , S22 , etc. Reflections at plane interfaces between two uniform media are governed by 0001 the intrinsic wave 0001impedances of the media, η1 and η2 , respectively, where η1 = µ∗1 /ε1∗ , and η2 = µ∗2 /ε2∗ , where µ∗1 , µ∗2 , ε1∗ and ε2∗ are the complex relative permeabilities and permittivities of the two media, respectively. By analogy with (18.8), the reflection coefficient in Medium 1 of a wave at normal incidence (i.e. at 0◦ angle of incidence) on Medium 2 is =
η2 − η1 η2 + η 1
(18.12)
Such reflections are dependent on the ratio of µ∗ and ε ∗ , whereas the transmission parameters defined in (18.9) are governed by the product of µ∗ and ε ∗ . In order to separate µ∗ and ε∗ we must normally, therefore, measure the specimen both in transmission and reflection (though other techniques are possible). This is readily achieved by measurements in transmission cells, such as the one shown in Figure 18.3, in which all four S-parameters are easily determined. If we are sure that we have a non-magnetic material, however, we have µ∗ = (1.0 − j0.0) and we can measure ε∗ either by transmission or by reflection methods. The choice should normally be made on the basis of which is the most accurate. For non-magnetic materials, the reflection
416 Microwave measurements Coaxial line: 50 Ω characteristic impedance S21
Forward travelling wave
S11
Port 1
Port 2
S22 S12 Dielectric specimen
Figure 18.3
Reverse travelling wave
Electromagnetic travelling waves in a coaxial measurement cell that contains a dielectric specimen. The cell is placed in a measurement system in which there are waves travelling in both directions, designated forward and reverse waves. The figure shows the reflection coefficients of the specimen, S11 and S22 , for the forward and reverse wave, respectively, and the corresponding transmission coefficients, S21 and S12 . The S-parameter subscripts refer to the measurement ports (that is the two ends) of the coaxial cell
from a dielectric interface between two media with permittivities ε1∗ and ε2∗ travelling at normal incidence from Medium 1 to 2 is 0001 ∗ 0001 ∗ ε − ε n∗ − n∗2 (18.13) = 0001 1∗ 0001 2∗ = 1∗ n1 + n∗2 ε1 + ε2 where n1 * and n2 * are the complex refractive indices of the two media. For freefield measurements in which the angle of incidence is not necessarily normal these equations may be generalised for any angle of incidence by using Fresnel’s Equations [10,19]. In the free-field it is also important to take account of whether the electric field polarisation of the incoming radiation is parallel to the dielectric surface or in a plane perpendicular to the surface. There are two sets of Fresnel’s equations – one each for the parallel and perpendicular cases.
18.3.3 Resonators, cavities and standing-wave methods Resonance methods are generally used for measuring the loss of low-loss dielectrics. The cell in such measurements is commonly referred to as a cavity or resonator. In such cells the real permittivity, ε0005 , is typically determined by measuring the change in resonant frequency when the specimen is inserted into the resonator or else it can be measured by changing the length (or some other key dimension) of the
Measurement of the dielectric properties of materials 417 RF source Inductance coil
Specimen
To high impedance detector Micrometer-driven electrode
Admittancecell
Figure 18.4
The basic principles of the Hartshorn and Ward method for low-loss specimens
resonator to return it to resonance at the same frequency. These contrasting methods are known, respectively, as the frequency-change and length-change methods for determining ε 0005 . It is possible to measure ε 0005 by the length-change method because the wavelength in the dielectric medium, λ, differs from that in free-space (18.11). The determination of dielectric loss, ε00050005 or tan δ, in such resonators usually proceeds via the measurement of Quality-Factor, otherwise known as Q-factor or Q [20], (see Section 18.7). Both lumped-impedance and wave techniques can be employed in resonators. In the former case an admittance cell can be resonated with an external inductor; (Section 18.9.2 and Figure 18.4). This RF ‘dielectric-test-set’ method was first used for measuring low-loss dielectrics in the 1930s. At higher frequencies where wave methods are more appropriate, the resonator is often modelled using standing-wave equations rather than a travelling-wave analysis. Note that wave resonance methods are also often referred to as ‘multi-pass techniques’ because a travelling-wave in the cell, in bouncing backwards and forwards between the two ends of the resonator, will pass through the dielectric specimen many times before it is absorbed. This concept helps to explain why resonant methods are more sensitive to low-losses than single (transmission) and double-pass (reflection) techniques.
18.3.4 The frequency coverage of measurement techniques It is worthwhile drawing attention to the frequency coverage of the various techniques used in different parts of the spectrum. At MW frequencies we generally need to adapt equipment dimensions to the radiation wavelength (this is almost a definition of what ‘microwave’ means in practice). We therefore tend to need many differently sized measurement cells in this region of the spectrum. In contrast, at LF and from THz frequencies upwards (above approximately 300 GHz), a single instrument/cell combination may measure over many decades of frequency. For example, a bridge/admittance cell combination can cover five decades of frequency at LF, while a single Fourier transform spectrometer [21] can cover five decades in the sub-millimetre to infrared regions of the spectrum. Note also that many resonance techniques operate at one spot-frequency only! We need to bear these limitations in mind when we set out to measure dielectrics – as explained at the end of Section 18.4, measurements at a few spot frequencies may suffice to characterise a low-loss material over a wide frequency band, but much more detailed frequency coverage is needed for high-loss materials.
418 Microwave measurements
18.4
Loss processes: conduction, dielectric relaxation, resonances
It is important, before we set out to measure our dielectric materials, that we know something about the physics of dielectric response behaviour. The most relevant physical processes here are those that give rise to power loss in bulk dielectrics. In the RF and MW region of the spectrum such power losses arise largely from four different physical processes – see [22–24] or [5] for details and [12] for an introduction. These four physical processes are associated with mechanisms for generating loss – that is, conversion of EM energy into other forms of energy – and so are commonly called ‘loss processes’. They are (1) Electrical Conduction, (2) Dielectric Relaxation, (3) Dielectric Resonance and (4) Loss from Non-Linear Processes. (1) Electrical Conduction in which charge carriers (electrons, ions or holes) in a material medium are relatively free to move physically through the medium under the influence of an electric field. The ease of conduction is quantified by the conductivity of the medium, σ , measured in siemens per metre (S m−1 ). In general, σ will depend on frequency, temperature, concentration of carriers, etc., though in many materials σ will change only slowly with frequency in the RF and MW range. In metals the effective conductivity depends on the physical properties of the metal surface (e.g. scratches, machining or grinding marks or debris) and so σ will depend on frequency because the skin-depth [18] is a function of frequency. (2) Dielectric Relaxation refers to the response of the electric dipoles in a material medium to the applied alternating EM-fields. Many different types of dipole can be present in dielectric media. Some materials have permanent molecular dipoles inside them and they are called polar materials. Their molecules are referred to as polar molecules. Materials in which the dipoles are induced only by the application of the electric field itself are called non-polar materials. Polar molecules typically exhibit a number of different relaxation processes. If they are in a liquid phase they can rotate bodily to try to align themselves with the field, giving rise to rotational polarisation. Otherwise portions of large molecules can move with respect to each other, giving rise to one or more distortional polarisation processes, each with its own relaxation behaviour. Any interfaces in a material that prevent or inhibit the passage of charge carriers will have dipolar layers set up across them when the electric field is applied and they give rise to interfacial polarisation, a phenomenon, essentially similar to the Maxwell–Wagner effect [5,22], which exhibits its own relaxation behaviour. The membranes in the cells of biological tissues typically exhibit this behaviour [25]. In a complex medium, many or all of these relaxation processes may be present, giving rise to very complex relaxation behaviour. Each process will have its own strength, which is a parameter that measures the extent to which it contributes to the total magnitude and behaviour of ε0005 and ε00050005 . All relaxations give rise to very slow changes in ε 0005 and ε00050005 with frequency. The behaviour shown in Figure 18.5 for water is typical.
Measurement of the dielectric properties of materials 419 80 70 ε′
Permittivity
60 50 40 30
ε″
20 10 0 108
Figure 18.5
fr 10
9
10
10 1011 Frequency (Hz)
1012
1013
A typical Debye Relaxation response, see (18.14). This plot is for deionised water. The diagram omits the effects of all other loss processes in the water, for example, conduction. The use of a logarithmic scale demonstrates just how slowly dielectric properties change with frequency when governed by a relaxation process
(3) Dielectric Resonance. Dielectric polarisation resonance should not be confused with dielectric relaxation. The physics of relaxations and resonances is completely different and the two should not be confused (see Figures 18.6 and 18.7). A resonance may appear either as a sharp or broad feature in the frequency domain, depending on its Q-factor (see Section 18.7), whereas relaxations always exhibit very broad spectral features. Furthermore, a resonance gives rise to a frequency dependence for ε 0005 in which ε0005 can either fall or rise with frequency, whereas in relaxation behaviour ε 0005 (or µ0005 ) can only fall with frequency. The physics of linear, homogeneous, non-composite solid and liquid dielectrics does not normally allow a resonance to occur at RF and MW frequencies. The molecules of such materials, because of their close proximity to one another, interact to such an extent that all potential resonances are damped effectively into non-existence. (This is not the case with gases in which spectral lines, that is, resonances in the EM response can readily be distinguished at MW frequencies). Therefore, it is a useful rule of thumb that for linear, homogeneous, non-composite solid and liquid dielectric materials any sharp features that we appear to measure in the spectrum of ε0005 and ε00050005 at RF and MW frequencies, and any apparent increases in ε0005 with frequency are invariably caused by non-intrinsic effects, usually imperfections in our measurement cells! There are, however, genuine dielectric resonances in the infrared region in the spectra of solids and liquids. These processes give rise to small but measurable effects at RF and MW, usually a slowly increasing
420 Microwave measurements
C1
C2 R
Figure 18.6
An equivalent circuit of a Debye Relaxation C
Figure 18.7
L
R
An equivalent circuit of a dielectric resonance
value of tan δ with frequency caused by the LF tail of the resonance – this is only visible in low-loss materials. Special notice should also be taken of RF and MW resonances that can occur in composite materials. Resonances can occur within the meso- or macroscopic particles and structures that make up such materials. This is particularly prominent if one component of the material is a high permittivity low-loss component, such as a sintered ceramic. Bear in mind that if√the free-space wavelength is λ0 , the wavelength in the material will be λ0 / ε 0005 . So, if ε 0005 for a particle is approximately 1000, resonances can occur in the millimetre-wave region of the spectrum even if the typical particle width, referred to as its structure-length, is as small as 0.1 mm. It is usually this phenomenon that limits the useful upper frequency of dielectric composites. (4) Loss from non-linear processes. It is well known that hysteresis in magnetic materials leads to loss [26]. Ferroelectrics [1,27] can exhibit much the same phenomenon in their electrical properties, leading to an independent source of electrical loss. The relative magnitude of these non-linear effects usually rises with the amplitude of the applied fields. Having listed the four likely sources of loss in dielectrics we should return to dielectric relaxation (2) because it is the most characteristic of dielectric loss processes in the RF and MW region of the spectrum.
Measurement of the dielectric properties of materials 421 Relaxation Models. The Debye Relaxation is our simplest relaxation model [5,13,22]. It corresponds to the equivalent circuit in Figure 18.6. Three real-number parameters (corresponding to the three lumped components in the equivalent circuit) are used to characterise the frequency response of the relaxation: (1) the ‘static’ permittivity, εs , is the value of ε0005 at very LFs; (2) the relaxation frequency, fr , giving the typical speed of the relaxation; and (3) the high-frequency permittivity limit, ε∞ , is the value of ε 0005 at high frequencies, well above fr . All three parameters are functions of temperature. The Single-Debye dielectric response is then described by the following equation: ε ∗ = ε∞ +
εs − ε∞ 1 + j f /fr
(18.14)
A typical response is shown in Figure 18.5. This behaviour is exactly analogous to the behaviour of the equivalent circuit shown in Figure 18.6 with fr = 1/2π RC1 Debye relaxations are exhibited by a number of liquids including water at RF and MW frequencies, but many other materials have more structured responses with frequency, for example, they exhibit Double-Debye or Multiple Debye responses [28,29], or else they relax even more slowly with frequency, as typified by the ColeCole [30], Cole-Davidson [31] or Havriliak–Negami relaxation formulae [32]. In most complex structured materials many different relaxation processes contribute to the dielectric response, which can therefore be quite difficult to describe in terms of any one simple model. In scientific studies, variable temperature measurements are always carried out because the features of relaxations (e.g. loss peaks) typically shift in frequency by different rates as temperature is varied, so temperature variation can be used to differentiate between the various processes. In all of these relaxation models the contribution from dielectric relaxations to the real permittivity, ε0005 , always falls with frequency (or else, in the limit, at very low and high frequencies, it may asymptotically be approximately constant; see Figure 18.5). Given (1) that free particle conductivity, σ , has no effect upon ε0005 ; (2) that intrinsic dielectric resonance does not occur in homogeneous non-composite dielectric solid and liquid materials in the RF and MW region; and (3) that dielectric behaviour in this region is normally dominated by relaxations, we can make the following general statement: In the RF and MW region of the spectrum ε 0005 always falls with frequency (or, in the limit, remains stationary) in homogeneous solids and liquids that exhibit a linear response to the applied fields.
Note though (as discussed above) that this statement does not necessarily apply to (1) gases, (2) composite materials with a structure-length close to the EM wavelength in any one of the components in the material and (3) non-linear materials. There are other important features of relaxations that we should know about. For example, the Kramers–Kronig relations [23,33] provide a formula which relates ε 0005 ( f ) to ε00050005 ( f ) over a broadband of frequencies. In 1971 Arnold Lynch derived and published [34] a simplified equation for relating changes in ε0005 with frequency to tan δ when the electrical response of the material is determined by dielectric relaxation behaviour. It is good practice to use such formulae to check our measurements; see
422 Microwave measurements also [1]. Another important practical rule of thumb follows from consideration of the Kramers–Kronig relations and from inspecting relaxation models such as the Debye relaxation of (18.14): In the RF and MW region of the spectrum for low-loss materials both ε 0005 and ε 00050005 change very slowly with frequency, so we do not need to measure them at all frequencies.
Thus, the fact that we normally use resonators to measure low-loss materials and that the resonators may be restricted to one frequency only is mitigated to some extent: we need to use only a few such resonators to cover a broad bandwidth. In fact, it is usually a waste of time and effort to measure low-loss materials at frequencies more closely spaced than once every octave (i.e. more closely than f , 2f , 4f , etc.). This statement does not apply to high-loss materials for which continuous frequency coverage is usually advisable.
18.5
International standard measurement methods for dielectrics
Internationally agreed standard methods of measurement allow us to share good practice and ensure the compatibility of measurements that are made in different laboratories. These methods are of particular importance when specifying a procedure for the determination of properties of a material for a well-defined end-use. That said, however, methods outlined in such standards often lag behind the state-of-the-art in metrology. This is inevitable because test houses and product-control laboratories cannot be expected to be as up-to-date or as well equipped as calibration laboratories or those that have the task of developing new measurement methods for new types of material. Standard methods can be read as a guide to the art of measurement and they clearly must be followed, where possible, in many commercially oriented measurements. But there are many areas of dielectric metrology where effective written standards do not exist or else where significant practical detail is lacking from them. In these circumstances one often has to fall back on the scientific literature for a more detailed account of the methods. Dielectric standards may be found in the American Society for Testing and Materials (ASTM) catalogs and in the International Electrotechnical Commission (IEC) and Comité Européen de Normalisation (CEN) systems. British Standards (BS) are nowadays subsumed into the IEC and CEN ranges. Note that CEN electrical standards are normally referred to as ‘CENELEC’ standards. A short overview of RF and MW dielectric standards is given in Reference [1].
18.6
Preliminary considerations for practical dielectric measurements
Please see the Good Practice Guide [1] for more details on the points that follow.
18.6.1 Do we need to measure our dielectric materials at all? Perhaps we can consult manufacturers’ data sheets or consult the scientific literature. Either option can be adequate for the early design stages of the system development
Measurement of the dielectric properties of materials 423 process, but for end-use applications it is usually advisable to measure (or have measured) the materials that are being used. There are a number of reasons for this. For example, the dielectric properties of all ceramics depend critically on how they are prepared and sintered, so there is no such thing as a ‘standard’ or ‘representative’ batch of sintered alumina. Likewise, a polymeric material like ‘PVC’ is far from being a uniquely defined substance – polyvinyl chloride is prepared in many different ways, having different amounts of plasticiser and other additives admixed with it. Both the additives and the processing of the polymer give rise to a whole range of different ‘PVC’ polymers with varying dielectric properties, so the uncritical adoption of data on ‘PVC’ from a database will not do. Usually, if we have a ‘one-off’ job, unless we already have a suitable measurement system available, it will be most cost-effective to ask a test house or calibration lab to perform measurements for us. If we have a long-term interest in measuring or testing dielectric materials we may well decide to set up a measurement system ourselves, but even in this case it may be more cost-effective to seek advice from an experienced laboratory first.
18.6.2 Matching the measurement method to the dielectric material Dielectric materials come in many different forms, physical phases, shapes and sizes. For example, high-loss solids (e.g. RAM), low-loss solids (e.g. quartz and other pure crystals, and ceramic dielectric resonator materials), hard or malleable solids, liquids with very different viscosities, toxic materials (e.g. many liquid organics and some solid inorganics like beryllia), magnetic solids, thin films, dielectric resonators, substrates, materials available only in small quantities (e.g. expensive crystals, trial samples of ceramic), materials available in copious quantities (e.g. radome materials, some substrates), composite materials, anisotropic materials, significantly inhomogeneous materials (e.g. many composites, foodstuffs, human tissues, etc.), moist materials and powders and so on. It is not too much of an exaggeration to say that each of these different physical classes of dielectric requires a different measurement technique for optimum measurement in the most accurate or the fastest way. Cost often forces us to carry out measurements on non-ideal equipment but it is good to bear in mind that we should ideally think of adapting the methods we use to the material rather than the other way around. Section 18.9 provides a short survey of methods and tells us which material types they are best used for. However, the following rule generally holds. 18.6.2.1 For low-loss materials It is invariably best to use a resonance method to obtain better sensitivity for loss. As noted above such methods may either be lumped-impedance methods (typically at RF) or standing wave methods (typically at MW frequencies and above). 18.6.2.2 For medium to high-loss materials It is usually better to use non-resonant methods. At RF, below approximately 1 GHz, the use of admittance bridges and admittance cells is effective. At MW frequencies, where it is appropriate to think in terms of travelling waves, the use of single-pass (transmission) or double-pass (reflection) techniques is usually more appropriate.
424 Microwave measurements 18.6.2.3 Cleanliness, specimen decomposition and contamination Dielectric specimens can be easily contaminated – the net result in many cases is that one measures a spuriously high-loss for the specimen. Especially in the case of low-loss materials, it is important to keep them clean and never touch them directly with the human hand – use clean tweezers or gloves instead – sweat from human fingers can enter the matrix of sintered materials and increase their loss considerably. In the case of hygroscopic liquids (e.g. organic liquids such as short-chain alcohols) it is important to store them in a well-sealed container as they will readily pick up moisture from the atmosphere. Some materials decompose in bright light (typically ultraviolet or sunlight), so store materials in the dark; other materials oxidise in the atmosphere so store them in sealed containers. 18.6.2.4 Specimen dimensions and preparation It is important to know that, with few exceptions, the uncertainty with which a specimen can be measured depends critically on one or more of its dimensions, typically either its thickness or diameter. Therefore one should use micrometers or optical techniques to measure critical specimen dimensions, and not less accurate methods, for example, callipers. For all but the most rudimentary or preliminary measurements, it is usually worthwhile ensuring that critical specimen dimensions are machined carefully to a uniform and known size. Grinding is often more accurate (though more expensive) than turning and low tool speeds are recommended for some polymers (to prevent melting the polymer). Cutting fluids must be avoided if they will contaminate the specimen. Specimen thickness, ts , should ideally be measured at a representative number of points across the area to be tested in order to check its uniformity. Remember that the thickness of hard specimens measured by micrometer may be too high, as it will only measure the high points, while for soft specimens it may measure too low if the specimen is compressed. Care should be taken to detect and correct for these effects in accurate measurements. For most techniques the actual specimen size, and not just its uniformity, will itself also have a major effect on the measurement accuracy. It is therefore good practice to model the measurement method numerically beforehand to determine the dimensions that the specimen should have to optimise measurement accuracy. Of course, in many cases we will not be able to choose the specimen dimensions ourselves and we will then have to do the best we can, but it is often worthwhile asking our specimen suppliers whether they can produce specimens of a more optimum size or shape. In some techniques specimen diameter is a critical parameter, for example, in the coaxial line method of Figure 18.3 and Section 18.9.6. It has been found that the use of air-gauging [35] is cost-effective and particularly convenient for the measurement of inner and outer diameters of both specimens and the coaxial cells in which they are contained. 18.6.2.5 Anisotropic and magnetic materials It is important to know whether the material one is measuring is an anisotropic or a magnetic material. Some measurement methods assume isotropy of the specimen’s dielectric properties or else they assume a non-magnetic material – if these conditions
Measurement of the dielectric properties of materials 425 do not hold they can lead to significant errors in the dielectric measurements. Some of the methods described in Section 18.9 can measure anisotropy or magnetic properties and it will sometimes be necessary to use such methods (perhaps in a preliminary study) if one does not know the EM properties of one’s materials at all. 18.6.2.6 Inhomogeneous, composite and structured materials As explained in Section 18.4, when discussing dielectric resonances it is always important to consider the structure-length of the inhomogeneities in the material (i.e. the typical linear dimension of the particles or components in the material) in relation to the wavelength inside the components of the material. If the structurelength and wavelength are comparable in size the component parts may resonate and the material may scatter radiation rather than reflect or transmit it. Except in (‘meta-’)materials which are specifically designed to do this – for example, photonic band gap (PBG) or frequency selective (FS) materials – this behaviour is usually undesirable, so that most composites will have an upper frequency limit of usefulness. But there is another reason for being aware of the structure-length in inhomogeneous dielectrics: one wants the specimen that one is measuring to be sufficiently large to be statistically representative of the material as a whole and this should influence one’s choice of method: for example, one would choose a large waveguide cell to measure foodstuffs rather than a small coaxial cell. The alternative may be to measure a large number of small specimens and take a statistical average, but this can be time consuming. Significantly, inhomogeneous materials can never be measured as accurately as homogeneous specimens and often the inhomogeneity will be the greatest source of uncertainty in the measurement. 18.6.2.7 Ferroelectrics and high-permittivity dielectrics, ε 0001 > 100 The RF and MW properties of ferroelectrics [11,12,27] are most easily measured by techniques that can measure thin film specimens, for example, the split-post resonator, see Section 18.9.4. Very high permittivity ferroelectric films may only be measurable if they are of sub-micron thickness, so special thickness measurement techniques must be used. Thicker specimens may be measured in admittance cells at RF frequencies if their permittivity is not excessively high (e.g. if ε0005 < 3000, depending on frequency and specimen size) by applying metal electrodes to both surfaces.
18.7
Some common themes in dielectric measurement
Section 18.9 presents a survey of a number of techniques used for RF and MW measurements upon dielectric materials. However, there are many practical features that these techniques have in common and we consider some of them together briefly here. The details are covered in much greater detail in the Good Practice Guide [1].
18.7.1 Electronic instrumentation: sources and detectors At MW frequencies it is common practice to use automatic network analysers (ANAs) connected to dielectric measurement cells as source/detector combinations. ANAs
426 Microwave measurements [15,16,36,37] are the ‘workhorses’ of microwave laboratories and are described in detail in other chapters. ANAs can be used both for measuring S-parameters of reflection/transmission cells (as in Figure 18.3) and for measuring frequency changes and Q-factors of resonance cells or cavities. Some ANA models have a synthesised time domain facility as one of their features [38]. This can be useful in a number of techniques for gating or de-embedding the S-parameters of a specimen from any mismatched components and imperfect transmission lines that lie between it and the ANA. ANAs can also be used at RF, but at lower frequencies, say below 100 MHz, and especially where the dielectric measurement cells are significantly mismatched to 50 0011, it is often better to use Impedance Analysers, ‘Materials Analysers’, Admittance or Impedance Bridges or Frequency Response Analysers (FRAs) [39,40] as they can be more accurate and sensitive. Some FRAs can work down to frequencies as low as a few microhertz (µ Hz) while others have an upper limit at about 100 MHz. FRA manufacturers provide accessories and cells that are specifically designed for dielectric measurements as a function of temperature, time, DC and AC voltage bias.
18.7.2 Measurement cells General advice: keep cells clean so that they do not contaminate specimens. It is important to be aware of the EM-field configuration in one’s cell in order to choose the optimum size and shape for specimens. Note, in particular, that electric fields usually pass through, that is, from face to face of, laminar specimens in ‘lumpedimpedance’ methods (see Sections 18.9.1 and 18.9.2) but, in contrast, they usually lie in the plane of the lamina in travelling- and standing-wave cells (see Sections 18.9.3, 18.9.4, 18.9.6, 18.9.9, 18.9.11 and 18.9.12). This fact can be important if the material to be characterised is anisotropic (i.e. if ε∗ is a function of electrical field direction). With the exceptions of (1) free-field measurements and (2) some resonance measurements, it is usually best to keep the measurement volume of cells as small as possible, consistent with their achieving the required resolution for ε 0005 and tan δ. Also keep connections as small and simple as possible to reduce impedance residuals and mismatches. If a cell is to be actively temperature controlled, small cell size may also be an advantage because power requirements can be lower and temperature-settling times faster. However, in some cases a contrary policy may be advantageous. Whenever a high resolution for a measured quantity such as capacitance is required, it can be an advantage to have a cell with a long thermal time-constant (a ‘massive’ cell), so that the constant temperature cycling of a temperature-control system does not compromise resolution. Cavities and resonators form a special class of measurement cells; see [8–10,41] for background theory. In general, we use resonators for measuring specimens of low-loss, and so we need to know how to reduce loss in the resonator itself and in its coupling mechanisms – this will increase the resonator Q-factor and increase its resolution for specimen loss. The benefits of resonators do not arise only in the measurement of dielectric loss – the increased resolution offered by resonator techniques also applies to real permittivity ε0005 : some of the most accurate methods for measuring ε 0005 at MW and millimetre-wave frequencies are resonator methods.
Measurement of the dielectric properties of materials 427 In resonators, we are also concerned with the measurement of Q-factor, which we consider next.
18.7.3 Q-factor and its measurement Q-factor is measured in resonance techniques to determine the loss of dielectric specimens. This is a topic that requires a book in its own right to cover – see the book by Kajfez [42] and the Good Practice Guide [1]. The term Q-factor is actually a contraction of ‘Quality Factor’ and its symbol is usually Q. It is defined in the frequency domain for resonating systems as follows: Q = 2π ×
Energy stored in the resonance Energy lost per cycle
(18.15)
In the resonators with which we are concerned here the ‘energy stored’ is the EM energy stored in the fields in the resonator, the ‘energy lost’ is the EM energy lost by whatever means from such storage and ‘per cycle’ refers to a cycle of the sinusoidal resonating EM signal at the frequency that is present in the resonator. For a typical resonator we can write 1 1 1 1 = + + + ··· (18.16a) Q Qspecimen Qresonator walls Qcoupling where Qspecimen accounts for the dielectric loss in the specimen – this is the parameter we are trying to measure, Qresonator walls accounts for the power lost in the metal walls of the resonator due to conduction losses, Qcoupling accounts for power lost through all coupling mechanisms into the resonators: note that power is lost both through output and input coupling ports. There are usually many other sources of loss in resonators, as illustrated in Figure 18.8. In a typical resonance measurement we must distinguish between the influence of the loss of the dielectric material on the Q-factor and the loss from all other causes. Our measurement technique must be designed either (1) to allow us to estimate these other sources of loss, or else (2) it must cancel them out, for example, by use of a substitution method. For our purposes (18.16a) can further be refined as follows [1]: 1 1 1 = Ff tan δ + + + ··· Ql Qresonator walls Qcoupling
(18.16b)
where tan δ is the loss tangent of the specimen and Ff is the ‘filling-factor’ of the specimen in the resonator defined as follows: Ff =
Average EM energy contained in the speciman(Ws ) Average EM energy contained in the whole resonator(Wr )
(18.17)
Ff can be seen to be another important factor which depends on the cavity and specimen dimensions and on the specimen positioning. We need to know the value of Ff in order to measure the dielectric properties of the specimen. The value of Ff can vary enormously from one technique to another. For example, Ff = 1 if the specimen completely fills the resonator but Ff can be less than 0.01 in perturbation techniques
428 Microwave measurements G F H D
B A
O
C E
H
F Input waveguide
Figure 18.8
G
Output waveguide
Power transfer and loss processes in a resonator. An open-resonator (see Section 18.9.11) is used as an example. The resonator has two small coupling apertures for input and output from waveguides (shown overscale for clarity). (A) Power coupled from the input into the resonant mode, (B) input power reflected by mismatch, (C) attenuation of input signal by the ‘cut-off’section of the input coupling aperture, (D) power coupled through the input aperture that does not enter the resonant mode, (E) power lost from the resonant mode via the input coupling aperture, (F) dissipation in the metal reflectors (conversion to heat), (G) diffraction at reflector edges, (H) scattering (diffraction) from the coupling apertures and (O) power transmitted to the output waveguide. Losses (E) to (O) load (i.e. reduce) the Q-factor of the resonant mode (After Clarke and Rosenberg [102].)
(see Section 18.9.10). Ff also affects the extent to which the resonant frequency, fr , is shifted when a specimen is placed in a resonator, and so it is also an important parameter in the measurement of real permittivity, ε0005 as well as loss. Computation of Ff requires an analytical model of the resonator, many of which can be found in the scientific literature. Q-factor is traditionally measured by the resonance-width technique, (Figure 18.9). With fully automatic detection systems such as ANAs it is often better to use curve-fitting techniques, which can take account of signal leakage in the detection system and can be more immune to noise. Signal leakage can give rise to apparently distorted resonances and so to significant measurement errors for Q-factor – the traditional technique is prone to these errors. If the ANA employed is a Vector ANA, that is, one that measures the S-parameters of the resonator as complex parameters, one should carry out a full complex-parameter fitting of the S-parameters to gain maximum benefit from the measurement technique [1,42]. One should always bear in mind that many resonators exhibit a number of resonances that may overlap in the frequency domain – they may in fact be completely degenerate (i.e. coincide in frequency). This is a condition that should be tested for and avoided or compensated for in any serious measurement.
Measurement of the dielectric properties of materials 429 Vc Vi
2
3 dB ∆f
fr (1 – 1/2Q)
Figure 18.9
18.8
fr
fr (1 + 1/2Q)
frequency
A typical resonator resonance curve, showing how the width of the curve, 0012 f , at the ‘half power’ or ‘3dB’ points can be used to measure the Q-factor by the resonance-width method: thus Q ≈ fr /0012 f , where fr is the resonant frequency. The vertical axis gives the square of the voltage excitation of the resonance, that is, it is proportional to the power in the resonance
Good practices in RF and MW dielectric measurements
It is not always possible to follow these practices in every measurement, but one can try to abide by their spirit. (1) Calibrate all significant equipment traceably to international standards. (2) Once the measurement system has been calibrated and prior to the measurements upon the specimens under test, check the calibration, either by a measurement upon a check specimen that has known dielectric properties or else by measuring a Traceable Dielectric Reference Material [29,43]. This can save considerable time and embarrassing problems if the calibration is faulty! (3) Measure a number of specimens of the same material but of different thickness (or length, diameter, and so on as appropriate for the technique) to check for systematic errors. However, when the aim of the measurements is to determine the differences in the intrinsic dielectric properties of a number of similar specimens, they should all have the same size and shape, so as to remove differences caused by systematic errors. (4) Whenever possible measure specimens across a broad frequency range to check for consistency of properties across that range. (5) All dielectric specimens should be individually identified. To prevent similar specimens from getting mixed up only one specimen at a time should be out of its container. Record the provenance of specimens. (6) Dielectric properties usually change rapidly with temperature. The temperature of dielectric measurements should always be recorded. In the case
430 Microwave measurements of ambient temperature measurements, an uncertainty of ±0.2 ◦ C or better should ideally be achieved, though this may not be possible at elevated temperatures. A relative humidity of less than 50 per cent is recommended for measurements, unless otherwise required by one’s experiment. In some cases, especially with low-loss specimens, it will be necessary to record relative humidity at the time of measurement and possibly also during the prior storage of the specimen. (7) Record all relevant information on measurements in a lab book or computer file. If doubts arise about a measurement at a later date, this may enable you to trace the cause of the problem. On the other hand, if there is nothing wrong with the measurement, the record will help you to demonstrate this fact at a later date and so provide confidence in the measurement. (8) It is good practice to generate a measurement uncertainty budget following the practices of ‘The Guide’ (GUM) [44] or of the UKAS document M3003 [45]. (9) Be Safety Conscious: always be aware that many materials are toxic or flammable. Follow COSHH guidelines [46] for handling and disposing of materials, especially liquids. Never accept a material for measurement unless you know what it is and how to handle it safely.
18.9
A survey of measurement methods
In this survey we attempt only to illustrate the wide range of methods that have been developed to meet the challenge of the wide range of material types discussed in Section 18.6. Some indication is given of the main purpose of the methods and the types of material they are best suited to, but the reader is referred to the Good Practice Guide [1] and the other references provided for more details.
18.9.1 Admittance methods in general and two- and three-terminal admittance cells If the admittance, Y , is measured between any two electrodes with and without a dielectric material of complex permittivity ε ∗ present, we have ε∗ =
(Y when the space around the electrodes is completely filled with the dielectric) (Y when it is completely filled by a vacuum) (18.18)
This equation forms the basis for a wide range of dielectric measurement techniques that are in use almost from DC up to 1 GHz – the higher the frequency the smaller is the cell that must be used. The most common methods are those based on adjustable parallel-plate electrode systems (see Figure 18.10). Liquid dielectrics will readily fill the full volume of a measurement cell, whereas solid specimens cannot do so and this gives rise to measurement errors for solids caused by electrode/specimen air-gaps and by fringing-fields. By immersing a solid specimen in a liquid of similar permittivity,
Measurement of the dielectric properties of materials 431 these disadvantages can be overcome. This principle is used in Liquid Immersion Techniques for solids – see the standards BS 7663:1993 and ASTM D1531-01 and the Guide [1]. A more common way of avoiding errors which arise with two electrodes is to use a guard electrode around the low voltage electrode – this ensures that the electric field lines through the specimen and between the measurement electrodes are parallel, which greatly simplifies the computation of the permittivity, as we have Y = jω
ε0 ε ∗ A d
(18.19)
where ω is the angular frequency = 2π f , A is the area of either of the two measurement electrodes and d is their separation, assuming that the dielectric completely fills the gap between the electrodes. Corrections to this formula can account for the small gap I in Figure 18.10, but they are usually very small. Such a cell is referred to as a three-terminal cell. Cells as shown in Figure 18.10 with only two electrodes are referred to as two-terminal cells. There are many ways of using such two- and three-terminal cells for dielectric measurements and the best for any given specimen must depend on its properties. In some cases it is better to leave a deliberate air-gap above the specimen and measure its (a)
Guard electrode
(b)
Figure 18.10
High voltage electrode
I
I
Low voltage electrode
Guard electrode
(c)
(a) A three-terminal admittance cell. ‘I ’ is a thin low-loss insulating ring (it is exaggerated in thickness for clarity in the diagram), which separates the low voltage measurement electrode from the annular guard electrode. (b) In a two-terminal cell the E-field lines fringe out around the edge of the electrodes, giving rise to a fringing-field that can pass partly through the specimen, thereby generating measurement errors. (c) In a three-terminal cell the field lines between the high and low voltage measurement electrodes are straight and the field is uniform so measurement errors caused by fringing-fields are removed
432 Microwave measurements dielectric properties by adjusting the gap d with and without the specimen to produce the same capacitance across the cell in both cases. For some materials (especially those of high permittivity) it is better to metallise the specimen. Please see [1] for details. These cells are usually used at LF and RF frequencies in conjunction with admittance or impedance analysers or FRAs, (see Section 18.7). They can be employed over many decades of frequency for dielectric measurements. Two-terminal admittance cells come into their own at higher RF where it is difficult to keep the guard ring in the three-terminal technique at ground potential. Traditionally their uncertainty of measurement has been much lower than that of three-terminal cells (often worse than ±5 per cent for ε0005 ) because of the presence of fringing fields around the electrodes, as in Figure 18.10, the effect of which was difficult to calculate. However with the advent of EM-field modelling packages such as finite difference time domain (FDTD) or finite integration (FI), modern software can correct for the fringing-field errors, if one so desires.
18.9.2 Resonant admittance cells and their derivatives Two-terminal techniques came into use many years ago when interest in measuring dielectrics in the 100 kHz to 100 MHz range first arose. A resonant two-terminal cell method was very widely used for many years from the 1930s onwards [47], and was named the Hartshorn and Ward (H & W) Technique, after the two NPL scientists who developed the method. It was used both for medium and low-loss specimens until the advent of sensitive impedance analysers in the 1970s, which were found to be more convenient and accurate for medium-loss specimens. However, the method may still be used to advantage for low-loss specimens. The principle of the method is to resonate a micrometer-driven admittance cell with an inductor, as shown in Figure 18.4. One commonly measures the permittivity by adjusting the gap between the electrodes with and without the specimen so as to resonate the system at the same frequency in both cases – this approach is often called an ‘equivalent-thickness method’. Loss is computed from the change of Q-factor. A given specimen can be measured at a range of frequencies by using a number of inductance coils. The H & W cell is the lowest frequency member of a family of resonance cells that can be employed all the way up through the spectrum into the microwave region (see Figure 18.11). They have in common the feature that the E-field passes directly through the specimen from bottom to top, as shown in the figure, so for cylindrical specimens, they are sensitive √ to ε ∗ in a direction parallel to the axis of the cylinder. In such a resonator fr ≈ 1/ LC so the resonant frequency of measurement cells in this family can be increased either by reducing L or by reducing C, or both. One can reduce L by abandoning the coil inductors of the H & W method (Figure 18.11a) and by effectively ‘wrapping’ the inductance L around the capacitor, as shown in Figure 18.11b. This configuration gives one a re-entrant cavity or hybrid cavity. Such cavities can be used conveniently in the frequency range 100 MHz to 1 GHz. To resonate at even higher frequencies one can effectively reduce C by using a thicker and narrower specimen. One ends up with the TM010 –mode (or TM020 –mode)
Measurement of the dielectric properties of materials 433
L
L E
E
(a)
Figure 18.11
L
C
E
C
C
(b)
(c)
A family of dielectric measurement resonators. (a) The principle of the Hartshorn and Ward method: the admittance cell is resonated with an inductor. (b) The re-entrant cavity is a coaxial cavity with a capacitance gap in its inner-conductor where the dielectric specimen is placed. The inductance L is that of the magnetic field in the region between the inner- and outer-conductors. (c) The TM010 -mode cavity can, in principle, be seen as a re-entrant cavity that has its innerconductor fully retracted so that only a cylindrical cavity remains. This reduces the capacitance, C, of the specimen, which in the TM010 cavity typically takes the form of a rod, as shown
cylindrical cavity shown in Figure 18.11c. Such cavities typically operate in the range 1–10 GHz. Re-entrant cavities should always be considered as an option for low-loss materials in the range 100 MHz to 1 GHz as other forms of cavity (see below) are physically large in this frequency range. Details of measurement methods are described in International Standard IEC 60377-2, ‘Part 2: Resonance Methods’ and in [48]. The TM010 –mode cavity (Figure 18.11c) is the next in our family of resonators (see also Figure 18.12a), typically used from 1 to 10 GHz. The last subscript ‘0’ in TM010 indicates that the strength of the E- and H-fields does not change as one moves from top to bottom along the axis of the cavity. The axial E-field is at a maximum on the axis of the cavity and falls away to zero amplitude on the cylindrical sidewall, as required by the electrical boundary conditions there. As in the re-entrant cavity, the magnetic or H-fields loop around the axis of the resonator and so the coupling arrangements are similar. Specimens normally take the form either of rods [49] or else tubes, which can be used for containing liquid dielectrics [50,51]. Specimens commonly reach from top to bottom of the cavity, but this is not necessary [5]. Traditionally [52,53] this method was used as a perturbation method; (see Section 18.9.11.) If perturbation computations are used, the diameter of the specimen must be small compared with that of the resonator. However, more recently, advantage has been taken of the relatively simple internal geometry of the TM010 -mode cavity to employ modal analysis to derive exact equations for the cavity [54]. With such an analysis the diameter of the specimen need not be restricted. Similar advantages
434 Microwave measurements (a)
(b) Electric field Zero surface current ring Thin dielectric rod specimen
Input Coupling loop
H
Output Magnetic field
Specimen H r
TM010 E Resonant frequency determined by diameter
Figure 18.12
r
(a) A TM010 -mode cavity resonator containing a dielectric rod specimen, which in this case is introduced though two small holes (not shown to scale) on the axis of the resonator. (b) A TM020 -mode cavity resonator, showing the position of the circle on the top of the resonator where there are no surface currents, this is the best place to make a break in the surface if a lid is needed (After [5].)
accrue if discretised FDTD or FI modelling packages are used for the modelling – such packages are available commercially. One disadvantage of the TM010 -mode cavity arises if its lid has to be removed to insert a specimen. Currents in the top of the cavity have to cross the gap between the lid and the rest of the cavity. Thus, whenever a lid is removed in order to introduce/remove the specimen, contact impedances can change, introducing measurement errors for tan δ. With the TM010 -mode it is impossible to find any points or lines in the walls or the top or bottom of the cavity where currents do not flow (except the two points on the axis of the cavity). Fortunately this problem can be avoided by using the TM020 mode rather than the TM010 -mode, as explained in Figure 18.12b. Both cavities are relatively easy to use, especially if employed with the perturbation method [5,53].
18.9.3 TE01 -mode cavities The TE01 -mode cavity [55,56] (see Figure 18.13), is used for measurements on laminar low-loss specimens, typically in the 8–40 GHz range. These resonators have a high resolution for low-losses and they are typically used for measuring cylindrical disc specimens that notionally have the same diameter as the resonator. The electric fields in the resonator are circularly or (‘azimuthally’) polarised with respect to the resonator (z-) axis, as in dielectric resonators (see Section 18.9.8). Tuning can be achieved easily, as shown in the figure, by changing the resonance length of the cavity with a micrometer-driven metal piston. Typically, the cylindrical dielectric specimen
Measurement of the dielectric properties of materials 435 Small coupling apertures to waveguide
Resonant frequency determined by length Piston for tuning
Helical waveguide
E Dielectric (disc) specimen Lagging or temperature control
Micrometer
Figure 18.13
A micrometer-tuned TE01 -mode cavity for dielectric measurements
sits on the piston during measurements. As the electric field must fall to zero on the outer wall of the resonator, the specimen itself need not be an exact fit to the diameter of the cavity. Typically the specimen can be up to 0.5 mm smaller in diameter in a 50 mm diameter cavity without having a significant effect on the measurement accuracy. The technique can be used across a range of temperatures [57]. One potential problem with the TE01 -mode in a circular cylinder is that it is always degenerated with (i.e. it always resonates at the same frequency as) the TM11 -mode, so a method must be found for filtering out the latter. One of the most effective methods was implemented at NPL in the 1970s [55,58], when the cylinder of the cavity was manufactured from helical waveguide to remove axial currents in the walls, which are necessary for the TM11 -mode to resonate. Coupling into the cavity is typically from waveguide via small coupling holes, as shown in Figure 18.13, delivering a high insertion loss of the cavity on resonance. As in many resonant techniques ε0005 can be measured by a length-change/equivalentthickness method. Q-factors may be as high as 60,000 at 10 GHz for the mode with nine half-wavelengths along the cavity in a 50 mm diameter cell. As in many standing wave techniques (e.g. also in open resonators, Section 18.9.11) specimens should ideally be an integral number of half guide-wavelengths thick, both because this renders the measurements insensitive to surface contamination on the specimen (both
436 Microwave measurements surfaces are at a field node) and because it can be shown that this is the condition that gives best uncertainties. Experience over many years with such a cavity operating at 10 GHz shows that resolutions for loss angles may be as low as 10µ rad, while uncertainties for ε 0005 < 5 can be as low as ±0.5 per cent for ‘ideal’ specimens (i.e. for flat homogeneous low-loss specimens that are an integral number of half-wavelengths thick).
18.9.4 Split-post dielectric resonators The split-post dielectric resonator (SPDR) (Figure 18.14) was developed by Krupka and his collaborators [59] and is one of the easiest and most convenient techniques to use for measuring microwave dielectric properties. It uses a fixed-geometry resonant measurement cell for characterising low- or medium-loss laminar specimens (such as substrates and thin films) in the frequency range 1–36 GHz. The main drawback with this technique is that each SPDR can only operate at a single fixed frequency, but it is practicable and cost-effective to measure the same specimen in several SPDRs operating at different frequencies. The SPDR uses two identical dielectric resonators of the usual cylindrical disc or ‘puck’ shape. They are placed coaxially along the resonator axis leaving a small laminar gap between them into which the specimen is placed for measurement. Once the SPDR is fully characterised, only three parameters need to be measured to determine the complex permittivity of the specimen: its thickness and the changes in resonant frequency, 0012 f , and in the Q-factor, 0012Q, obtained when it is placed in the resonator. Specimens are typically a millimetre or so in thickness, but the method is also suitable for thin films. The resolution for thin specimens can be improved by stacking a number of them in the gap. The two dielectric pucks resonate together in a coupled resonance in the TE01δ mode, and so a circularly polarised evanescent E-field exists in the gap region between z
Dielectric resonators
Support
C
C
Specimen under test
Figure 18.14
Metal enclosure
A Split-Post Dielectric Resonator (SPDR) cell for dielectric measurements. Transmission coupling is via both dielectric resonators, ‘C’ marks the coupling loops
Measurement of the dielectric properties of materials 437 them. The geometry of the system is such that simple analytical models cannot be used to relate ε ∗ to 0012 f and 0012Q, so numerical solutions must be employed. The geometry of the SPDR lends itself to modelling by mode-matching or Finite Difference (FD) techniques. The main limitation of the SPDR technique is that its resolution for very lowlosses is reduced by the Q-factors of the two dielectric resonators it employs, but it can typically be used to measure loss angles down to 100 µrad with reasonable accuracy. Typical uncertainties can be ±1 per cent for ε0005 up to 10 and ±5 per cent for tan δ. A conference paper [60] gives details of studies that show that measurements on reference specimens in SPDRs agree well with those carried out by other wellestablished methods.
18.9.5 Substrate methods, including ring resonators Substrate and printed-circuit manufacturers need to know the dielectric properties of their substrates. Special techniques have been developed to enable them to measure these properties with the facilities commonly at their disposal. Most notable among these are facilities for depositing metal resonant structures lithographically onto substrate surfaces. Such structures include ring [61,62], T-shaped [63] and strip-line [64] resonators, all of which may be used to measure dielectric properties at a number of harmonically related frequencies across a wide band. The main advantage of this approach is that it gives designers of integrated circuits precisely the information that they need: an effective value for permittivity, εe0005 , that is appropriate for their applications. This is not necessarily the absolutely ‘true’ value of ε0005 for the substrate material because, like all measurements, these measurements are subject to systematic errors. However, if one is using a strip-line technique to determine a parameter, εe0005 , subsequently to be used for designing similar strip-line circuits, some degree of beneficial compensation of errors must occur. Problems can arise here if one is interested in measuring loss. High-temperature processes used in manufacture can cause deposited metal to in-diffuse into a substrate, so measured properties may differ from those of pure bulk material. The loss tangent of low- and medium-loss substrate materials is generally not measurable by these techniques because radiative and conductivity losses (surface and bulk) in the deposited metal structure tend to dominate: in practice the measured Q-factors can be below 100 even for low-loss materials.
18.9.6 Coaxial and waveguide transmission lines This method makes use of annular specimens, which should fit closely between the inner- and outer-conductors of the coaxial conductors of precision coaxial airline, as shown in Figure 18.3. The air-line should ideally be fitted with precision connectors that allow for a well-matched coaxial connection to an ANA. The complex permittivity and permeability of specimens are computed from the S-parameters of the specimen, as measured by the ANA. Similar techniques apply with other types of uniform air-line – the use of rectangular waveguide for such measurements is very common.
438 Microwave measurements The first of such methods was the Roberts and Von Hippel method [65] – in which the specimen is placed hard up against a short-circuit and its reflection coefficient is measured. Such one-port techniques may still be recommended in many instances (e.g. for high-temperature measurements) but there are two advantages to be gained from measuring both reflection from and transmission through specimens in a matched transmission-line. (1) For purely dielectric specimens up to 10 mm in length, one often finds that reflection coefficient measurements tend to be more accurate at lower frequencies (<500 MHz), while transmission measurements tend to be more accurate at higher MW frequencies. The combination therefore allows broadband measurements to be performed on just one specimen from, say, 100 MHz to 18 GHz in a 7 mm diameter air-line, taking advantage of the best uncertainties from both methods. (2) As explained in Section 18.3, the measurement of both transmission and reflection coefficients allows one to determine the magnetic properties of the specimen as well as its dielectric properties. For magnetic materials, both transmission and reflection data are normally required, though reflection-only data can be used if the specimen is moved axially in the line. Inevitably, for solid specimens metrological problems arise from the presence of air-gaps between the specimen and the inner- and outer-conductors of the line. They dilute the apparent permittivity obtained from the measurement but, more seriously for accurate measurements, they also help to launch higher-order modes. Both effects give rise to significant measurement errors. Air-gap problems do not usually arise for liquid measurements, but a well-designed liquid cell is required instead. The liquid must be contained between solid dielectric windows, as shown in Figure 18.15, so a multi-layer theory based on cascaded two-ports is necessary for the S-parameter analysis of the specimen/cell combination. Liquid specimen
To ANA Port 1
To ANA Port 2
Windows
Figure 18.15
A coaxial line cell for measuring liquid dielectrics
These transmission-line methods are often the most cost-effective choice for (1) broadband measurements, (2) magnetic materials, (3) medium- to high-loss materials and (4) materials that are only available in small volumes. Uncertainties for ε 0005 can be as low as ±1 per cent for low-permittivity materials if a correction for air-gaps is made but it may be higher than ±5 per cent for high permittivity materials, so use of other methods is advisable if more accurate measurements are needed.
Measurement of the dielectric properties of materials 439 NIST Technical Note 1341 [66] provides an excellent guide to the theory of this method as does the NIST follow-up work by Baker-Jarvis and his colleagues [67,68]. The paper by Jenkins et al. [43] explains how uncertainties can be computed in these measurements. It is concerned with dielectric liquid measurements but with the exception of the uncertainties caused by air-gaps, the analysis can be extended to solids. The NIST Technical Note provides the formulae that correct for air-gaps, based on a simple capacitative model. There are two published standard methods for the transmission-line technique: ASTM D5568-01 and a UTE (Union Technique de L’Electricité) standard from France [69]. The paper by Vanzura et al. [68] illustrates just how dominant the resonances of higher-order modes can be at higher frequencies. It shows that it is not advisable to use this method at frequencies above these resonances. Most of the considerations discussed for coaxial transmission lines apply also to waveguide measurements. The main advantage of using a waveguide is that one does not have to machine axial holes through the specimen to tight tolerances to allow it to be fitted onto a coaxial inner-conductor. The absence of the inner-conductor also makes waveguide cells more suitable for temperature control. The main disadvantage of waveguide is that one is normally restricted in frequency coverage to a single waveguide band (less than an octave in frequency coverage). Please see [1] and [66] for more details of measurements in both types of line.
18.9.7 Coaxial probes, waveguide and other dielectric probes Coaxial probes [43,70–76] (see Figure 18.16) are extremely popular measurement tools. The principle of operation of the conventional flat-faced probe is illustrated in Figure 18.16. A TEM travelling-wave propagates in the coaxial line up to its end where it launches fringing EM-fields from the open end of the probe into the dielectric specimen. Their magnitude and geometry depends on the complex permittivity, ε∗ , of the dielectric, so the reflection coefficient of the TEM-wave from the end of the probe will depend on the value of ε∗ . One can relate the measured reflection coefficient, , to ε ∗ by using (1) a modal analysis of the fields in the coaxial line and (2) an analysis of the fields in the dielectric under test (DUT) that treats the probe as an antenna. Simpler analyses have been used, especially those based on capacitative models for the fringing-fields, but they have their limitations [70]: at sufficiently high frequencies the probe must be treated as an antenna as it actually radiates into the dielectric specimen so that | | < 1.0 even if the dielectric is lossless [43]. Flat-faced coaxial probes, such as the one shown in Figure 18.16, represent just one member of a whole family of reflectometric and non-invasive probe designs that can be used for dielectric measurements. Another flat-faced probe option is the open-ended waveguide probe [77–79]. This type of probe has the capacity to measure anisotropic materials [80]. Coaxial probes are widely used for characterising lossy solids like biological tissues because of their ability to perform measurements by contacting just one face of the specimen, rather than having to machine the specimen to fit into a measurement cell. This makes them very convenient to use. They are also ideal for measuring lossy liquids and are widely used for SAR liquid characterisation;
440 Microwave measurements Flange Coaxial line
Figure 18.16
Dielectric specimen
A coaxial probe, showing the fringing-fields that emerge from its ends. The field lines shown are those of the electric field, which is seen to fringe out into the dielectric specimen at the end of the probe
see British Standard BS EN 50361:2001, and IEEE Standard P1528 (D1.2). But with liquids one does not need to use a flat-faced probe and there are often advantages to be gained by using other geometries (see below). A single flat-faced coaxial probe can typically operate effectively over a frequency range of about 30:1 (e.g. 100 MHz to 3 GHz for a 15 mm diameter probe) whilst retaining a reasonable uncertainty performance of the order of ±4 per cent for ε 0005 for suitable materials. The actual frequency range depends on the diameter of the coaxial aperture of the probe and the permittivity of the dielectric specimen. The coaxial probe method has its limitations. Measurement uncertainties are usually of the order of ±3 per cent at best for ε0005 and ε 00050005 and a number of other techniques described in this survey can be more accurate (e.g. coaxial cells for liquids; Section 18.9.6). There are many types of measurement for which the probe would be the wrong choice. Thus, the assumption is commonly made in the theory that is used to relate ε ∗ to , that there are reflections of waves neither from the extremities of the specimen nor from permittivity steps or gradients within inhomogeneous specimens. In small, layered or low-loss specimens this is usually not the case. Furthermore coaxial probes are much better suited to measuring malleable materials (or liquids) that accommodate themselves to the shape of the probe than to hard specimens because they invariably leave uneven air-gaps between the specimen face and the probe face. The conventional theory assumes that there are no such air-gaps, and as the probe is particularly sensitive to the permittivity of the material closest to its face, even a small gap can give rise to a large error of measurement [81]. Layered structures and air-gaps can be modelled [73,74], however, see Figure 18.17, if the thickness of the layers is known, and the utility of the probe extended thereby. The measurement geometry of coaxial and waveguide probes, even for complex geometries similar to those shown in Figure 18.17, can be analytically calculable. An alternative approach that widens the range of probe designs and their range of application is to reduce one’s dependence on full calculability and to rely more on probe calibration with a set of known reference liquids to supply the accuracy that the theory lacks. Thus, one may prefer to use a probe without a flange (e.g. [75]) – it
Measurement of the dielectric properties of materials 441 (a)
(b)
Laminar dielectric specimen Conducting plane
Figure 18.17
etc.
ε1, t1 ε2, t2 ε3, t3
Use of a coaxial probe (a) for measuring a dielectric lamina backed by a metal conducting plane, (b) for measuring a multi-layered specimen. Each layer, i, has thickness ti and permittivity εi
is smaller and more convenient than a calculable probe with a (supposedly infinite) flange. One can regard probes having other non-calculable shapes as ‘black boxes’: whenever they have the property of being reasonably stable and of presenting one with a one-to-one and smoothly varying relationship between and ε∗ they can be effective. By measuring a suitably large number of reference liquids having known ε ∗ values, one can interpolate measured values of to calculate ε∗ for other dielectrics. Probes that are used in this way may be called non-calculable probes (e.g. [82]). Some of these probe designs can have much better field penetration into the specimen than coaxial probes [83,84]. Dielectric probes are normally used in conjunction with ANAs, so suitable calibration schemes must be developed for the ANA/probe combination. Typically for a coaxial probe one calibrates with (1) an open-circuit into air, (2) a short-circuit and (3) a measurement of a known reference liquid (e.g. [29]). Great care must be taken, particularly with the short-circuit, where one has to make a good electrical contact to the inner-conductor, and also with the reference liquid, which can easily change temperature by evaporation or absorb contaminants from the atmosphere, for example, water vapour. Both temperature change and contamination can easily lead to the dielectric properties of the liquid not being close to those assumed by the calibration software, and so they can result in significant calibration errors. Given such calibration difficulties it is always good practice to measure a second dielectric reference liquid immediately after a calibration to check calibration validity. It is not uncommon for calibrations to have to be repeated a number of times until a good calibration is obtained. This can be very time consuming. One approach that has been developed to overcome this problem is to use a least-squares calibration technique [1]. Least-squares calibration has another advantage as well: it enables some of the errors and uncertainties of the measurement to be estimated statistically. For liquid specimens it is often better to extend the outer-conductor of the probe to form a cell – see Figure 18.18 [43]. Extension of the inner-conductor as well, as in Figure 18.18b increases the capacitance of the cell and so makes it more sensitive at lower frequencies. The liquid can be poured in until its meniscus is sufficiently far away from the end of the inner-conductor for no change in reflection coefficient to be detected if more liquid is poured in.
442 Microwave measurements (a)
(b)
Semi-infinite circular waveguide section
Liquid specimen
Coaxial section
Measurement and calibration plane
Semi-infinite circular waveguide section
Liquid specimen Measurement and calibration plane
Bead Bead
Figure 18.18
Liquid Cells. (a) A modification of the coaxial probe shown in Figure 18.16 to allow easy measurement of liquids. (b) The Discontinuous Inner-Conductor Cell: a further modification that can be used to increase the measured capacitance of the dielectric liquid. For a given liquid, geometry (b) will be more sensitive at lower frequencies than (a). The inner-conductor extension is of any appropriate length. Both cells are fully calculable
Open-ended rectangular waveguide probes [77–79] are used less often than coaxial probes, partly because, like all waveguide-based systems, they are limited in frequency range and they may be physically quite large. However, the required probe size for a given frequency range can be reduced if the probe waveguide is itself filled with a ‘loading’ dielectric material. Reference [80] describes one such probe, based on a WG16 (normally 8.2–12.4 GHz) waveguide adaptor, which was loaded with glass dielectric (ε0005 ≈ 6) to allow it to operate in the range 3.5–5 GHz. Waveguide probes offer two potential advantages [80] over coaxial probes for specific applications. One is the fact that such probes are better matched for measuring lower permittivity than coaxial probes of similar size and at a similar frequency. The other perhaps more important advantage is that waveguide probes, being linearly polarised, can measure anisotropy in dielectrics [80].
18.9.8 Dielectric resonators Dielectric resonators (DRs) are widely used in electronics and telecommunications applications as high-Q components for narrow-band filters. The theory of their resonances is well developed [85]. The resonators typically take the form of ‘puck’-shaped cylinders of dielectric material. They can retain the EM-fields that are resonating inside them because the fields are totally internally reflected from the interior of the dielectric surfaces. A formal analysis of the fields reveals that there are also EM evanescent fields in the air (or other dielectric medium) that surrounds the resonator and that these fields decay exponentially in magnitude as one moves away from the resonator. It is the presence of these fields that allows one to couple RF and MW power into the DR, typically via coupling loops at the end of coaxial line feeds. However, these fields also interact with other objects in the vicinity of the resonator (e.g. its support or its container) and if these nearby objects are lossy the resonance
Measurement of the dielectric properties of materials 443 (a)
To micrometer drive
(b) Cavity lid
Flat copper plates
C
Dielectric resonator
Figure 18.19
C
C
Cavity Quartz support
Dielectric resonator
C
Quartz support
Dielectric resonator cells. (a) A Hakki-Coleman Cell, otherwise known as the Courtney Holder or the Parallel Plate Cell, and (b) a Cavity Cell. In both diagrams ‘C’ marks the coupling loops.
becomes loaded and the Q-factor falls, giving rise to errors if one is measuring the loss of the resonator. Figure 18.19 shows the coupling geometry for two configurations commonly used in dielectric metrology. Typical resonator sizes range from tens of centimetres on a side in 900 MHz cell-phone base-station applications, down to a centimetre on a side or less at around 10 GHz. The frequency depends on the size and the permittivity of the resonator. Dielectric measurements on ‘puck’-shaped specimens offer one of the most accurate and sensitive methods available to us for measuring the permittivity and loss of low-loss dielectric materials. They have a major advantage over other resonant techniques for characterising low-loss materials: the attainable filling-factors, Ff (see Section 18.7), in this technique are normally close to unity because most of the energy in the resonance is contained in the dielectric itself. Measurements are usually performed using the TE01δ -mode in which the E-field is azimuthally circularly polarised, but higher-order ‘whispering-gallery modes’ have also been used to obtain dielectric data at much higher frequencies [86,87]. When viewed on an ANA or spectrum analyser, one can see that DRs resonate in many different modes. One of the main preliminary steps to be undertaken before measurement, therefore, is to identify the TE01δ mode. TE01δ -mode resonators must be used in a container or cell, otherwise their Q-factors are loaded by radiative losses. The two types of cell most commonly employed in dielectric metrology are shown in Figure 18.19 and they are designed to prevent this. In the Courtney Holder or Hakki–Colemen Cell of Figure 18.19a the distance between the top and bottom plates must be less than λ/2 in air if this radiation loss is to be avoided. (NB. radiation loss is not so important for whispering-gallery modes). The Cavity Cell of Figure 18.19b prevents radiation escaping by completely enclosing the specimen with metal walls. These walls should be well separated, ideally by at least one specimen diameter, from the specimen to minimise losses from currents flowing in them. For the same reason, the specimen is normally placed on a small post or tube made from low-loss dielectric (e.g. quartz) to displace it away from the base of the cavity. Cells are often made
444 Microwave measurements from copper because its high conductivity reduces the metal losses in the walls. See Reference [1] for the relative advantages and disadvantages of the two types of cell in Figure 18.19. There may be two reasons why we may wish to perform DR dielectric measurements. First, we may wish to know the intrinsic dielectric properties of the DR specimen material: its real permittivity, ε 0005 , and loss tangent, tan δ, or we may ultimately wish to evaluate it as a dielectric resonator, for example, as a component of a filter in an electronic circuit. In the latter case we will want to measure its extrinsic parameters: its resonant frequency, Q-factor and its temperature coefficient of resonant frequency (TCRF). Similar measurement configurations can be used for either type of measurement, but extra analysis is required for intrinsic measurements. The TCRF is one of the most important factors in practical applications: one normally wishes it to be as close to zero as possible. Examples of the recent use of DRs for dielectric measurements can be found in the literature [88] and they demonstrate the versatility of the technique. Use of dielectric resonators for dielectric measurements is also described in some International Standards, for example, IEC 61338, Sections 18.1–18.3 and IEC 60377-2, Part 2.
18.9.9 Free-field methods Figure 18.20 shows three typical geometries employed for free-field measurements on dielectrics. These methods are best suited for materials that are intended for enduses in the free-field, as they are likely to be the only materials available in large enough cross sections to allow free-field methods to be effective. Typical materials are RAM – high-loss materials used for absorbing free-field waves – and Radome materials – typically low-loss materials used for protecting antennas from the elements (rain, wind, snow, etc.). Free-field methods may be categorised by three contrasting pairings of practical approaches to measurement: (1) Transmission or Reflection methods; (2) Intrinsic or Extrinsic methods. Intrinsic measurements determine the intrinsic dielectric and magnetic properties of the specimen, that is, ε∗ and µ∗ while Extrinsic measurements measure extrinsic parameters like reflectivity or scattering from materials and transmission through materials; (3) Focused (Quasi-Optical)-Beam or Unfocused-Beam Methods. Free microwave fields are typically launched as diverging beams from antennas, as in the unfocused measurement systems of Figure 18.20. The inevitable diffraction around the edges of antennas and specimens in these methods limits their accuracy. In focused-beam or quasi-optical methods, see Figure 18.21, lenses or concave mirrors are used to prevent the divergence of the beam. An attempt may also be made to ensure that it is fully calculable in its geometry. Such beams can be launched from corrugatedhorn antennas [89,90] as Gaussian Beams (GBs) [3,91,92]. They are potentially fully calculable all along their length, they decay exponentially to insignificant amplitudes as one moves away from their axis of propagation and they can be focused by concave mirrors or bloomed lenses [92]. Thus, diffraction problems may potentially be made negligible.
Measurement of the dielectric properties of materials 445 (a)
(b)
(c) Specimen
Input horn
Specimen
Figure 18.20
Output horn
Input horn
0001 Output horn
Horn
Free-field methods: (a) normal transmission through a specimen between two horn antennas, (b) normal reflection from a specimen and (c) measurement of transmission as a function of the angle of incidence, see text Waist of beam
Launch antenna
Gaussian beam
Receive antenna Lenses
Figure 18.21
A focused free-field measurement system. The specimen is placed at the waist of the beam. If corrugated-horn antennas are used, then the beam can be launched as a calculable Gaussian Beam
End-users of free-field materials such as RAM and radome laminates are often more interested in their extrinsic parameters, such as reflection or transmission coefficient, than the intrinsic parameters ε ∗ and µ∗ . Intrinsic measurements are required, however, for design and optimisation purposes. The actual measurement set-ups needed to implement these two approaches may be very similar, but extrinsic measurements ought ideally to be performed in a geometry that approximates to that of the end use of the material. For example, if the reflectivity of RAM at a 45◦ angle of incidence is required, then extrinsic measurements of reflectivity should be performed at this angle, whereas intrinsic measurements can be performed by any suitable method and the reflectivity at 45◦ incidence can subsequently be computed from Fresnel’s equations [10,19]. Free-field travelling-wave methods have much in common with guided travellingwave methods in that ε0005 is generally determined from the phase change of the transmission coefficient and dielectric loss from the attenuation of the beam on insertion of the specimen. The method of time domain gating [38] is particularly useful for improving the accuracy of free-field measurements (especially unfocused measurements) as it allows the wanted signals from the dielectric specimen to be separated from spurious reflections originating from elsewhere in the measurement system and from elsewhere in one’s laboratory!
446 Microwave measurements There are many approaches to unfocused free-field measurement, they range from the The Arch Method for RAM at arbitrary angles [93,94], to normal incidence methods [95,96], to Brewster angle methods [97] and to measurement of transmission as a function of the angle of incidence [98]. Focused or quasi-optical methods usually use travelling GB waves [91]. Complete measurement systems for laminar specimens are constructed either with lenses [99] or mirrors [94] for focusing – the latter generally give better performance.
18.9.10 The resonator perturbation technique High-Q cavity resonators are very sensitive measurement devices and this makes it possible to measure very small dielectric specimens inside them. If a sufficiently small specimen is inserted into a resonator and if no other changes are made to the measurement geometry, the resonant frequency fr and Q-factor, Q, of the resonator will both change by a small amount: 0012 fr and 0012Q, respectively. If both 0012 fr /fr and 0012Q/Q are small (typically less than 5 per cent) and the volume of the specimen is small compared with the volume of the resonator, first-order perturbation theory may be used to calculate the permittivity, ε0005 , and the loss tangent, tan δ, of the specimen. Such measurement techniques are referred to as Resonator (or Cavity) Perturbation Techniques [41]. One example of this approach is the application of perturbation theory to measurements in TM010 or TM020 -mode cavities when they are used with narrow rod specimens as described in Section 18.9.2. A number of advantages can accrue from using such a perturbation technique: (1) The measurement theory is much simpler: ε 0005 is usually proportional to 0012 fr and tan δ to 0012Q. (2) Even high-loss materials may be measured, if the specimens are sufficiently small, and if 0012Q/Q is also small. In fact, perturbation methods are normally the only resonator methods commonly used for measuring high-loss materials. (3) By placing small specimens in a cavity at points where the direction of the E- and/or H-fields are well defined, the anisotropy of permittivity, ε ∗ , and of permeability, µ∗ , can be measured. The perturbation method has been in use at least since the 1940s [52,53], but Waldron later extended and popularised it in the 1960s. His book [41] still provides one of the best guides to its application, both for permittivity and permeability measurement. There are a number of more recent applications described in the scientific literature, however, for example [100,101].
18.9.11 Open-resonators Open-resonators are millimetre-wave Fabry–Perot interferometers [102,103]. They provide one of the most accurate methods for low-loss dielectrics at millimetre-wave frequencies. Achievable uncertainties can be as low as ±0.2 per cent for ε 0005 below 3 and better than ±1 per cent for ε0005 ≈ 50. Uncertainties better than ±10 per cent for tan δ are also possible for specimens with loss angle above 200 µrad, while resolutions for loss down to 20 µrad or less are possible if the unloaded Q-factor of the resonator is greater than 150,000. A typical open-resonator configuration for dielectric measurement is shown in Figure 18.22. Typical sources of loss in an openresonator are shown in Figure 18.8, Section 18.7. An advantage of open resonators
Measurement of the dielectric properties of materials 447 Input
Output Waveguide coupling
Concave
mirror Coupling apertures
Beam diameter
Dielectric
Specimen
Plane mirror
Waist of beam Mirror position micrometer driven
Micrometer
Figure 18.22
An open-resonator geometry that can be used for characterising dielectrics at millimetre-wave frequencies
over most microwave cavities (e.g. TE01 , TM01n and TE01δ ) is that the resonant mode employed in these measurements is the fundamental transverse electromagnetic (TEM) mode which is linearly polarised – thus enabling specimen anisotropy to be measured [104]. The resonant mode used in the open-resonator is the fundamental TEM00n GB mode [91] and the high Q-factor resonance itself acts as a filter that ensures that this GB mode can be very pure. The cross-sectional shape and size of specimens for open-resonators is not important provided they are large enough to encompass the whole cross section of the GB at its waist, where it is narrowest. Specimens are flat laminas, their required minimum diameters depend on frequency. The following are typical: at 10 GHz typically 200 mm diameter, at 36 GHz 50 mm and at 72 GHz 35 mm diameter. The best practice is to compute the radius, w0 , of the GB at its waist and then use a specimen diameter of at least 5 × w0 . To achieve lower measurement uncertainties, specimens should be an integral number of half-wavelengths thick. Though they are potentially very accurate, open-resonator measurements are prone to many errors that have to be checked for and so measurements can be quite
448 Microwave measurements time consuming. Significant sources of error include mode coincidence, warped specimens and gaps between specimens and mirrors. Errors in estimated loss can also occur if the specimen is anisotropic but is not known to be so. The errors and how to avoid them are described in detail in the Good Practice Guide [1]. The use of open-resonators for dielectric measurements has been described in great detail in a number of reviews, scientific papers and books [102,103,105,106], and the reader is referred to these sources for full details of methods and measurement theory. The microwave open-resonator technique came into its own for low-loss millimetre-wave measurements in the 1970s and it has been continuously developed since then. Work at NPL in the early 1990s addressed the measurement of mediumloss specimens and investigated new techniques for measuring specimen loss [107], while studies down to cryogenic temperatures in Germany [108] have much improved the resolution for loss by increasing resonator Q-factor through better coupling methods.
18.9.12 Time domain techniques Time domain reflectometry (TDR) using pulse or step generators and sampling methods for detection, see Figure 18.23, was introduced in the second half of the twentieth Century [109] for dielectric measurements and is still widely used [110,111]. It is convenient to use for the purposes of scientific study, being a cost-effective broadband method which requires only small specimens, making temperature-control relatively easy. Solid specimens typically fit into a 7 mm coaxial line. The main limitation of the method is its absolute accuracy, which is not generally as good as that of reflectometry based on a calibrated ANA. The main reason for the continued popularity of TD methods using pulse/step generators is that they are cheaper than fully automated ANA measurements, and they are often more convenient to use. These days it is possible to employ synthesised time domain techniques [38] because it is a feature available in ANAs. In both ANAs and conventional TDR systems time domain gating or de-embedding can be used to improve the accuracy of dielectric measurements: for example, by removing the effects of unwanted reflections in a cell by gating them out in the time domain. Reflected signal Specimen Pulse generator
Sampling head Matched transmission line
Data processing Sampling oscilloscope
Figure 18.23
Block diagram of a typical time domain reflectometer
Measurement of the dielectric properties of materials 449
18.10 How should one choose the best measurement technique? Answers to this question are covered in some detail in the Good Practice Guide [1] in the light of the policy (Section 18.6) that one should ideally match the method to the material. A checklist taken from the Guide demonstrates just how many parameters and issues one has to take into account: • • • • • • • • • • • • • • •
The frequency range of interest. The dielectric loss (high, medium or low) and expected permittivity range. The type of material, for example, hard, malleable or soft solids, volatile or viscous liquids. Specimen machining imperfections and tolerances and their influence on uncertainty. Specimen shape and size and their influence on measurement uncertainty. Specimen anisotropy and homogeneity and their influence on measurement uncertainty. Inhomogeneity and the presence of surface layers on specimens. The possibility that the specimen may be made from a magnetic and anisotropic material. The required uncertainties. What level of uncertainty can be achieved by available methods? The specimen composition (e.g. does the specimen have a laminated structure). The availability of suitable methods for machining and grinding specimens. The presence of surface inclusions and pores, surface conditions in solid specimens. Toxicity, contamination and evaporation of liquid specimens. The cost of machining specimens and performing measurements: costeffectiveness. The time taken to perform the measurements – labour-intensiveness and the labour cost of measurements.
It is generally unlikely that one will have a completely free choice of method: more typically one will be asking questions like (1) how best can I press into service the facilities that I already have to perform the required measurement as accurately as possible? (2) Which techniques are best suited to checking consistency, rather than providing absolute accuracy. (3) Which techniques can be de-skilled? How proof are the various techniques against inexperience? (4) Which are most cost-effectively used in production control? All of these questions are addressed in the Guide [1].
18.11
Further information
The Good Practice Guide [1], scientific papers, textbooks and International Standards have all been discussed above but there are other sources of useful information such as manufacturers’ literature, including catalogues, manuals and application notes, as in Reference 24. National Measurement Institutes (NMIs) other than NPL produce
450 Microwave measurements detailed technical notes, reports and guides on measurement techniques, notably NIST in the USA. NPL runs an Electromagnetics Measurements Club. Other societies, clubs and associations including the ARMMS RF & Microwave Society (general microwave topics) and the Ampere Association (microwave processing) can also provide support. A number of learned societies also run active dielectrics groups, notably the Institute of Physics, or groups that cover dielectric-related topics, notably the Institution of Engineering and Technology in the UK. Further details of all of these organisations can be found on the Internet.
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454 Microwave measurements 65 Roberts, S., and Von Hippel, ‘A new method for measuring dielectric constant and loss in the range of centimetre waves’, Journal of Applied Physics, 1946; 17:610–16 66 Baker-Jarvis, J.: Transmission/Reflection and short-circuit line permittivity measurements (NIST Technical Note 1341, The National Institute of Standards and Technology, Boulder, CO, 1990) 67 Baker-Jarvis, J., Vanzura, E. J., and Kissick, W. A.: ‘Improved technique for determining complex permittivity with the Transmission/Reflection method’, IEEE Transactions on Microwave Theory Techniques, 1990;MTT-38: 1096–103 68 Vanzura, E. J., Baker-Jarvis, J. R., Grosvenor, J. H., and Janezic, M. D.: ‘Intercomparison of permittivity measurements using the Transmission/ Reflection Method in 7 mm coaxial lines’, IEEE Transactions on Microwave Theory Techniques, 1994;MTT-42:2063–70 69 UTE Standard 26-295, Mesure de la permittivité et de la permeabilité de materiaux homogenes et isotropes a pertes dans le domaine des micro-ondes – Methode de mesure en guide coaxial circulaire (UTE (Union Technique de l’Electricite et de la Communication), see C26-295, France, 1999) 70 Grant, J. P., Clarke, R. N., Symm, G. T., and Spyrou, N.: ‘A critical study of the open-ended coaxial line sensor technique for RF and microwave complex permittivity measurements’, Journal of Physics E: Scientific Instruments, 1989; 22:757–70 71 Jenkins, S., Warham, A. G. P., and Clarke, R. N.: ‘Use of an open-ended coaxial line sensor with a laminar or liquid dielectric backed by a conducting plane’, IEE Proc. H, Microw. Antennas Propag., 1992;139:1792 72 Jenkins, S., Hodgetts, T. E., Symm, G. T., Warham, A. G. P., Clarke, R. N., and Preece, A. W.: ‘Comparison of three numerical treatments for the open-ended coaxial line sensor’, Electronics Letters, 1990;24:234–5 73 Gregory, A. P., Clarke, R. N., Hodgetts, T. E., and Symm, G. T.: RF and microwave dielectric measurements upon layered materials using a reflectometric coaxial sensor, NPL Report DES 125, NPL, March 1993 74 Clarke, R. N., Gregory, A. P., Hodgetts, T. E., and Symm, G. T.: ‘Improvements in coaxial sensor dielectric measurement: relevance to aqueous dielectrics and biological tissue’, in Kraszewski, A. (ed.) Microwave Aquametry – papers from the IEEE 1993 MTTS Workshop on Microwave Moisture and Water Measurement (IEEE Press, Piscataway NJ, 1996) 75 Marsland, T. P., and Evans, S.: ‘Dielectric measurements with an open-ended probe’, IEE Proc. H, Microw. Antennas Propag., 1987;134:341–9 76 Evans, S. ‘The shielded open-circuit probe for dielectric material measurements’, Proceedings of the 8th International British Electromagnetic Measurements Conference, NPL, Teddington, UK, 1997, Paper 5-2 Marsland, T. P., and Evans, S. ‘Dielectric measurements with an open-ended coaxial probe’, IEE Proc. H, Microw. Antennas Propag., 1987;134:341–9 77 Gardiol, F. E.: ‘Open-ended Waveguide: Principles and Applications’, Advances in Electronics and Electron Physics, 63:139–65
Measurement of the dielectric properties of materials 455 78 Sphicopoulos, T., Teodoridis, V., and Gardiol, F.: ‘Simple nondestructive method for the measurement of material permittivity’, Journal of Microwave Power, 1985;20:165–72 79 Sibbald, C. L., Stuchly, S. S., and Costache, G. I.: ‘Numerical analysis of waveguide apertures radiating into lossy media’, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 1992;5:259–74 80 Clarke, R. N., Gregory, A. P., Hodgetts, T. E., Symm, G. T., and Brown, N.: ‘Microwave measurements upon anisotropic dielectrics-theory and practice’, Proceedings of the 7th international British Electromagnetic Measurements Conference (BEMC), NPL, Teddington, 1995, Paper 57 81 Arai, M., Binner, J. G. P., and Cross, T. E.: ‘Estimating errors due to sample surface roughness in microwave complex permittivity measurements obtained using a coaxial probe’, Electronics Letters, 1995;31:115–17 82 Stuchly, S. S., Gajda, G., Anderson, L., and Kraszewski, A.: ‘A new sensor for dielectric measurements’, IEEE Transactions on Instrumentation and Measurement, 1986;IM-35:138–41 83 Preece, A. W., Johnson, R. H., and Murfin, J.: ‘RF penetration from electrically small hyperthermia applicators’, Physics in Medicine and Biology, 1987; 32:1591–601 84 Johnson, R. H., Pothecary, N. M., Robinson, M. P., Preece, A. W., and Railton, C. J.: ‘Simple non-invasive measurement of complex permittivity’, Electronics Letters, 1993;29:1360–1 85 Kajfez, D., and Guillon, P. (eds), Dielectric Resonators (Vector Fields, Oxford MS, 1990) 86 Krupka, J., Derzakowski, K., Abramowicz, A., Tobar, M. E., and Geyer, R. G.: ‘Whispering-gallery modes for complex permittivity measurements of ultra-low loss dielectric materials’, IEEE Transactions on Microwave Theory Techniques, 1999;MTT-47:752–9 87 Krupka, J., Blondy, P., Cros, D., Guillon, P., and Geyer, R.: ‘Whisperinggallery modes in magnetized disk samples, and their applications for permeability tensor measurements of microwave ferrites at frequencies above 20 GHz’, IEEE Transactions on Microwave Theory Techniques, 1996;MTT-44: 1097–102 88 Krupka, J., Derzakowski, K., Riddle, B., and Baker-Jarvis, J.: ‘A dielectric resonator for measurements of complex permittivity of low loss dielectric materials as a function of temperature’, Measurement Science and Technology, 9:1751–6 Krupka, J., Derzakowski, K., Abramowicz, A., et al.: ‘Bounds on permittivity calculations using the TE01δ dielectric resonator’, Proceedings of the XIV International Conference MIKON, Gdansk, Poland, 2002 89 Clarricoats, P. J. B., and Olver, A. D.: Corrugated horns for microwave antennas, IEE Electromagnetic Waves Series 18 (Peter Peregrinus on behalf of the IEE, London, 1984) 90 Wylde, R. J.: ‘Millimetre-wave Gaussian beam modes optics and corrugated feed horns’, IEE Proc. H, Microw. opt. Antennas, 1984;131:258–62
456 Microwave measurements 91 Kogelnik, H., and Li, T.: ‘Laser beams and resonators’, Proceedings of the IEEE, 1966;54:1312–29 92 LeSurf, J.: Millimetre-wave Optics, Devices and Systems (Adam Hilger, Bristol, 1990) 93 Lederer, P. G.: ‘The fundamental principles of ram reflectivity measurement’, Symposium on the Measurement of Reflectivity of Microwave Absorbers (DRA now QinetiQ), Malvern, February 1993) 94 Qureshi, W. M. A., Hill, L. D., Scott M., and Lewis, R. A.: ‘Use of a Gaussian beam range and reflectivity arch for characterisation of radome panels for a naval application’, Proceedings of the International Conference on Antennas and Propagation (ICAP), University of Exeter (IEE, 2003) 95 Cook, R. J., and Rosenberg, C. B.: ‘Measurements of the complex refractive index of isotropic and anisotropic materials at 35 GHz using a free-space microwave bridge’, Journal of Physics D: Applied Physics, 1979;12:1643–52 96 Cook, R. J.: The propagation of plane waves through a lamella, NPL Report DES 52, August 1979 97 Campbell, C. K.: ‘Free space permittivity measurements on dielectric materials at millimetre wavelengths’, IEEE Transactions on Instrumentation and Measurement, 1978;IM-27:54–8 98 Shimabukuro, F. I., Lazar, S., Chernick, M. R., and Dyson, H. B.: ‘A quasioptical method for determining the complex permittivity of materials’, IEEE Transactions on Microwave Theory Techniques, 1984;MTT-32:659–65, 1504 99 Gagnon, N., Shaker, J., Berini, P., Roy, L., and Petosa, A.: ‘Material characterization using a quasi-optical measurement system’, IEEE Transactions on Instrumentation and Measurement, 2003;IM-52:333–6 100 Li, S., Akyel, C., and Bosisio, R. G.: ‘Precise calculations and measurement on the complex dielectric constant of lossy materials using TM010 perturbation techniques’, IEEE Transactions on Microwave Theory Techniques, 1981; MTT-29:1041–148 101 Parkash, A., and Mansingh, A.: ‘Measurement of dielectric parameters at microwave frequencies by cavity-perturbation technique’, IEEE Transactions on Microwave Theory Techniques, 1979;MTT-27:791–5 102 Clarke, R. N., and Rosenberg, C. B.: ‘Fabry-Perot and open-resonators at microwave and millimetre-wave frequencies, 2–300 GHz’, Journal of Physics E: Scientific Instruments, 1982;15:9–24 103 Vaughn, J. M.: The Fabry-Perot Interferometer – history, practice and applications, Adam Hilger series on optics and optoelectronics (Adam Hilger, Bristol, 1989) 104 Jones, R. G.: ‘The measurement of dielectric anisotropy using a microwave open-resonator’, Journal of Physics D: Applied Physics, 1976;9:819–27 105 Cullen, A. L., and Yu, P. K.: ‘The accurate measurement of permittivity by means of an open-resonator’, Proceedings of the Royal Society of London, Series A, 1971;325:493–509 106 Jones, R. G.: ‘Precise dielectric measurements at 35 GHz using a microwave open-resonator’, Proc. Inst. Electr. Eng., 1976;123:285–90
Measurement of the dielectric properties of materials 457 107 Lynch, A. C., and Clarke, R. N.: ‘Open-resonators: improvement of confidence in measurement of loss’, IEE Proc. A Sci. Meas. Technol., 1992;139:221–5 108 Heidinger, R., Schwab, R., Königer, F., and Parker, T. J. (ed.): ‘A fast sweepable broad-band system for dielectric measurements at 90-100 GHz’, Twenty-third International Conference on Infrared and Millimeter Waves, Colchester, UK, 1998, pp. 353–4 Heidinger, R., Dammertz, G., Meiera, A., and Thumm, M. K.: ‘CVD diamond windows studied with low- and high-power millimeter waves’, IEEE Transactions on Plasma Science, 2002;PS-30:800–7 Danilov, I., and Heidinger, R.: ‘New approach for open resonator analysis for dielectric measurements at mm-wavelengths’, Journal of the European Ceramic Society, 2003;23 (14):2623–6 109 van Germert, M. J. C.: ‘Evaluation of dielectric permittivity and conductivity by time domain spectroscopy. Mathematical analysis of Felner-Feldegg’s thin cell method’, Journal of Chemical Physics, 1974;60:3963–74 110 van Germert, M. J. C.: ‘Multiple reflection time domain spectroscopy ii. a lumped element approach leading to an analytical solution for the complex permittivity’, Journal of Chemical Physics, 1975;62:2720–6 111 Feldman,Y., Andrianov, A., Polygalov, E. et al.: ‘Time domain dielectric spectroscopy’, Review of Scientific Instruments, 1996;67:3208–15 112 Berberian, J. G., and King, E. ‘An overview of time domain spectroscopy’, Journal of Non-Crystalline Solids, 2002;305:10–18 113 Baker-Jarvis, J.: Transmission/Reflection and short-circuit line permittivity measurements (NIST Technical Note 1341, National Institute of Standards and Technology, Boulder, CO, 1990)
Chapter 19
Calibration of ELF to UHF wire antennas, primarily for EMC testing M. J. Alexander
19.1
Introduction
Wire antennas such as monopoles, biconical and log-periodic dipole array (LPDA) antennas are used for electromagnetic compatibility (EMC) testing, and typically, cover the frequency ranges 1 kHz to 30 MHz, 30–300 MHz and 200 MHz to 2 GHz, respectively. The primary parameter of interest is the maximum gain. EMC implies that the radiated emission from a product does not impair the performance of a ‘victim’ product, so that, for example, a radio and television set will operate satisfactorily when placed next to each other. It is useful to know the strength of the E-field that one product is ‘bathing’ the other product in. For this reason the antenna gain is given in terms of antenna factor (AF) which enables a direct conversion to E-field magnitude. Uncertainties for EMC-radiated emission measurements tend to be of several decibels; therefore, the AF data are generally not needed to uncertainties better than ±0.5 dB. The antenna return loss is usually measured during the calibration of AF so that the mismatch uncertainty of the receiver reading during an EMC test can be estimated. Above 30 MHz, EMC measurements are made with the antenna both vertically and horizontally polarised so the cross-polar discrimination of the antenna is required as a component of the uncertainty budget. EMC measurements below 1 GHz are made over conducting ground planes or in free-space environments, either outdoors or in an anechoic chamber, whose imperfections will be ‘seen’ according to the directivity of the antenna, so knowledge of the radiation pattern is necessary. Monopole- and dipolelike antennas, including biconicals, have an omni-directional pattern in the H-plane which means that they are equally sensitive to E-fields arising from reflections in every direction about the H-plane. Below about 200 MHz it is difficult to achieve good free-space conditions in a fully lined anechoic chamber so measurements are
460 Microwave measurements generally made over a ground plane. The reflection from a good quality ground plane can be accurately calculated and taken into account when deriving AF from the measured coupling between two or more antennas. However, the presence of a metal plane in proximity to the antenna can also alter the AF from its free-space value because the antenna will couple with its own image in the ground plane. Knowledge of this alteration can be used to correct the antenna output voltage, or more commonly, to estimate its uncertainty. An EMC measurement is made at a specified distance from the product under test, so in order for an LPDA antenna to remain at a fixed location, it is necessary to correct the receiver reading for the variation of the LPDA phase centre with frequency. This chapter covers the following topics: overview of traceability of E-field strength, measurement of free-space AFs, measurement of AFs over a ground plane, measurement of radiation pattern, cross-polar response, phase centre, balun imbalance and return loss.
19.2
Traceability of E-field strength
The units of E-field strength are volts per metre. The volt is traceable to the Josephson Junction and DC voltage can routinely be measured to an uncertainty of two parts in 107 . The metre is traceable to the wavelength of a helium–neon laser and is routinely measurable to an uncertainty of one part in 107 . To measure electric field, a sensor (e.g. an antenna) is placed in the field and a reading is obtained in volts, or more usually a power reading in watts, which can be converted into volts knowing the impedance characteristics of the transmission line. With the present state-of-the-art, field strength can be measured with wire antennas to an uncertainty of only about two parts in 102 , which is equivalent to 0.17 dB. Four methods, claimed to give traceability of field strength for the purpose of calibrating antennas or field probes, are all based on formulas that derive from Maxwell’s equations. A simplified treatment will be given here to show the principles. This is followed by a typical uncertainty budget for field strength in an EMC-radiated emission measurement. A big advantage of the methods described in Sections 19.2.2 and 19.2.3 is that the quantity measured is attenuation, which can be measured to an uncertainty of better than ±0.01 dB.
19.2.1 High feed impedance half wave dipole The first method is to place a half wave dipole in the field and measure the voltage at the feed point of the dipole. The open circuit voltage is related to the E-field and wavelength, λ, by the following formula: π E = Voc · (19.1) λ This can be realised in practice by placing a diode at the dipole feed point and measuring the rectified voltage [1]. It is necessary to calibrate the rectifying circuit by using an RF signal of known power level. The larger part of the uncertainty lies
Calibration of ELF to UHF wire antennas, primarily for EMC testing 461 in this calibration. Standards Laboratories can measure power in the VHF and UHF ranges to an uncertainty of around ±1.5 per cent. Reference [1] has a refinement on the above formula, which takes into account the diameter of the dipole. Advantages of this method are its simplicity in concept and the fact that the high feed impedance of the dipole makes it insensitive to coupling with its image in a ground plane. Disadvantages are the loss of frequency selectivity and therefore reception of all fields present, and the need for high field levels to generate sufficient voltage, which are not permitted by the broadcasting regulators in some countries. A further disadvantage is that the combined uncertainty is higher than for the methods described in Sections 19.2.2 and 19.2.3.
19.2.2 Three-antenna method The three-antenna method [2] uses the Friis formula to relate the insertion loss between two antennas to the product of their gains: 0001 0002 λ 2 PR = PT GT GR (19.2) 4πR where PR and PT are the powers received and transmitted, and GR and GT are the gains of the receive and transmit antennas. R is the separation distance between the antennas and λ is the wavelength, both in the same unit. Uncertainties of gain as low as ±0.04 dB can be obtained [3] using the threeantenna method if the antennas have relatively high gain, for example, 20 dB standard gain horn antennas. This is possible because the high-directivity horns will radiate only a small amount of power away from the main beam, so reflections from the surroundings will be low, combined with affordable low-reflectivity absorber. This is a popular method for measuring the gain of EMC horn antennas to 40 GHz. If the extrapolation method is used, the strength of the launched E-field can be calculated at any given distance from the antenna for a known RF power into the antenna. The insertion loss (ohmic) of the antenna must be known, and this together with power is the main component of uncertainty. By the principle of reciprocity an unknown incident E-field can be found by measuring the output power of the antenna. Realised gain, G, which includes mismatch into 50 0003, can be converted to AF, using the following equation: AF2 =
4π ZF Gλ2 Z0
(19.3)
where λ is the wavelength, ZF is free-space impedance (approximately 377 0003) and Z0 is the characteristic impedance of the antenna input transmission line, commonly 50 0003. The three-antenna method is also a very accurate method for measuring the AF of dipole antennas providing the ground plane is sufficiently large and flat. A straightforward formula [4] can be used for removing the ground reflected ray, provided the antennas are in each other’s far-field – for dipoles a separation of three wavelengths is sufficient for an uncertainty of better than ±0.15 dB to be achieved [5].
462 Microwave measurements It must be borne in mind that the measured AF applies for that height above a ground plane, that is, it includes the effects of coupling with its image; also the measurement uncertainties are generally greater for vertical polarisation because of reflections from structures such as the vertically dropping feed cable and the antenna mast. In addition to this, vertical polarisation is associated with greater sensitivity to site effects, such as edge diffraction (i.e. reflections from the edges of the ground plane).
19.2.3 Calculability of coupling between two resonant dipole antennas The third method involves comparing the measured and calculated insertion loss between two antennas [6]. This method is useful for dipole antennas that have uniform H-plane patterns and for which it is difficult to avoid reflections from the surroundings. By configuring the antennas over a large flat ground plane outdoors this ensures one electromagnetically well-defined source of reflection and an upper hemisphere with no reflections. Using method of moments code [7], it is possible to predict the measured insertion loss between two wire antennas above a ground plane to an uncertainty of less than ±0.3 dB, and hence AF to less than ±0.15 dB [8]. This includes the effect of mutual coupling of the antenna to its image in the ground plane, which for normal usage of EMC antennas can alter the gain by as much as 100 per cent.
19.2.4 Calculable field in a transverse electromagnetic (TEM) cell The fourth method of providing traceability for field strength is to deduce the field between the two conductors of a transmission line from the power input to the line. A TEM cell [9] is a coaxial line with an expanded cross section. Provided the characteristic impedance, Z0 , of the line is preserved with change in cross section, it is possible to achieve uncertainties better than 0.3 dB (3.5 per cent) in the E-field strength between the plates of the TEM cell [10]. A TEM cell is useful for the calibration of field probes at frequencies below 1 GHz. The field strength E (V m–1 ) is given from the power input to the cell P (Watt) and the plate separation b (metre) by the following formula: √ PZ0 (19.4) E= b For best accuracy the probe being tested should be electrically small to reduce coupling with the sidewalls, and it should occupy a relatively small volume within the cell so that the TEM wave is perturbed as little as possible.
19.2.5 Uncertainty budget for EMC-radiated E-field emission A statement of uncertainties implies traceability to national standards. In order for measurements to have a common meaning, and to support trade, within and across national boundaries, it is necessary that they are traceable to national standards. In turn, national standards laboratories take part in international intercomparisons to ensure that they are in step with the rest of the world [11]. Traceability of measurements in industry is assisted by the accreditation of test and calibration laboratories.
Calibration of ELF to UHF wire antennas, primarily for EMC testing 463 For this purpose Accreditation Bodies are set up whose job is twofold, first to ensure traceability of physical parameters and second to ensure that laboratories have a Quality System in place which ensures that the laboratory is able to deliver the traceability to the uncertainty which it claims it is capable of, and that this has been verified by appointed technical experts. The magnitude of uncertainty commonly used is the Standard Uncertainty multiplied by a coverage factor of k = 2, providing a level of confidence of approximately 95 per cent. An EMC radiated emission test often involves a product with power and data cables that make it difficult to get a reproducible result, giving rise to large uncertainties, of the order of ±10 dB. However the uncertainty contributions from the measuring site and equipment can be minimised, for example, uncertainties associated with the antenna can be quantified. Typical uncertainty components are listed in Table 19.1. Just because EMC uncertainties are very large compared with uncertainties for other physical parameters, such as voltage, does not mean that the evaluation of EMC uncertainties is pointless. Indeed the process of setting up an uncertainty budget highlights the largest components and directs the effort to reducing these. Table 19.1 shows a budget comprising the main components that could affect the E-field magnitude measured during emission testing using either a biconical antenna or a LPDA antenna. For AF the uncertainty is likely to be given in a certificate. If it is given to a confidence level of 95 per cent the probability distribution will be Gaussian (or Normal) with a k value of 2. If the specification of the instrument does not refer to a standard uncertainty one has to assume that the measurement could lie anywhere within the specified accuracy limits, and without further information about the distribution of repeated results this is assumed to correspond to a rectangular distribution. The method by which uncertainty components with different probability distributions are summed is given in the ISO Guide [12]. However this Guide is comprehensive and can be a challenge on first reading. It has been presented in a more amenable form [13] for the subject of EMC. The fourth component in Table 19.1 relates to antenna directivity, which is relative to a tuned dipole stipulated by CISPR 16-1-4:2004. Varying the height of the receive antenna over a ground plane means there are two ray paths between the equipment under test (EUT) and the antenna which diverge from the bore sight direction. For a biconical antenna the error is for vertical polarisation only, it being zero for horizontal polarisation because the H-plane directivity is uniform. The error is positive because it represents only loss of signal. The 12th component, site imperfections, relates to normalised site attenuation (NSA) performance. Simply put, this term indicates how close the test site is to an ideal environment. Since the site is only required to meet a criterion of NSA within ±4 dB of the theoretical value, strictly the value of this uncertainty component should be ±4 dB. However, it has been set to ±1 dB because this is the intention in Annex F of CISPR 16-1-4:2004 [14] and because good sites are likely to meet ±1 dB. The last components for ambient interference and cable layout have not been given values because these vary widely from site to site and operator to operator. These two components can increase by many decibels the expanded uncertainty of ±3.8 dB in Table 19.1. Further explanation of this table can be found in Reference [13] and CISPR 16-4-2.
464 Microwave measurements Table 19.1
Uncertainty budget for emission measurements on a 3 m open area test site
Component
Probability
Uncertainty dB
distribution
Biconical
LPDA
Antenna factor calibration Cable loss calibration Receiver specification Antenna directivity
Normal (k = 2) Normal (k = 2) Rectangular Rectangular
Antenna factor variation with height Antenna phase centre variation Antenna factor frequency interpolation Antenna balun imbalance Measurement distance error ±2 cm Height of antenna above ground plane (height error ±2 cm) Height of EUT above ground plane (height error ±2 cm) Site imperfections Mismatch System repeatability Ambient interference Reproducibility of EUT/cable layout Combined standard uncertainty uc (y)
Rectangular Rectangular Rectangular Rectangular Rectangular Rectangular
±1.0 ±0.5 ±1.5 +0.5 −0 ±2 0 ±0.25 ±1.0 ±0.1 ±0.1
Rectangular
±0.05
±1.0 ±0.5 ±1.5 +2 −0 ±0.5 ±2 ±0.25 ±0 ±0.3 +1.0 −0 ±0.05
Rectangular U-shaped Normal − − Normal
±1.0 ±1.1 ±0.5 Large Poor +1.92 −1.90 ±3.8 −
±1.0 ±0.5 ±0.5 Large Poor +2.1 −1.8 +4.2 −3.6
Expanded uncertainty U
19.3
Normal (k = 2) −
Antenna factors
Ideally AF should be independent of the antenna surroundings. However, the standard method for EMC testing is to measure emission over a ground plane at a distance of 10 m from the product under test. Signal nulls are caused by destructive interference of the direct and ground-reflected ray paths between the antenna and the product. To avoid measuring in nulls the antenna is height scanned between 1 and 4 m and the maximum signal is recorded. Height scanning brings into play the effects of the radiation pattern and mutual coupling of the antenna with its image, resulting in errors of around ±2 dB (refer to Table 19.1). A widely used method for calibrating antennas is the American National Standard Institute (ANSI) procedure [15] which mimics the EMC radiated test method in that it uses the same geometry, including height scanning, to perform the three-antenna method. The product is replaced by a transmitting antenna at a fixed height of 1 or 2 m. This method will give low uncertainties for EMC testing in cases where the product
Calibration of ELF to UHF wire antennas, primarily for EMC testing 465
Figure 19.1
The 60 × 30 m ground plane at the National Physical Laboratory, Teddington, UK, whose surface is flat to within ±15 mm over 95 per cent of its area
behaves like that antenna, radiating at that fixed height, but more likely the product will radiate anywhere from the floor, via its cabling, to the top of the unit which may be more than 1 m from the ground. The height of the radiating source on the EUT varies with frequency and it is not practical to predict the height of maxima, as we do for a single antenna source during an ANSI calibration, and therefore the correct choice of receiving AF becomes an issue. A compromise would be to use an average of the receiving AF measured with the transmitting antenna at a range of heights. A study performed at NPL [17], in which the AF of a biconical antenna was both computed and measured (Figure 19.1) at a range of heights showed that the AF averaged over different heights was within ±0.5 dB of the free-space AF (AFFS ), and that the AF measured by the ANSI method on a 10 m site was also within ±0.5 dB of AFFS . There are techniques in which it is possible to measure AFFS more efficiently and more accurately than by height scanning, and in view of the good comparisons cited, AFFS is a sound basis from which to quantify antenna-related uncertainties of measurement. Furthermore AFFS is a basic property of an antenna, with no built-in mutual coupling effects. Alternative methods of performing radiated emission tests in free-space conditions are being developed, such as the fully anechoic room, in which AFFS will give the lowest uncertainties. CISPR, a sub-committee of the IEC (International Electrotechnical Commission) is defining acceptable methods of calibration of antennas that are used for EMC testing, and the methods will be described in a future issue of CISPR 16-1-5.
466 Microwave measurements
19.3.1 Measurement of free-space AFs Free-space conditions are defined as the illumination of an antenna in free-space by a plane wave, which implies that the antenna is in the far-field of the source. Antennas are often used in non-free-space conditions with the antenna above a ground plane or close to absorber lined walls and illuminated by a non-uniform field. It can be difficult to unravel these effects in order to quantify uncertainties but the best starting point is the free-space AF. Absorbing material can be very effective above 200 MHz and a relatively small amount can be used to set up free-space conditions for the calibration of LPDA antennas. With ingenuity one can set up affordable methods for measuring AFFS of dipole-like antennas below 200 MHz. These methods are outlined below. Uncertainties of ±0.5 dB can be routinely achieved for dipole, biconical and LPDA AFs [16,17].
19.3.2 The calculable dipole antenna This method gives the lowest uncertainty obtainable for AF. The calculable dipole antenna is used by National Laboratories as a primary standard antenna. The antenna comprises two thin dipole elements fed in anti-phase by a 3 dB hybrid coupler. The verification of AF of the calculable dipole is given in References [6] and [8]. The AF is calculable either for free-space conditions or with the antenna mounted above a ground plane. The dipole antenna can be used as an accurate broadband dipole using numerical methods such as NEC [7]. As mentioned in Section 19.2.3 the uncertainty in the AF, above a ground plane or in free-space is better than ±0.15 dB. The calculable dipole is especially useful in providing traceability for tuned dipole and broadband antennas, and also evaluating the quality of EMC test sites.
19.3.3 Calibration of biconical antennas in the frequency range 20–300 MHz In this frequency range, dipole-like antennas of length less than 1.5 m are fairly omnidirectional and it is not so practicable to measure free-space AF by conventional methods. This is because the antennas have to be several wavelengths away from conducting surfaces, including the ground. This implies heights of greater than 10 m if the antennas are horizontally polarised – the problem with vertical polarisation is that it is difficult to reduce reflections from the input cable to an acceptable level, also the mast is a vertical structure and will be a source of reflection. At frequencies above 300 MHz the usual solution is to line a large room with pyramidal RF absorbing material (RAM). This is not practicable at 30 MHz. Ferrite tiles of about 6 mm thickness are used to line EMC chambers but their return loss is typically less than 15 dB, whereas reflections must be less than –25 dB to measure gain to uncertainties of less than ±0.5 dB. It is possible to simulate free-space conditions without using absorber. One method is to mount the antenna vertically polarised at 2 m height above a ground plane. At this height mutual coupling to the ground image is negligible at the resonant
Calibration of ELF to UHF wire antennas, primarily for EMC testing 467 frequency (where it is most sensitive) of the biconical antenna, around 70 MHz, and below resonance the high self-impedance makes the antenna insensitive to its ground image. A sufficiently plane wave to illuminate the antenna can be set up by placing a source antenna close to the ground at a distance of around 20 m. The standard antenna method is used with the broadband calculable dipole antenna as the standard. The cable must be extended horizontally behind the antenna several metres before dropping vertically in order to reduce the effect of reflections.
19.3.4 Calibration of LPDA antennas in the frequency range 200 MHz to 5 GHz The traditional way to calibrate LPDA antennas is by the ANSI method at a distance of 10 m across a ground plane. A typical antenna for this frequency range is 0.65 m long. If the separation of the antennas is measured from their centres, the uncertainty in AF at the top and bottom frequencies is 0.3 dB due to the movement of the LPDA phase centre. Also in the UK, when limited to using the allowed transmit power, there is relatively high interference from TV transmissions. A more elegant method is to calibrate the antennas at fixed heights above RAM. If the phase centre is known at each frequency the separation can be reduced, overcoming ambient signals and reducing the amount of RAM required. Phase centre can be found in a variety of ways. The methods used at NPL are (1) from the mechanical dimensions of LPDA elements, (2) from measurement of signal phase as the antenna is rotated in free-space and (3) using NEC modelling. The results agree well and phase centre is typically known to better than ±1 cm. NPL uses a mid-antenna separation of 2.5 m which allows an uncertainty in AF of ±0.5 dB to be achieved. The same method is used for conical log spiral antennas to an uncertainty of ±1 dB.
19.3.5 Calibration of hybrid antennas A conical-hybrid antenna is a physical combination of a biconical antenna and a log antenna into one antenna with a typical frequency range of 26 MHz to 2 GHz. At NPL these are calibrated to uncertainties of less than ±0.7 dB using the two methods described in Sections 19.3.3 and 19.3.4. The AF data are ‘sewn’ together within the frequency overlap. One reason that the uncertainty is higher than ±0.5 dB is that the phase centre at frequencies in the region between the ‘biconical element’ and the longest log-periodic element is only estimated by linear interpolation. Another reason is that hybrid antennas can be very large and day-to-day alignment on the mast is not so precise as for the smaller LPDA.
19.3.6 Calibration of rod antennas Rod antennas are conventionally calibrated by replacing the monopole element with a capacitor of approximately 12 pF. This can give AF to within ±1 dB below about 15 MHz but it does not work so well above this frequency. This method might be
468 Microwave measurements suited to antenna manufacturers because they can design a power splitter jig for their own model of antenna, but it is a big overhead for a calibration laboratory to develop the right jig for all types of rod antenna. Because this method is essentially a substitution of the real element there are some important aspects in the construction of the calibration jig, which may lead to incorrect AF values if wrongly done ([17], Section 9.10). NPL’s principal method involves placing the rod antenna with its base on a large (60 × 30 m) ground plane and illuminating it with a source 20 m away. The standard antenna method is used. The standard is a calculable rod antenna whose AFs are calculated using NEC. Because of the difficulty with getting enough radiated signal below 10 MHz, calibrations below this frequency are done in a MEB1750 GTEM cell. The validity of using the GTEM cell was demonstrated by comparison with results obtained on the NPL ground plane. For this test a very large strip line, 2.5 m high, was built on the ground plane and the reception by a standard antenna was compared with that from the antenna under test (AUT).
19.3.7 Calibration of loop antennas Loop antennas can be calibrated in a TEM cell to uncertainties of less than ±1 dB, typically over the frequency range 20 Hz to 30 MHz. The power output of the cell is measured and used to calculate the field strength between the plates, in which the loop is immersed. The validity of using the TEM cell was demonstrated by building a standard loop whose current was measured and the generated field could therefore be calculated; the AUT was placed on a common axis in a nearby parallel plane to the transmitting loop. The magnetic AF may then be calculated by the AUT response in the known field.
19.3.8 Other antenna characteristics There are undesirable characteristics of antennas that can cause a great deal of trouble to practicing engineers. A Measurement Good Practice Guide [17] identifies the main problems and gives guidance on how to deal with them and more generally gives tips on calibrating antennas. This section deals with baluns, cross polar discrimination and breakdown of RF connection in antenna elements. 19.3.8.1 Balun imbalance In the early stages of establishing a calibration service NPL discovered that some models of popularly used biconical antennas had severe balun imbalance. All one had to do was to invert the vertically polarised antenna and get a change in received signal of ±5 dB. The cause was imbalance of the balun which set up common mode currents on the cable, which radiated and interfered with the antenna. The effect is related to the size of current and the proximity of the vertically hanging cable to the vertically polarised antenna elements. Since the 1970s engineers have noticed problems with the reproducibility of readings for certain models of antenna. A substantial literature including this topic has been spawned, giving advice on the orientation of the antenna, the layout of
Calibration of ELF to UHF wire antennas, primarily for EMC testing 469 cables and the use of ferrites to suppress braid currents. Balun imbalance has been the cause of many man-days of wasted effort at many test sites, particularly with site validation. Putting ferrite toroids on the cable close to the antenna input can make some improvement, but alternative proprietary models of antenna that do not have this problem are readily available. The majority of dipole-like antennas pass the test in CISPR 16-1-4 with a balance of better than ±0.5 dB. Text has been included in clause 4.4.2 of CISPR 16-1-4, which describes the measurement of balun imbalance and imposes a limit on the magnitude of the imbalance allowed. 19.3.8.2 Cross-polar performance The following text has been included in clause 4.4.3 of CISPR 16-1-4: When an antenna is placed in a plane-polarised electromagnetic field, the terminal voltage when the antenna and field are cross-polarised shall be at least 20 dB below the terminal voltage when they are co-polarised. It is intended that this test apply to LPDA antennas for which the two halves of each dipole are in echelon. The majority of testing with such antennas is above 200 MHz, but the requirement applies below 200 MHz. This test is not intended for in-line dipole and biconical antennas because a cross-polar rejection greater than 20 dB is intrinsic to their symmetrical design. Such antennas, and horn antennas, must have a cross-polar rejection greater than 20 dB; a type test by the manufacturer should confirm this.
19.3.8.3 Mechanical construction of antennas Some models of antenna have given poor repeatability of measured signal because of mechanical defects. The most common one is breakdown of RF contact between the elements on a log antenna and the transmission line they are screwed to. This can be caused by a build-up of metal oxide in the joint or simply a loose joint. 19.3.8.4 Return loss It is assumed that the calibration of an antenna includes the measurement of return loss, with the antenna mounted in free-space conditions. This enables the operator to calculate the mismatch uncertainties of the emission result.
19.4
Electro-optic sensors and traceability of fields in TEM cells
There are two fundamental methods that are used to provide traceability for E-field strength. One is to use a calculable dipole to measure (or set up) the field, and the other is to generate the field in a TEM waveguide from a known input power. An electro-optic field sensor is an ideal device to make an intercomparison between the two methods because of its small size, high sensitivity. It is also non-intrusive to the field because of minimal use of metal parts and the use of an optical fibre to feed it. The field in a TEM cell is calculable at frequencies below the resonant frequency of the first higher-order mode. The uncertainties of the field at the centre of the cell arise from measurements of the insertion loss from the input to the centre of the cell,
470 Microwave measurements the input power, the impedance of the (loaded) cell at the centre compared with the design impedance, and the effect on the field of placing the field sensor or other object at the centre of the cell. The onset of resonance dictates the maximum frequency of the cell, which is inversely proportional to the size of the cell. A cell that operates up to 1 GHz is small (of the order of 0.1 m). Such a cell has been developed at Physikalisch-Technischen Bundesanstalt (PTB) as a standard to calibrate small field probes [10] which in turn provide traceability for larger antennas. NPL investigated the calibration of a TEM cell by using a transfer standard to trace the field strength to the calculable dipole [18]. The calculable dipole has a length of half a wavelength and by definition cannot fit between the plates of a cell. Also the current design is fed by a coaxial cable and this would cause uncertainties when inserting the dipole into the cell. The electro-optic transfer standard is a short dipole embedded in a lithium niobate crystal fed by optical fibres. An agreement of less than ±0.3 dB has been demonstrated between the field measured by a calculable dipole antenna and the field in a TEM cell. This should enable commercial field probes to be calibrated in TEM cells with uncertainties of less than ±0.5 dB.
Acknowledgements Acknowledgements are due to the National Measurement System Policy Unit of the DTI for funding this work through several Electrical Programmes, and to staff of the RF & Microwave Group who contributed to the developments.
References 1 Camell, D. G., Larsen, E. B., and Ansen, W. J.: ‘NBS calibration procedures for horizontal dipole antennas’, International Symposium on Electromagnetic Compatibility, Seattle, 1988, pp. 390–394 2 IEEE Standard Test Procedures for Antennas, ANSI/IEEE Std 149-1979 3 Gentle, D. G., Beardmore, A., Achkar, J., Park, J., MacReynolds, K. and de Vreede, J.P.M.: CCEM Key Comparison RF-K3.F, Measurement Techniques and Results of an Intercomparison of Horn Antenna Gain in IEC-R 320 at 26.5, 33.0 and 40.0 GHz, NPL Report CETM 46, Sep 2003. Search for ‘RF-K3.F’ at http://kcdb.bipm.org/ appendixB/KCDB_ApB_search.asp [Accessed 2007] 4 Smith, A. A.: ‘Standard-site method for determining antenna factors’, IEEE Transactions on Electromagnetic Compatibility, 1982;24:316–22 5 Morioka, T., and Komiyama, K.: ‘Measurement of antenna characteristics above different conducting planes’, IEEE Transactions on Instrumentation and Measurement, 2001;50 (2):393–6 6 Alexander, M. J., and Salter, M. J.: ‘Low measurement uncertainties in the frequency range 30 MHz to 1 GHz using a calculable standard dipole antenna and national reference ground plane’, IEE Prococeedings-Science, Measurement and Technology, 1996;143 (4):221–8
Calibration of ELF to UHF wire antennas, primarily for EMC testing 471 7 Logan, J. C., and Burke, A. J.: Numerical Electromagnetic Code (Naval Oceans Systems Centre, CA, USA, 1981) 8 Alexander, M. J., Salter, M. J., Loader, B. G., and Knight, D. A.: ‘Broadband calculable dipole reference antennas’, IEEE Transactions on Electromagnetic Compatibility, 2002;44 (1):45–58 9 Crawford, M. L.: ‘Generation of standard EM fields using TEM transmission cells’, IEEE Transactions on Electromagnetic Compatibility, 1974;16 (4): 189–95 10 Münter, K., Pape, R., and Glimm, J.: ‘Portable E-field strength meter system and its traceable calibration up to 1 GHz using a µGTEM cell’, Conference of Precision Electromagnetic Measurements, Braunschweig, 1996, pp. 443–444 11 Alexander, M.: ‘International comparison CCEM.RF-K7.b.F of antenna factors in the frequency range 30 MHz to 1 GHz’, Metrologia, 2002;39:309–17 12 Guide to the Expression of Uncertainty in Measurement. International Organisation for Standardisation, Geneva, Switzerland, 1993 13 The Treatment of Uncertainty in EMC Measurements, LAB34, UKAS, April 2002 (update on NIS81 May 1994) 14 CISPR publication 16. Specification for Radio Disturbance and Immunity Measuring Apparatus and Methods, Part 1-4:2004 Apparatus, Part 160-2-3:2004 Methods, Central office of the IEC, 3 rue de Varembé, Geneva, Switzerland 15 ANSI C63.5:2004. Calibration of antennas used for radiated emissions measurements in electromagnetic interference (EMI) control 16 Alexander, M. J.: ‘The measurement and use of free-space antenna factors in EMC applications’, Proceedings of 13th International Symposium on Electromagnetic Compatibility, Zurich, 1999, paper F6 17 Alexander, M.J., Salter, M.J., Gentle, D.G., Knight, D.A., Loader, B.G., Holland, K.P.: Measurement Good Practice Guide No. 73: Calibration and use of Antennas Focusing on EMC applications, Dec 2004. www.npl.co.uk/publications 18 Loh, T.H., Loader, B., Alexander, M.: ‘Comparison of electric field strentgh at VHF frequencies generated by dipoles and TEM cells’, 18th International Zuric symposium on EMC, Sep 2007
Index
AFs (antenna factors) 464–9 about AFs 459, 464–5 ANSI procedure 464 and Balun imbalance 468–9 biconical antenna measurements 466–7 calculable dipole antenna method 466 CISPR acceptable calibration methods 465 and cross-polar performance 469 free-space measurement 466 hybrid antenna calibration 467 loop antennas calibration 568 LPDA antenna calibration 467 National Physical Laboratory (UK) ground plane 465 and return loss 469 rod antenna calibration 467 see also E-field strength traceability; EMC (electromagnetic compatibility) measurement/testing air lines (precision air-dielectric coaxial transmission lines) 188–93 about air lines 188–9 characteristic impedance 190–1 conductor imperfections 192–3 fully supported air lines 190 partially supported air lines 189–90 phase change 191–2 RF impedance 194–8 lossless lines 194–5 lossy lines 195–8 propagation constant 197 skin depth issues 192–3 standards 190–2 unsupported air lines 189
amplitude modulation measurement, with spectrum analysers 383–4 antenna factors: see AFs (antenna factors) attenuation measurement about attenuation measurement 91 basic principles 91–3 calibration standards 116 definition of attenuation 91–2 detector linearity 112–14 measurement uncertainty budget 114 insertion loss 91–3 mismatch error/uncertainty 92–3, 110–12 two-resistor power splitter 111–12 repeatability 115–16 RF leakage 112–13 stability and drift 115 system noise 115 system resolution 115 attenuation measurement systems AF substitution method 104–5 automatic network analyser 108–10 vector network analyser 108–9 IF substitution method 105–7 piston attenuator 105–6 inductive voltage divider 98–104 attenuation 98 automated system 99–100 commercial attenuation calibrator 102–3 construction 98 dual channel system 101 error 99 gauge block system 100 IFR 2309 FFT signal analyser 103–4
474 Index attenuation measurement systems (Cont.) power ratio method 94–7 power sensor linearity problem 94–5 range switching/resolution problem 95–7 signal generator amplitude drift problem 94 zero carry over problem 95 RF substitution method 107–8 rotary vane attenuator 107–8 voltage ratio method 97–8 attenuation measurement worked example, 30db attenuation 116–19 contributions to uncertainty, Type A random uncertainty 117 detector linearity 117 leakage 117 power meter resolution 117 uncertainty spreadsheet 118 automatic network analysers (ANAs) 108–10, 425–6 see also calibration of automatic network analysers; network analysers; one-port devices/error models; scalar network analysers; TRL calibration; two-port error model for measurement; vector network analysers (VNAs); verification of automatic network analysers avalanche diode noise sources 163–4 balanced device characterisation 305–28 about balanced device characterisation 305–7, 309–10 about balanced and unbalanced systems 305–6 conversion parameters 310 de-embedding 326–8 differential structure issues 306–9 differential through connection example 321–6 Far End Crosstalk (FEXT) measurements 320 ideal devices 307–8 mixed-mode-S-parameter-matrix 318–19 modal decomposition method 312–18 Near End Crosstalk (NEXT) measurements 320 real devices 307–10 SAW-filter measurement example 326–7 self parameters 310
single-ended to balanced device characterisation 319–20 typical measurements 320–1 using network analysis 310 using physical transformers 310–11 virtual ideal transformers 311 Balun imbalance 468–9 Bessel zero method/Bessel nulls 385–6 biconical wire atennas, with EMC testing 459, 467 bolometers 333–4 and microbolometers 249 Boltzmann’s constant 159 calibration of automatic network analysers 263–89 about calibration 263 see also network analysers; one-port devices/error models; scalar network analysers; TRL calibration; two-port error model for measurement; vector network analysers (VNAs) calorimeters 334–6 cascaded receivers, noise 169 cascade matrix, S-parameter matrix 27–8 Cavity cell 443 Central Limit Theorem 46, 50–1 characterisation: see balanced device characterisation characteristic impedance measurement 35–6 non-TEM waveguides 33–5 one-port devices 21–2 real and imaginary parts 32–3 and S-parameter measurements 30–6 transmission lines, with losses 30–3 transmission lines, no losses 4 coaxial air lines historical perspective 181 see also air lines (precision air-dielectric coaxial transmission lines) coaxial connectors 59–90 about coaxial connectors 59–60, 66 airline handling 61 bead resonances 188 buffer adapters 65 cleaning 63–4 normal procedure 64 static sensitive devices 64 connector recession 65–6 connector savers 65
Index 475 dial gauges and test pieces 87–8 calibrating 87 gauge calibration blocks 88 measurement resolution 87–8 push on/screw on types 87 electrical characteristics 187–8 frequency ranges of common types 66–7, 188 future developments 200 gauging connectors 62–3 higher-order mode resonances 188 historical perspective 180–1 insertion loss repeatability for connector pairs 85 life expectancy 65 line sizes 60 repeatability issues 61–2 specifications 62 torque wrench setting values 86 ‘Traceability to National Standards’ 59 coaxial connector types 1.0 mm (Agilent W) connector 82–5 1.85 mm (V™ ) connector 81–2 2.4 mm (Type Q) connector 80–1 2.92 mm K connector 79–81 3.5 mm connector 77–9 7/16 connector 73–6, 201 7 mm precision connector 68–71 connection procedure 68–70 disconnection procedure 71 14 mm precision connector 66–8 compatibility possibilities 185–6 electrical discontinuities from 186 GPCs (general precision connectors) 60, 185 line diameters summary 186 LPCs (laboratory precision connectors) 60, 185 mechanical characteristics 185–7 N 7 mm connectors (rugged) 71–4 dimensions chart 74 gauging type N connectors 73 precision/non precision 183–5 sexed connectors 183 sexless (hermaphroditic) connectors 60, 182–3 SMA connectors 76–8 dimensions chart 78 coaxial lines structures and properties 148–50 applications 149–50
dispersion characteristics 149 complex refractive index 412 complex relative magnetic permeability 412 connectors: see air lines (precision air-dielectric coaxial transmission lines); coaxial connectors conversion parameters 310 coplanar waveguides (CPW) probes 231–2 structures and properties 153–4 couplers, power measurement 343 coupling factor 209–10 Courtney Holder cell 443 Debye relaxation 419, 420, 421–2 decibels 330 delay line discriminators, for phase noise measurement 400–1 Dicke (switching) radiometer 164, 166 dielectric rod probe 249–50 dielectrics, basic concepts about dielectrics 409–10 absolute permittivity 410 basic parameters 410–13 complex refractive index 412 complex relative magnetic permeability 412 equivalent circuits 411 loss tangent 412 magnetic hysteresis 412 microradian 412 permittivity of free space 410 power absorption coefficient 413 radiation absorbing materials (RAM) 412 relative permittivity 410 dielectrics, basic measurement theory 413–17 about dielectric measurement 413 dielectric-test-set method 417 frequency-change methods 417 frequency coverage of the methods 417 length-change methods 417 lumped-impedance methods 414 admittance cells 414 cell admittance 414 lumped equivalent circuits 414 multi-pass techniques 417 Q-factor (Quality Factor) 417 resonance methods 416 cavities 416 wave methods 414–16 attenuation constant 415
476 Index dielectrics, basic measurement theory (Cont.) Fresnel’s equations 416 guided wave media 414 phase constant 415 propagation/transmission parameters 415 Scattering Parameters 414 standing-wave methods 414 travelling-wave methods 414, 416 dielectrics, loss processes 418–22 dielectric relaxation 418–22 Debye relaxation 419, 420, 421–2 interfacial polarisation 418 Kramers-Kronig relations 421–2 Maxwell-Wagner effect 418 polar/non-polar materials 418 relaxation frequency 421 rotational polarisation 418 dielectric resonance 419–20 electrical conduction/conductivity 418 non-linear processes 420 dielectrics, measurement methods about choosing a method 449 admittance methods 430–2 Hartshorn and Ward (H & W) technique 432–3 liquid dielectrics 430–1 perturbation method 433–4 resonant admittance cells 432–4 three-terminal cells 431–2 TM010 -mode cavity 434 two-terminal cells 432 Cavity cell 443 coaxial probes 439–41 coaxial transmission lines 437–9 Courtney Holder cell 443 dielectric probes 441 dielectric resonators (DRs) 442–4 free field methods 444–6 Hakki-Colemen cell 443 open-ended rectangular waveguide probes 442 open resonators 446–8 resonator perturbation technique 446 ring resonators 437 Roberts and Von Hippel method 438 split-post dielectric resonators (SPDR) 436–7 substrate methods 437 TE01 -mode cavities 434–6
time domain techniques 448 waveguide probes 440–1 dielectrics, measurement practicalities 422–30 about the need to measure 422–3 anistropic materials 424–5 automatic network analysers (ANAs) 425–6 cleanliness aspects 424 dimensions and preparation 424 ferroelectrics 425 frequency response analysers (FRAs) 426 good practices 429–30 high-permittivity dielectrics 425 hygroscopic materials 424 inhomogeneous materials 425 international standard measurement methods 422 low-loss materials 423 magnetic materials 424–5 matching method to material 423 measurement cells 426–7 medium/high-loss materials 423 Q-factor (Quality Factor) measurement 427–9 dielectric waveguide 154–5 diode power sensors 333 dispersion, waveguides 148 dispersion effect, transmission lines with losses 9–10 DMMs (digital multimeters) 122, 124–5 digitising DMMs 124–5 DVMs (digital voltmeters) 97–8 effective directivity 274, 277, 293–6 E-field strength traceability 460–4 about E-field strength 460 with electro-optic sensors 469–70 high feed impedance half wave dipole 460–1 TEM cell, calculable field 462 three-antenna method 461–2 two resonant dipole antennas, coupling calculability 462 uncertainty budget 462–4 see also AFs (antenna factors); EMC (electromagnetic compatibility) measurement/testing electrical conduction/conductivity 418 electrical sampling scanning-force microscopy 254
Index 477 electric-field probing 251–4 electron beam probing 251 electro-optic sampling 252–4 electro-optic sensors, and E-field strength traceability 469–70 EMC (electromagnetic compatibility) measurement/testing 459–70 about EMC testing 459–60 with spectrum analysers 392, 392–3 see also AFs (antenna factors); E-field strength traceability ENR (excess noise ratio) 160, 163 equivalent circuit modelling (ECM) 226–8 error term verification for two port measurements 293–300 effective directivity 293–6 effective source match 296–9 offset load/airline method 295–6 sliding load method 294–5 time domain gating 297–8 effective isolation 299 effective linearity 300 effective load match 299 time domain and de-embedding 300 transmission and reflection tracking 299–300 Far End Crosstalk (FEXT) measurements 320 fast sampling DMMs 124–5 FFTs (fast Fourier transforms) 401 finline transmission line 154 flicker noise 159 FM discriminators 404–5 free space permeability 10–11 frequency modulation analysis, with spectrum analysers 384–5 frequency response analysers (FRAs) 426 frequency spectrum 122 frequency stability/phase noise: see phase noise/frequency stability measurement Fresnel’s equations 416 gas discharge tubes 163 Gaussian distributions 46–7 probability density function 158 generalised scattering parameters 22–4 generator measurement tracking, with spectrum analysers 378–9 GPCs (general precision connectors) 160, 185
group velocity, waveguides 16 GSM pulse specification 346 GUM (Guide to the Expression of Uncertainty in Measurement) 43–52 see also uncertainty and confidence in measurements Gunn diodes 246 Hakki-Colemen cell 443 harmonic content, with voltage measurement 137–8 harmonic distortion measurement, with spectrum analysers 378 Hartshorn and Ward (H & W) technique 432–3 HEMT technology 248 hermaphroditic (non-sexed) connectors 60 see also coaxial connectors high feed impedance half wave dipole 460–1 impedance and admittance parameters 24–7 inductive voltage divider: see attenuation measurement systems insertion loss 91–3 interfacial polarisation 418 intermodulation measurement/analysis, with spectrum analysers 380–2 intrinsic impedance 11 inverse Fourier transform (IFT) 221 Josephson Junction 460 Kramers-Kronig relations 421–2 Kuhn’s rules, signal flow graphs 37 Lorentz reciprocity relation 37–8 losslessness, scattering parameters 39–40 loss tangent 412 LPCs (laboratory precision connectors) 160, 185 LPDA (log-period dipole array) antennas, with EMC testing 459–60, 467 magnetic-field probing 250–1 magnetic hysteresis 412 Maxwell’s equations 11 Maxwell-Wagner effect 418
478 Index measurement verification 301–4 about measurement verification 301 customised verification example 301–2 manufacturer supplied verification example 302–4 MEMS (Micro Electro-Mechanical Systems) 336 microbolometers 249 microradian 412 microstrip transmission lines, structures and properties 151–2 dispersion 152 microwave frequency spectrum 122 microwave network analysers: see network analysers microwave voltage measurement: see voltage measurement mismatched loads, one-port devices 20 mismatch error 92–3 mixed-mode-S-parameter-matrix 318–19 MMIC (monolithic microwave integrated circuit) (or RFIC) 217–55 about S-parameter measurement 217–18, 254–5 bolometers/microbolometers 249 cryogenic measurements 247–8 HEMT technology 248 dielectric rod probe 249–50 electric-field probing 251–4 electrical sampling scanning-force microscopy 254 electron beam probing 251 electro-optic sampling 252–4 opto-electronic sampling 252 photo-emissive sampling 252 electromagnetic field probing 249–50 magnetic-field probing 250–1 thermal measurements 246–7 Cascade Microtech Summit Evue system 247 Cascade Microtech Summit S300-863 system 246 Gunn diodes 246 MMIC/RFIC probe station measurements 230–45 about probe station measurements 230–1 advantages of probe station measurements 231 DC biasing 240–1 layout considerations 241–3
low-cost multiple DC biasing technique 243 measurement errors 240 passive microwave probe design 231–6 ACP probe (Cascade Microtech) 233–5 Picoprobe™ (GGB) 232 tapered coplanar waveguide (CPW) probes 231–2 waveguide input infinity probe 231–5 probe calibration 236–40 about probe calibration 236–8 automated probes 239–40 LRM technique 238–9 Short Open Load Reflect routine 240 SOLT technique 238 stability checking 240 TRL technique 238–9 upper-millimetre-wave measurements 243–5 MMIC/RFIC test fixture measurements 218–30 about test fixture measurements 218–20 calibration kits 219 calibration methods summary 219–20 one-tier calibration 229–30 text fixture design guidelines 230 two-tier calibration 220–8 banded VNA 221 broadband VNA 221 equivalent circuit modelling (ECM) 226–8 in-fixture calibration 225–6 synthetic-pulse TD reflectometry 221 T-D reflectometry (TDR) 221–5 time domain gating 221–5 VNA reference planes 220 modal decomposition method for characterisation 312–18 monopole wire antennas, with EMC testing 459 Near End Crosstalk (NEXT) measurements 320 network analysers 108–9, 207–16 about network analysers 207–8 block diagrams 208, 214–16 built-in signal source 209 coupling factor 209–10
Index 479 diode detectors 211–12 directional bridge 210–11 directional coupler 209–10 dynamic range 214 reference plane 208 sampler systems 213–14 signal separation hardware 209–11 tuned receivers 212–14 see also automatic network analysers (ANAs); scalar network analysers; vector network analysers network analysis characterisation 310 noise 157–64 about noise 157–8 available noise power 160 effective noise power 160 ENR (excess noise ratio) 160, 163 equivalent input noise temperature 161 flicker noise 159 Gaussian distribution probability density function 158 noise factor/figure 161–2 noise performance of receivers 161 noise temperature 162 quantum noise temperature 159 and sensitivity 157 shot noise 159 thermal noise 158–9 noise measurement 164–76 accuracy of measurement 166–71 automated measurement 174–6 noise figure meters/analysers 175 on-wafer measurements 175–6 cascaded receivers 169 correlated noise 173 Dicke (switching) radiometer 164, 166 mismatch effects/factor 171–4 noise resistance 173 passive two-ports 169–71 radiometer sensitivity 166 receivers and amplifiers 172–4 total power radiometer 164–6 uncertainties (type A and B) 167–9 noise sources 162–4 about thermal noise 162 avalanche diodes 163–4 gas discharge tubes 163 temperature-limited diodes 163 Nomographs, with spectrum analysers 383 n-port devices, scattering parameters 24–7
Omni-Spectra SMA connector/wedge-shaped board socket 228 one-port devices/error models 19–22, 273–6 characteristic impedance 21–2 effective directivity 274, 277 frequency response (tracking) error 275 mismatched loads 20 open circuit termination model 276, 278 ‘perfect load’ termination model 276 phasor notation 21 power 21–2 reflection coefficient 20–1, 273–5 short circuit termination model 276, 278 see also transmission lines opto-electronic sampling 252 oscillator phase noise performances 396–7 see also phase noise/frequency stability measurement oscilloscopes for voltage measurement 127–9 analogue 128–9 calibrator calibration 138–40 digital 128–9 sampling 129 switched input impedance 129–30 permeability of a medium 10–11 permittivity 11, 410–11 absolute permittivity 410 permittivity of free space 11, 410 relative permittivity 11, 410 phase constant/wave number 11 phase locked loops 402–3 phase noise/frequency stability measurement 395–407 about phase noise 395–6, 406–7 delay line discriminator technique 400–1 FM discriminator method 404–5 future possible methods 406 measurement uncertainty issues 405–6 oscillator phase noise performances 396–7 quadrature technique 401–3 fast Fourier transforms (FFTs) 401 phase locked loops 402–3 spectrum analyser techniques 397–9 improvement with band-pass filters 399–400 limitations 398 summary of methods 406–7 phase velocity/phase constant, lossless transmission lines 5–6
480 Index phase velocity, waveguides 15 phasor notation 21 photo-emissive sampling 252 Picoprobe™ (GGB) 232 Planck’s constant 159 plane/transverse electromagnetic (TEM) waves 10–12 polar/non-polar materials 418 power flow, sinusoidal waves, lossless transmission lines 6–7 power measurement: see RF power measurement power sensors 333–6 acoustic meters 336 calorimeters 334–6 diode sensors 333 flow calorimeters 334–6 force and field based sensors 336 MEMS (Micro Electro-Mechanical Systems) 336 microcalorimeters 334 thermistors/bolometers 333–4 thermocouples/thermoelectric sensors 333 twin load calorimeters 334 power splitters 339–43 direct method for splitter output 341–3 output match measurement 340–1 splitter properties 340 two resistor splitters 339–40 probe station measurements: see MMIC/RFIC probe station measurements pulsed modulation display/analysis 389–91 pulsed power 344–6 Q-factor (Quality Factor) measurement 417, 427–9, 443 quantum noise temperature 159 radiation absorbing materials (RAM) 412 radio frequency integrated circuit (RFIC): see MMIC radiometers: see noise measurement reciprocity 37–8 rectangular metallic waveguides: see waveguides, rectangular metallic reference plane 208 reflection coefficient lossless transmission lines 5 one-port devices 20–1
reflectometers, power measurement 343–4 return loss, lossless transmission lines 7 RF frequency spectrum 122 RFIC (radio frequency integrated circuit): see MMIC RF impedance air lines 195–8 lossless lines 194–5 lossy lines 195–8 historical perspective 181–2 terminations 198–200 mismatched terminations 199–200 near-matched terminations 199 open-circuits 198–9 short-circuits 198 RF millivoltmeters 125–6 RF power measurement 329–46 basic theory 329–32 calibration factor 332 calibration/transfer standards 338–9 couplers 343–4 direct power measurement 337 effective efficiency 332 GSM pulse specification 346 incident, reflected and delivered power 330–1 mismatch uncertainty 332 pulsed power 344–6 ratio measurements 338–9 reflectometers 343–4 substitution techniques 330 uncertainty budgets 337–8 see also power sensors; power splitters RF voltage measurement: see voltage measurement ridged waveguides 150–1 ring resonators 437 Roberts and Von Hippel method 438 rotational polarisation 418 sampling RF voltmeters 126–7 scalar network analysers 263–6 applied power level problem 269 calibration reflection measurements 267–8 transmission measurements 267 fully integrated analysers 265–6 limited dynamic range problem 269 see also network analysers; vector network analysers (VNAs)
Index 481 scattering parameters: see S-parameters (scattering parameters) self parameters 310 shot noise 159 signal flow graphs, scattering parameters 36–7 Kuhn’s rules 37 skin effect 2 slot guides, structure and properties 152–3 SMA printed circuit board socket 228 S-parameters (scattering parameters) about S-parameters 19 generalised S-parameters 22–4 impedance and admittance parameters 24–7 losslessness 39–40 measurements with MMIC/RFIC 217–18 wave methods 414 n-port devices 24–7 reciprocity 37–8 self parameters 310 signal flow graphs 36–7 two-port networks 22–4 two-port transforms 40 see also one-port devices S-parameter matrix (scattering matrix) about S-parameters 23–4 cascade matrix 27–8 de-embedding 29–30 mixed-mode-S-parameter-matrix 318 network parameter examples 26–7 renormalisation 28–9 see also characteristic impedance S-parameters equations, two-port error model 283–4 spectrum analysers, applications 376–93 amplitude modulation measurement 383–4 EMC measurements 392–3 FM demodulation 386–7 frequency modulation analysis 384–5 with Bessel zero method 385–6 generator measurement tracking 378–9 harmonic distortion measurement 378 intermodulation intercept point 382–3 intermodulation measurement/analysis 380–2 meter mode 379–80 modulation AM/FM asymmetry 387–8 nomograph usage 383 overload dangers 392–3
phase noise/frequency stability measurement 397–9 pulsed modulation display/analysis 389–91 square wave spectrum 388–9 zero span mode 378–80 spectrum analysers, facilities and use 349–59 amplitude modulation analysis 351–3 basic usage 349–50 block diagram/description 354, 356–8 harmonic mixer concept 354–5 multiple responses problem 355–6 tracking generator 358–9 tracking preselectors 356 measurement domains 350 and network analysers 207–8 oscilloscope amplitude/time display 350–2 for amplitude modulation 351–2 pre-calibration (Auto Cal) 349–50 spectrum analyser amplitude/frequency display 351 for amplitude modulation 353 spectrum analysers, specification points 359–76 about the main controls 359 amplitude accuracy 372 display detection mode 376–7 dynamic range 366–72 intermodulation and distortion 367–8 internal distortion checking 371–2 local oscillator phase noise 369–70 noise 368–9 sideband noise 370–1 input attenuator/IF gain 360 input VSWR effect 372–3 noise/low-level signals 366 residual FM 374–5 residual responses 373–4 resolution bandwidth 361–2 shape factor 362–4 sideband noise characteristics 373, 374 sweep speed/span 360–1 uncertainty contributions 375–7 video averaging 365–6 video bandwidths 365 split-post dielectric resonators (SPDR) 436–7 square wave spectrum analysis 388–9 standing waves from sinusoidal waves, lossless transmission lines 7–8 switching (Dicke) radiometer 164, 166 synthetic-pulse TD reflectometry 221
482 Index tapered coplanar waveguide (CPW) probes 231–2 TDD (time-domain duplex) techniques 396 TDMA (time-domain multiple access) techniques 396 T-D reflectometry (TDR) 221–5 error sources 223–5 Telegraphist’s equations transmission lines, lossless 3–4, 9 transmission lines with losses 9 TEM: see transverse electromagnetic (TEM) cell/waves temperature-limited diodes 163 test fixture measurements: see MMIC/RFIC test fixture measurements thermal noise 158–9 thermal voltage converters (TVCs) 122–3 thermistors/bolometers 333–4 thermocouples/thermoelectric sensors 333 three-antenna method for E-field strength 461–2 time domain and de-embedding 300 time domain gating 221–5, 297–8 transmission lines, lossless waveguides: see one-port devices; waveguides, lossless transmission lines, structures and properties 147–55 about transmission lines 147–8 coaxial lines 148–50 coplanar waveguides 153–4 dielectric waveguide 154–5 finline 154 higher mode operation 148 microstrip 151–2 rectangular waveguides 150 ridged waveguides 150–1 slot guides 152–3 waveguide dispersion 148 transmission lines, two-conductor lossless basic principles 1–4 characteristic impedance 4 equivalent circuit 1–2 phase velocity/phase constant 5–6 power flow, sinusoidal waves 6–7 reflection coefficient 5 return loss 7 skin effect 2 standing waves from sinusoidal waves 7–8 Telegraphist’s equations 3–4
Voltage Standing Wave Ratio (VSWR) 7–8 wave equations 3–4 transmission lines, two-conductor with losses basic principles 8–9 dispersion effect 9–10 equivalent circuit 8 pulses, effect on 9–10 sinusoidal waves, general solution 10 Telegraphist’s equations 9 transverse electromagnetic (TEM) cell/waves 10–12, 19, 307 calculable field 462 transverse electromagnetic (TEM) waveguides, and E-field traceability 469–70 TRL calibration 284–9 basic principles 284–6 calibration procedure 287–9 four receiver operation 286–7 isolation 286 source match/load match 286 two-port error model for measurement 279–84 error sources 279–80 leakage/isolation 281–2 S-parameters equations 283–4 ‘through’ measurement 283 transmission coefficient 280 two-port networks, generalised scattering parameters 22–4 two-port transforms, scattering parameters 40 UHF measurement uncertainty 461 uncertainty analysis, voltage measurement 136–7 uncertainty budgets, RF power measurement 337–8 uncertainty and confidence in measurements 43–57 Central Limit Theorem 46, 50–1 combined standard uncertainty 50–1 coverage factor 51–2 expanded uncertainty 51 expectation value 45 flagpole example 48–51 GUM Type A and Type B evaluations 44 imperfect matching 45 normal distributions 46, 49, 51–2 normal/Gaussian probability distributions 47
Index 483 probability distributions 45–6 and standard uncertainties 49 purpose of measurement 44 quantity (Q) in uncertainty evaluation 43 sensitivity coefficients 48, 50 standard uncertainty 44 temperature uncertainty 48 uncertainty budget 56 U-shaped distributions 47 voltage reflection coefficients (VRCs) 53 uncertainty sources in RF and microwaves 52–7 calibration of coaxial power example 54–7 uncertainty budget 56 directivity 54 RF connector repeatability 54 RF mismatch errors 52–4 test port match 54 vector network analysers (VNAs) about VNAs 108–9, 266 calibration/accuracy enhancement 269–73 correctable systematic errors 270 directivity issues 270–1 frequency response (tracking) 273 isolation (crosstalk) 273 load match 272–3 non-repeatable random and drift errors 270 source match 271–2 VNA reference planes 220–1 see also calibration of automatic network analysers; MMIC; network analysers; one-port devices/error models; two-port error model for measurement; verification of automatic network analysers vector voltmeters 127–8 verification of automatic network analysers 291–304 about verification 291–3 calibration and verification 293 definition 291 see also error term verification; measurement verification; network analysers VHF measurement uncertainty 461 virtual ideal transformers 311 voltage measurement 121–43 about RF/microwave voltage measurement 121–2
capacitive loading 132–3 digital multimeters (DMMs) 122 digitising DMMs 124–5 fast sampling DMMs 124–5 input impedance effects 130–2 oscilloscopes, analogue/digital/sampling 127–9 switched input impedance 129–30 rectifier implementation 123–4 RF millivoltmeters 125–6 sampling RF voltmeters 126–7 source loading and bandwidth 132–3 thermal voltage converters (TVCs) 122–3 traceability 133–5 with micropotentiometers 134–5 with thermal converters 133–4 vector voltmeters 127–8 voltage standing wave ratio (VSWR) 129–31 wideband AC voltmeters 122–4 voltage measurement impedance matching/mismatch errors 135–43 about impedance matching/mismatch 135–6 harmonic content errors 137–8 oscilloscope calibration example 138–41 RF millivoltmeter calibration 140–3 uncertainty analysis considerations 136–7 oscilloscope bandwidth test example 137 VSWR issues 136 VSWR (voltage standing wave ratio) impedance matching issues 136 lossless transmission lines 7–8 oscilloscope voltage measurement 129–31 wave equations 3–4 waveguide, dielectric 154–5 waveguide dispersion 148 waveguide input infinity probe 231–5 waveguides, coplanar, structures and properties 153–4 waveguides, lossless 10–12 intrinsic impedance 11 permeability 10–11 phase constant/wave number 11 plane/transverse electromagnetic (TEM) waves 10–12 waveguides, rectangular metallic 12–17, 150 about rectangular waveguides 12–14
484 Index applications 150 cut-off frequency and wavelength 14–15, 17 general solution 16–17 group velocity 16 phase velocity 15 plane waves in 12–13
properties 150 reflection within 12–13 wave impedance 15–16 waveguides, ridged 150–1 wave impedance, waveguides 15–16 wave number 11 wideband AC voltmeters 122–4