IET ELECTRICAL MEASUREMENT SERIES 12 Microwave Measurements 3rd Edition Other volumes in this series: Volume 4 The current comparator W.J.M. Moore and P.N. Miljanic Volume 5 Principles ofmicrowave measurements G.H. Bryant Volume 7 Radio frequency and microwave power measurement A.E. Fantom Volume 8 A handbook for EMC testing and measurement D. Morgan Volume 9 Microwave circuit theory and foundations of microwave metrology G. Engen Volume 11 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 © 2007The 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 xvii Preface xix 1 Transmission lines – basic principles 1 R. J. Collier 1.1 Introduction 1 1.2 Lossless two-conductor transmission lines – equivalent circuit and velocity of propagation 1 1.2.1 Characteristic impedance 4 1.2.2 Reflection coefficient 5 1.2.3 Phase velocity and phase constant for sinusoidal waves 5 1.2.4 Power flow for sinusoidal waves 6 1.2.5 Standing waves resulting from sinusoidal waves 7 1.3 Two-conductor transmission lines with losses – equivalent circuit and low-loss approximation 8 1.3.1 Pulses on transmission lines with losses 9 1.3.2 Sinusoidal waves on transmission lines with losses 10 1.4 Lossless waveguides 10 1.4.1 Plane (or transverse) electromagnetic waves 10 1.4.2 Rectangular metallic waveguides 12 1.4.3 The cut-off condition 14 1.4.4 The phase velocity 15 1.4.5 The wave impedance 15 1.4.6 The group velocity 16 1.4.7 General solution 16 Further reading 17 2 Scattering parameters and circuit analysis 19 P. R. Young 2.1 Introduction 19 2.2 One-port devices 19 vi Contents 2.3 Generalised scattering parameters 22 2.4 Impedance and admittance parameters 24 2.4.1 Examples of S-parameter matrices 27 2.5 Cascade parameters 27 2.6 Renormalisation of S-parameters 28 2.7 De-embedding of S-parameters 29 2.8 Characteristic impedance 30 2.8.1 Characteristic impedance in real transmission lines 30 2.8.2 Characteristic impedance in non-TEM waveguides 33 2.8.3 Measurement of Z0 35 2.9 Signal flow graphs 36 Appendices 37 2.A Reciprocity 37 2.B Losslessness 39 2.C Two-port transforms 40 References 41 Further reading 41 3 Uncertainty and confidence in measurements 43 John Hurll 3.1 Introduction 43 3.2 Sources of uncertainty in RF and microwave measurements 52 3.2.1 RF mismatch errors and uncertainty 52 3.2.2 Directivity 54 3.2.3 Test port match 54 3.2.4 RF connector repeatability 54 3.2.5 Example – calibration of a coaxial power sensor at a frequency of 18 GHz 54 References 56 4 Using coaxial connectors in measurement 59 Doug Skinner 4.1 Introduction 59 4.1.1 Coaxial line sizes 60 4.2 Connector repeatability 61 4.2.1 Handling of airlines 61 4.2.2 Assessment of connector repeatability 61 4.3 Coaxial connector specifications 62 4.4 Interface dimensions and gauging 62 4.4.1 Gauging connectors 62 4.5 Connector cleaning 63 4.5.1 Cleaning procedure 64 4.5.2 Cleaning connectors on static sensitive devices 64 4.6 Connector life 65 Contents vii 4.7 Adaptors 65 4.8 Connector recession 65 4.9 Conclusions 66 4.A Appendix A 66 4.B Appendix B 66 4.C Appendix C 85 4.D Appendix D 86 4.E Appendix E 87 Further reading 88 5 Attenuation measurement 91 Alan Coster 5.1 Introduction 91 5.2 Basic principles 91 5.3 Measurement systems 93 5.3.1 Power ratio method 94 5.3.2 Voltage ratio method 97 5.3.3 The inductive voltage divider 98 5.3.4 AF substitution method 104 5.3.5 IF substitution method 105 5.3.6 RF substitution method 107 5.3.7 The automatic network analyser 108 5.4 Important considerations when making attenuation measurements 110 5.4.1 Mismatch uncertainty 110 5.4.2 RF leakage 112 5.4.3 Detector linearity 112 5.4.4 Detector linearity measurement uncertainty budget 114 5.4.5 System resolution 115 5.4.6 System noise 115 5.4.7 Stability and drift 115 5.4.8 Repeatability 115 5.4.9 Calibration standard 116 5.5 A worked example of a 30 dB attenuation measurement 116 5.5.1 Contributions to measurement uncertainty 117 References 119 Further reading 120 6 RF voltage measurement 121 Paul C. A. Roberts 6.1 Introduction 121 6.2 RF voltage measuring instruments 122 6.2.1 Wideband AC voltmeters 122 6.2.2 Fast sampling and digitising DMMs 124 viii Contents 6.2.3 RF millivoltmeters 125 6.2.4 Sampling RF voltmeters 126 6.2.5 Oscilloscopes 127 6.2.6 Switched input impedance oscilloscopes 129 6.2.7 Instrument input impedance effects 130 6.2.8 Source loading and bandwidth 132 6.3 AC and RF/microwave traceability 133 6.3.1 Thermal converters and micropotentiometers 133 6.4 Impedance matching and mismatch errors 135 6.4.1 Uncertainty analysis considerations 136 6.4.2 Example: Oscilloscope bandwidth test 137 6.4.3 Harmonic content errors 137 6.4.4 Example: Oscilloscope calibrator calibration 138 6.4.5 RF millivoltmeter calibration 140 Further reading 143 7 Structures and properties of transmission lines 147 R. J. Collier 7.1 Introduction 147 7.2 Coaxial lines 148 7.3 Rectangular waveguides 150 7.4 Ridged waveguide 150 7.5 Microstrip 151 7.6 Slot guide 152 7.7 Coplanar waveguide 153 7.8 Finline 154 7.9 Dielectric waveguide 154 References 155 Further reading 156 8 Noise measurements 157 David Adamson 8.1 Introduction 157 8.2 Types of noise 158 8.2.1 Thermal noise 158 8.2.2 Shot noise 159 8.2.3 Flicker noise 159 8.3 Definitions 160 8.4 Types of noise source 162 8.4.1 Thermal noise sources 162 8.4.2 The temperature-limited diode 163 8.4.3 Gas discharge tubes 163 8.4.4 Avalanche diode noise sources 163 Contents ix 8.5 Measuring noise 164 8.5.1 The total power radiometer 164 8.5.2 Radiometer sensitivity 166 8.6 Measurement accuracy 166 8.6.1 Cascaded receivers 169 8.6.2 Noise from passive two-ports 169 8.7 Mismatch effects 171 8.7.1 Measurement of receivers and amplifiers 172 8.8 Automated noise measurements 174 8.8.1 Noise figure meters or analysers 175 8.8.2 On-wafer measurements 175 8.9 Conclusion 176 Acknowledgements 176 References 176 9 Connectors, air lines and RF impedance 179 N. M. Ridler 9.1 Introduction 179 9.2 Historical perspective 180 9.2.1 Coaxial connectors 180 9.2.2 Coaxial air lines 181 9.2.3 RF impedance 181 9.3 Connectors 182 9.3.1 Types of coaxial connector 182 9.3.2 Mechanical characteristics 185 9.3.3 Electrical characteristics 187 9.4 Air lines 188 9.4.1 Types of precision air line 189 9.4.2 Air line standards 190 9.4.3 Conductor imperfections 192 9.5 RF impedance 193 9.5.1 Air lines 194 9.5.2 Terminations 198 9.6 Future developments 200 Appendix: 7/16 connectors 201 References 203 10 Microwave network analysers 207 Roger D. Pollard 10.1 Introduction 207 10.2 Reference plane 208 10.2.1 Elements of a microwave network analyser 208 10.3 Network analyser block diagram 214 Further reading 216 x Contents 11 RFIC and MMIC measurement techniques 217 Stepan Lucyszyn 11.1 Introduction 217 11.2 Test fixture measurements 218 11.2.1 Two-tier calibration 220 11.2.2 One-tier calibration 229 11.2.3 Test fixture design considerations 230 11.3 Probe station measurements 230 11.3.1 Passive microwave probe design 231 11.3.2 Probe calibration 236 11.3.3 Measurement errors 240 11.3.4 DC biasing 240 11.3.5 MMIC layout considerations 241 11.3.6 Low-cost multiple DC biasing technique 243 11.3.7 Upper-millimetre-wave measurements 243 11.4 Thermal and cryogenic measurements 246 11.4.1 Thermal measurements 246 11.4.2 Cryogenic measurements 247 11.5 Experimental field probing techniques 249 11.5.1 Electromagnetic-field probing 249 11.5.2 Magnetic-field probing 250 11.5.3 Electric-field