RED BOX RULES ARE FOR PROOF STAGE ONLY. DELETE BEFORE FINAL PRINTING.

WITH ADVANCED VNA TECHNIQUES

HANDBOOK OF

JOEL P. DUNSMORE

MICROWAVECOMPONENTMEASUREMENTS

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This book will be an invaluable guide for RF and microwave R&D and test engineers, satellite testengineers, radar engineers, power amplifier designers, LNA designers, and mixer designers. Universityresearchers and graduate students in microwave design and test will also find this book of interest.

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This book provides state-of-the-art coverage for making measurements on RF and MicrowaveComponents; both active and passive. A perfect reference for R&D and test engineers, with topicsranging from the best practices for basic measurements, to an in-depth analysis of errors, correctionmethods, and uncertainty analysis, this book provides everything you need to understand microwavemeasurements. With primary focus on active and passive measurements using a vector networkanalyzer, these techniques and analysis are equally applicable to measurements made with spectrumanalyzers or noise figure analyzers.

The early chapters provide a theoretical basis for measurements complete with extensive definitions anddescriptions of component characteristics and measurement parameters. The latter chapters give detailedexamples for cases of cable, connector and filter measurements; low noise, high-gain and high poweramplifier measurements, a wide range of mixer and frequency converter measurements, and a fullexamination of fixturing, de-embedding, balanced measurements and calibration techniques. The chapter on time domain theory and measurements offers a complete treatment on the subject, withdetails of the underlying mathematics and new material on time domain gating. As the inventor ofmany of the methods presented, and with 30 years as a development engineer on the most modernmeasurement platforms, the author presents unique insights into the understanding of modernmeasurement theory.

JOEL P. DUNSMORE, Ph.D., Agilent Fellow, Agilent Technologies, USA

DUNSMORE

WITHADVANCED

VNATECHNIQUES

A practical guide to the most modern techniques for microwave measurements

Key Features:Explains the interactions between the device under test (DUT) and the measuring equipmentby demonstrating the best practices for ascertaining the true nature of the DUT, andoptimizing the time to set up and measureOffers a detailed explanation of algorithms and mathematics behind measurements and error correctionProvides numerous illustrations (e.g., block-diagrams for circuit connections and measurementsetups) and practical examples on real-world devices, which can provide immediate benefitto the readerWritten by the principle developer and designer of many of the measurement methods described

HANDBOOK OF MICROWAVECOMPONENT MEASUREMENTS

HANDBOOK OFMICROWAVE COMPONENTMEASUREMENTS

HANDBOOK OFMICROWAVE COMPONENTMEASUREMENTSWITH ADVANCED VNA TECHNIQUES

Joel P. DunsmorePh.D., Agilent Fellow, Agilent Technologies, USA

A John Wiley & Sons, Ltd., Publication

This edition first published 2012© 2012 John Wiley & Sons, Ltd

Registered officeJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom

For details of our global editorial offices, for customer services and for information about how to apply forpermission to reuse the copyright material in this book please see our website at www.wiley.com.

The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright,Designs and Patents Act 1988.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in anyform or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UKCopyright, Designs and Patents Act 1988, without the prior permission of the publisher.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not beavailable in electronic books.

Designations used by companies to distinguish their products are often claimed as trademarks. All brand names andproduct names used in this book are trade names, service marks, trademarks or registered trademarks of theirrespective owners. The publisher is not associated with any product or vendor mentioned in this book. Thispublication is designed to provide accurate and authoritative information in regard to the subject matter covered. It issold on the understanding that the publisher is not engaged in rendering professional services. If professional adviceor other expert assistance is required, the services of a competent professional should be sought.

Library of Congress Cataloging-in-Publication Data

Dunsmore, Joel P.Handbook of microwave component measurements : with advanced VNA techniques / Joel P. Dunsmore.

pages cmIncludes bibliographical references and index.

ISBN 978-1-119-97955-51. Microwave devices–Testing. I. Title.

TK7876.D84 2012537.5′344–dc23

2012011804

A catalogue record for this book is available from the British Library.

ISBN 9781119979555

Typeset in 10/12pt Times by Aptara Inc., New Delhi, India

To my dear wife Dana

Contents

Foreword xv

Preface xvii

Acknowledgments xix

List of Acronyms xxi

1 Introduction to Microwave Measurements 11.1 Modern Measurement Process 21.2 A Practical Measurement Focus 31.3 Definition of Microwave Parameters 3

1.3.1 S-Parameter Primer 41.3.2 Phase Response of Networks 11

1.4 Power Parameters 131.4.1 Incident and Reflected Power 131.4.2 Available Power 131.4.3 Delivered Power 131.4.4 Power Available from a Network 141.4.5 Available Gain 14

1.5 Noise Figure and Noise Parameters 151.5.1 Noise Temperature 161.5.2 Effective or Excess Input Noise Temperature 161.5.3 Excess Noise Power and Operating Temperature 171.5.4 Noise Power Density 171.5.5 Noise Parameters 18

1.6 Distortion Parameters 181.6.1 Harmonics 191.6.2 Second-Order Intercept 191.6.3 Two-Tone Intermodulation Distortion 20

1.7 Characteristics of Microwave Components 221.8 Passive Microwave Components 23

1.8.1 Cables, Connectors and Transmission Lines 231.8.2 Connectors 281.8.3 Non-Coaxial Transmission Lines 39

1.9 Filters 421.10 Directional Couplers 44

viii Contents

1.11 Circulators and Isolators 461.12 Antennas 471.13 PCB Components 48

1.13.1 SMT Resistors 481.13.2 SMT Capacitors 501.13.3 SMT Inductors 511.13.4 PCB Vias 52

1.14 Active Microwave Components 521.14.1 Linear and Non-Linear 521.14.2 Amplifiers: System, Low Noise, High Power 531.14.3 Mixers and Frequency Converters 541.14.4 Frequency Multipliers and Limiters and Dividers 561.14.5 Oscillators 57

1.15 Measurement Instrumentation 571.15.1 Power Meters 571.15.2 Signal Sources 591.15.3 Spectrum Analyzers 601.15.4 Vector Signal Analyzers 611.15.5 Noise Figure Analyzers 611.15.6 Network Analyzers 62References 64

2 VNA Measurement Systems 662.1 Introduction 662.2 VNA Block Diagrams 67

2.2.1 VNA Source 702.2.2 Understanding Source Match 722.2.3 VNA Test Set 772.2.4 Directional Devices 802.2.5 VNA Receivers 872.2.6 IF and Data Processing 902.2.7 Multiport Extensions 922.2.8 High Power Test Systems 98

2.3 VNA Measurement of Linear Microwave Parameters 982.3.1 Linear Measurements Methods for S-Parameters 992.3.2 Power Measurements with a VNA 1012.3.3 Other Measurement Limitations of the VNA 1042.3.4 Limitations Due to External Components 107

2.4 Measurements Derived from S-Parameters 1082.4.1 The Smith Chart 1082.4.2 Transforming S-Parameters to Other Impedances 1142.4.3 Concatenating Circuits and T-Parameters 115

2.5 Modeling Circuits Using Y and Z Conversion 1172.5.1 Reflection Conversion 1172.5.2 Transmission Conversion 118

Contents ix

2.6 Other Linear Parameters 1182.6.1 Z-Parameters, or Open-Circuit Impedance Parameters 1192.6.2 Y-Parameters, or Short-Circuit Admittance Parameters 1202.6.3 ABCD Parameters 1212.6.4 H-Parameters or Hybrid Parameters 1222.6.5 Complex Conversions and Non-Equal Reference Impedances 123References 123

3 Calibration and Vector Error Correction 1243.1 Introduction 1243.2 Basic Error Correction for S-Parameters: Cal Application 125

3.2.1 Twelve-Term Error Model 1263.2.2 One-Port Error Model 1283.2.3 Eight-Term Error Model 128

3.3 Determining Error Terms: Cal Acquisition for 12-Term Models 1303.3.1 One-Port Error Terms 1313.3.2 One-Port Standards 1323.3.3 Two-Port Error Terms 1403.3.4 Twelve-Term to Eleven-Term Error Model 144

3.4 Determining Error Terms: Cal Acquisition for Eight-Term Models 1443.4.1 TRL Standards and Raw Measurements 1453.4.2 Special Cases for TRL Calibration 1483.4.3 Unknown Thru or SOLR (Reciprocal Thru Calibration) 1493.4.4 Applications of Unknown Thru Calibrations 1513.4.5 QSOLT Calibration 1533.4.6 Electronic Calibration or Automatic Calibration 153

3.5 Waveguide Calibrations 1573.6 Calibration for Source Power 1583.7 Calibration for Receiver Power 164

3.7.1 Some Historical Perspective 1643.7.2 Modern Receiver Power Calibration 1653.7.3 Response Correction for the Transmission Test Receiver 169

3.8 Devolved Calibrations 1723.8.1 Response Calibrations 1723.8.2 Enhanced Response Calibration 174

3.9 Determining Residual Errors 1763.9.1 Reflection Errors 1763.9.2 Using Airlines to Determine Residual Errors 178

3.10 Computing Measurement Uncertainties 1903.10.1 Uncertainty in Reflection Measurements 1903.10.2 Uncertainty in Source Power 1903.10.3 Uncertainty in Measuring Power (Receiver Uncertainty) 191

3.11 S21 or Transmission Uncertainty 1923.12 Errors in Phase 1963.13 Practical Calibration Limitations 197

x Contents

3.13.1 Cable Flexure 1973.13.2 Changing Power after Calibration 1983.13.3 Compensating for Step Attenuator Changes in Step Attenuators 2003.13.4 Connector Repeatability 2033.13.5 Noise Effects 2043.13.6 Drift: Short-Term and Long-Term 2053.13.7 Interpolation of Error Terms 2063.13.8 Calibration Quality: Electronic vs Mechanical Kits 208References 210

4 Time Domain Transforms 2114.1 Introduction 2114.2 The Fourier Transform 212

4.2.1 The Continuous Fourier Transform 2124.2.2 Even and Odd Functions and the Fourier Transform 2124.2.3 Modulation (Shift) Theorem 213

4.3 The Discrete Fourier Transform 2144.3.1 FFT (Fast Fourier Transform) and IFFT

(Inverse Fast Fourier Transform) 2144.3.2 Discrete Fourier Transforms 216

4.4 Fourier Transform (Analytic) vs VNA Time Domain Transform 2164.4.1 Defining the Fourier Transform 2174.4.2 Effects of Discrete Sampling 2174.4.3 Effects of Truncated Frequency 2194.4.4 Windowing to Reduce Effects of Truncation 2224.4.5 Scaling and Renormalization 224

4.5 Low-Pass and Band-Pass Transforms 2244.5.1 Low-Pass Impulse Mode 2244.5.2 DC Extrapolation 2254.5.3 Low-Pass Step Mode 2254.5.4 Band-Pass Mode 227

4.6 Time Domain Gating 2284.6.1 Gating Loss and Renormalization 229

4.7 Examples of Time Domain Transforms of Various Networks 2324.7.1 Time Domain Response of Changes in Line Impedance 2324.7.2 Time Domain Response of Discrete Discontinuities 2334.7.3 Time Domain Responses of Various Circuits 233

4.8 The Effects of Masking and Gating on Measurement Accuracy 2344.8.1 Compensation for Changes in Line Impedance 2344.8.2 Compensation for Discrete Discontinuities 2364.8.3 Time Domain Gating 2374.8.4 Estimating an Uncertainty Due to Masking 241

4.9 Conclusions 241References 242

Contents xi

5 Measuring Linear Passive Devices 2435.1 Transmission Lines, Cables and Connectors 243

5.1.1 Calibration for Low Loss Devices with Connectors 2435.1.2 Measuring Electrically Long Devices 2455.1.3 Attenuation Measurements 2505.1.4 Return Loss Measurements 2665.1.5 Cable Length and Delay 277

5.2 Filters and Filter Measurements 2785.2.1 Filter Classes and Difficulties 2785.2.2 Duplexer and Diplexers 2795.2.3 Measuring Tunable High-Performance Filters 2805.2.4 Measuring Transmission Response 2825.2.5 High Speed vs Dynamic Range 2875.2.6 Extremely High Dynamic Range Measurements 2905.2.7 Calibration Considerations 298

5.3 Multiport Devices 2995.3.1 Differential Cables and Lines 3005.3.2 Couplers 3005.3.3 Hybrids, Splitters and Dividers 3035.3.4 Circulators and Isolators 306

5.4 Resonators 3075.4.1 Resonator Responses on a Smith Chart 307

5.5 Antenna Measurements 3105.6 Conclusions 312

References 313

6 Measuring Amplifiers 3146.1 Amplifiers as Linear Devices 314

6.1.1 Pretesting an Amplifier 3156.1.2 Optimizing VNA Settings for Calibration 3176.1.3 Calibration for Amplifier Measurements 3186.1.4 Amplifier Measurements 3226.1.5 Analysis of Amplifier Measurements 3286.1.6 Saving Amplifier Measurement Results 338

6.2 Gain Compression Measurements 3426.2.1 Compression Definitions 3426.2.2 AM-to-PM or Phase Compression 3476.2.3 Swept Frequency Gain and Phase Compression 3486.2.4 Gain Compression Application, Smart Sweep and Safe-Sweep Mode 349

6.3 Measuring High-Gain Amplifiers 3546.3.2 Calibration Considerations 357

6.4 Measuring High-Power Amplifiers 3596.4.1 Configurations for Generating High Drive Power 3606.4.2 Configurations for Receiving High Power 3626.4.3 Power Calibration and Pre/Post Leveling 364

xii Contents

6.5 Making Pulsed-RF Measurements 3656.5.2 Pulse Profile Measurements 3696.5.3 Pulse-to-Pulse Measurements 3716.5.4 DC Measurements for Pulsed RF Stimulus 372

6.6 Distortion Measurements 3746.6.1 Harmonic Measurements on Amplifiers 3746.6.2 Two-Tone Measurements, IMD and TOI Definition 3786.6.3 Measurement Techniques for Two-Tone TOI 3826.6.4 Swept IMD 3826.6.5 Optimizing Results 3856.6.6 Error Correction 390

6.7 Noise Figure Measurements 3916.7.1 Definition of Noise Figure 3916.7.2 Noise Power Measurements 3926.7.3 Computing Noise Figure from Noise Powers 3946.7.4 Computing DUT Noise Figure from Y-Factor Measurements 3956.7.5 Cold-Source Methods 3976.7.6 Noise Parameters 3996.7.7 Error Correction in Noise Figure Measurements 4026.7.8 Uncertainty of Noise Figure Measurements 4046.7.9 Verifying Noise Figure Measurements 4056.7.10 Techniques for Improving Noise Figure Measurements 406

6.8 X-Parameters, Load Pull Measurements and Active Loads 4086.8.1 Non-Linear Responses and X-Parameters 4086.8.2 Load Pull, Source-Pull and Load Contours 411

6.9 Conclusions on Amplifier Measurements 416References 417

7 Mixer and Frequency Converter Measurements 4187.1 Mixer Characteristics 418

7.1.1 Small Signal Model of Mixers 4217.1.2 Reciprocity in Mixers 4257.1.3 Scalar and Vector Responses 427

7.2 Mixers vs Frequency Converters 4277.2.1 Frequency Converter Design 4287.2.2 Multiple Conversions and Spur Avoidance 429

7.3 Mixers as a 12-Port Device 4307.3.1 Mixer Conversion Terms 431

7.4 Mixer Measurements: Frequency Response 4347.4.1 Introduction 4347.4.2 Amplitude Response 4347.4.3 Phase Response 4377.4.4 Group Delay and Modulation Methods 4487.4.5 Swept LO Measurements 451

Contents xiii

7.5 Calibration for Mixer Measurements 4557.5.1 Calibrating for Power 4557.5.2 Calibrating for Phase 4577.5.3 Determining the Phase and Delay of a Reciprocal

Calibration-Mixer 4607.6 Mixers Measurements vs Drive Power 472

7.6.1 Mixer Measurements vs LO Drive 4727.6.2 Mixer Measurements vs RF Drive Level 476

7.7 TOI and Mixers 4807.7.1 IMD vs LO Drive Power 4817.7.2 IMD vs RF Power 4817.7.3 IMD vs Frequency Response 484

7.8 Noise Figure in Mixers and Converters 4867.8.1 Y-Factor Measurements on Mixers 4867.8.2 Cold Source Measurements on Mixers 488

7.9 Special Cases 4947.9.1 Mixers with RF or LO Multipliers 4947.9.2 Segmented Sweeps 4957.9.3 Measuring Higher-Order Products 4967.9.4 Mixers with an Embedded LO 5007.9.5 High-Gain and High-Power Converters 503

7.10 Conclusions on Mixer Measurements 504References 505

8 VNA Balanced Measurements 5068.1 Four-Port Differential and Balanced S-Parameters 5068.2 Three-Port Balanced Devices 5118.3 Measurement Examples for Mixed Mode Devices 512

8.3.1 Passive Differential Devices: Balanced Transmission Lines 5128.3.2 Differential Amplifier Measurements 5168.3.3 Differential Amplifiers and Non-Linear Operation 519

8.4 True Mode VNA for Non-Linear Testing 5238.4.1 True Mode Measurements 5268.4.2 Determining the Phase-Skew of a Differential Device 531

8.5 Differential Testing Using Baluns, Hybrids and Transformers 5338.5.1 Transformers vs Hybrids 5338.5.2 Using Hybrids and Baluns with a Two-Port VNA 537

8.6 Distortion Measurements of Differential Devices 5398.6.1 Comparing Single Ended IMD Measurement

to True Mode Measurements 5418.7 Noise Figure Measurements on Differential Devices 544

8.7.1 Mixed Mode Noise Figure 5458.7.2 Measurement Setup 546

8.8 Conclusions on Differential Device Measurement 550References 550

xiv Contents

9 Advanced Measurement Techniques 5529.1 Creating Your Own Cal Kits 552

9.1.1 PCB Example 5539.1.2 Evaluating PCB Fixtures 554

9.2 Fixturing and De-embedding 5699.2.1 De-embedding Mathematics 570

9.3 Determining S-Parameters for Fixtures 5729.3.1 Fixture Characterization Using One-Port Calibrations 573

9.4 Automatic Port Extensions 5789.5 AFR: Fixture Removal Using Time Domain 5839.6 Embedding Port-Matching Elements 5889.7 Impedance Transformations 5919.8 De-embedding High-Loss Devices 5929.9 Understanding System Stability 595

9.9.1 Determining Cable Transmission Stability 5959.9.2 Determining Cable Mismatch Stability 5969.9.3 Reflection Tracking Stability 597

9.10 Some Final Comments on Advanced Techniques and Measurements 598References 599

Appendix A Physical Constants 600

Appendix B Common RF and Microwave Connectors 601

Appendix C Common Waveguides 602

Appendix D Some Definitions for Calibration Kit Open and Shorts 603

Index 606

Foreword

The electronics industry has undergone revolutionary changes in the past 20 years. Sys-tem performance has significantly advanced, physical size of hardware has shrunk, qualityand reliability have greatly improved and manufacturing costs have dramatically decreased.Underlying these advances has been the phenomenal growth in RF test and measurement capa-bility. Modern-day RF test equipment has progressed to the point where it is not uncommon tomeasure signals below −100 dBm at milliseconds speed. Even more astounding is the abilityto marry RF test capability with analysis software whereby test equipment can produce linearand non-linear models of the device under test to significantly improve the life of the designengineer, using this capability.

RF and microwave components have played an important role in this revolutionary change.Component size has shrunk, parasitics have been reduced, quality standards have greatly im-proved and costs have reduced ten-fold. At the same time, test fixtures and interconnectshave improved to enable a higher level of precision during characterization and productionmeasurement. In parallel with these advances, test equipment has improved to an extent wherethere has been a revolution in the capabilities to make precise and fast measurements of RFand microwave components. The success of a manufacturer of RF and microwave componentsis directly linked to the quality and capability of measuring component performance duringthe design, qualification and production phase of the product life cycle. From a practical pointof view, the testing must be fast (1–2 seconds), the accuracy very precise (hundredths ofa dB), with a high degree of repeatability. Each phase of the life cycle imposes its uniquerequirements for measurement accuracy and data collection.

During the design phase, full characterization of performance, including amplitude andphase, is a must in order to establish a reference for future production runs. So it becomes anecessary requirement to characterize and de-embed the test setup and test fixtures to isolateactual device performance. Fortunately, the modern vector network analyzer provides supportin this regard. Consequently, the performance data obtained during the design phase becomesthe gold standard for evaluating statistical variation obtained from future production lots;and these lots are accepted or rejected based on the statistical results, with sigma generallybeing the statistic most closely watched by the test or QA engineer to evaluate production lotacceptance.

When published specs are provided for a component, it is very important to understandthat these specifications are simply markers which allow for a first impression or summaryreview of the component performance. However, only when performance data and performancegraphs are provided for all parameters, including both amplitude and phase, would the “real”

xvi Foreword

performance of the component be known. Furthermore, in characterizing components for usein customer evaluations, it is important to provide this data both within and outside the specifiedbandwidth. In non-linear components such as a frequency mixer, higher-order harmonics of theRF and LO signals are generated, and depending on the load impedance outside the specifiedfrequency range, these higher-order harmonics can get reflected back into the mixer, causing aninteraction between the desired signals and the unwanted harmonics. Fortunately, modern-dayanalyzers can make these harmonic measurements relatively quickly and easy.

Dr. Dunsmore has captured the essence of modern-day measurements. He provides a prac-tical understanding of measurement capabilities and limitations. He provides a means for thetest engineer to not only make measurements, but also to understand test concepts, anticipatemeasurement results and learn how to isolate and characterize the performance of the DUT,independent of potential errors inherent in the test environment. I am confident that this bookwill serve as a reference for understanding measurement methods, test block diagrams andmeasurement limitations so that correlation between the manufacturer and user would takeplace by using a common reference. This book has the potential to be an invaluable source tofurther the progress of the RF and microwave world.

Harvey KayliePresident and Founder of Mini-Circuits

Preface

This book is a bit of mixture between basic and advanced, and between theoretical and practical.Unfortunately, the dividing lines are not particularly clear, and depend considerably upon thetraining and experience of the reader. While primarily a text about measurement techniques,there is considerable information about device attributes that will be useful to both a designerand a test engineer, as one purpose of device testing is to ascertain the attributes that do notfollow the simplified models commonly associated with those devices. In practice, it is theunexpected responses that consume the majority of the time spent in test and troubleshootingdesigns, particularly related to active devices such as amplifiers and mixers.

The principal instrument for testing microwave components is the vector network analyzer(VNA), and recent advances have increased the test capabilities of this instrument to cover farmore than simple gain and match measurements. As a designer of VNAs for more than 30years, I have been involved in consulting on the widest range of microwave test needs fromcell phone components to satellite multiplexers. The genesis and goal of this book is to provideto the reader a distillation of that experience to improve the quality and efficiency of the R&Dand production test engineer. The focus is on modern test methods; the best practices havechanged with changing instrument capability and occasionally the difference between legacymethods and new techniques is sufficiently great as to be particularly highlighted.

Chapter 1 is intended as an introduction to microwave theory and microwave components.The first half introduces characterization concepts common to RF and microwave work. Someimportant mathematical results are presented which are useful in understanding the resultsof subsequent chapters. The second half of Chapter 1 introduces some common microwaveconnectors, transmission lines and components, as well as providing some discussion of thebasic microwave test instrumentation. This chapter is especially useful to engineers new to RFand microwave testing.

Chapter 2 provides a detailed look into the composition of common VNA designs alongwith their limitations. While this level of detail is not normally needed by the casual user, testengineers trying to understand measurement results at a very precise level will find it usefulto understand how overall results are affected by VNA test configuration. While the modernVNA can make a wide range of measurements, including distortion, power and noise figuremeasurements, still the principal use is in measuring S-parameters. The second half of Chapter2 illustrates many useful parameters derived from basic S-parameters.

Perhaps the most arcane aspect of using VNAs for test is the calibration and error-correctionprocess. Chapter 3 is a comprehensive discussion of the error models for VNAs, calibra-tion methods, uncertainty analysis and evaluation of calibration residuals. This chapter also

xviii Preface

introduces the idea of source and receiver power calibrations, about which, excluding thisbook, very little formal information is currently available. The chapter concludes with manypractical aspects of VNAs that affect the quality of calibrated measurements.

Chapter 4 is likely the most mathematically rigorous, covering the very useful topic oftime domain transforms used in VNAs. The topic of gating, its effects, and compensationmethods is examined in particular. These first four chapters comprise the introductory materialto microwave component measurements.

The remaining chapters are focused on describing particular cases for microwave componentmeasurements. Chapter 5 is devoted to passive microwave components such as cables andconnectors, transmission lines, filters, isolators and couplers. Best practices, and methods fordealing with common problems, are discussed for each component.

Chapter 6 is all about amplifier measurements, and provides the understanding needed forcomplete characterization. In particular, difficulties with measuring high gain and high poweramplifiers are discussed, including pulsed RF measurements. Non-linear measurements suchas harmonics and two tone intermodulation are introduced, and many of the concepts fordistortion and noise measurements are equally valid whether using a spectrum analyzer or amodern VNA for the test receiver.

Chapter 7 extends the discussion of active device test to that of mixers. Because few engi-neers have experience with mixers, and they are often only superficially covered in engineeringcourses, the chapter starts with a detailed discussion of the modeling and characteristics ofmixers and frequency converters. Measurement methods for mixers can be quite complicated,especially for the phase or delay response. Several key methods are discussed, with a newmethod of calibrating, using a phase reference, presented in detail for the first time. Besidesthe magnitude and phase frequency response, methods for measuring mixer characteristicsversus RF and local oscillator power are presented, along with distortion and noise measure-ments. This chapter is required reading for any test engineer dealing with mixers or frequencyconverters.

Chapter 8 brings in the concept of differential and balanced devices, and provides completedetails on the analysis and measurement methods for differential devices including non-linearresponses, noise figure and distortion.

Chapter 9 provides a collection of very useful techniques and concepts for the test engineer,particularly with respect to test fixturing, including a complete discussion of creating in-fixturecalibration kits.

Acknowledgments

Many of my colleagues assisted in the development and review of this book and I would liketo acknowledge their help here. Henri Komrij, my R&D manager, has been a great supporterfrom the initial concept, as well as Greg Peters, VP and general manager of the ComponentsTest Division. Many R&D engineers in our lab contributed to the review of the manuscriptand their expertise in each field is sincerely appreciated: Keith Anderson, Dara Sarislani, DaveBlackham, Ken Wong, Shinya Goto, Bob Shoulders, Dave Ballo, Clive Barnett, Cheng Ning,Xin Chen, Mihai Marcu and Loren Betts. They did an excellent job and any remaining errorsare entirely and regrettably my own.

Many of the new methods and techniques presented here rely on the difficult and preciseimplementation of measurement methods and algorithms and I’d like to thank our softwaredesign team, Johan Ericsson, Sue Wood, Jim Kerr, Phil Hoard, Jade Hughes, Brad Hokkanen,Niels Jensen, Raymond Taylor, Dennis McCarthy, Andy Cannon, Wil Stark, Yu-Chen Hu,Zhi-Wen Wong and Yang Yang, as well as their managers, Sean Hubert, Qi Gao and DexterYamaguchi for all their help over the years in implementing in our products many of thefunctions described here.

Finally I would like to remember here Dr. Roger Pollard, who as my Ph.D. adviser atUniversity of Leeds and as a colleague during his sabbaticals at HP and Agilent Technologies,provided advice, mentoring and friendship; he will be greatly missed.

Joel P. DunsmoreSebastopol, CA

List of Acronyms

ACPL adjacent channel power levelACPR adjacent channel power ratioADC analog-to-digital-converterAFR automatic fixture removalALC automatic level controlAM amplitude modulatedAPE automatic port extensionarb arbitrary-waveform generatorATF A-receiver transmission forwardATS automated test systembalun BALanced-UNbalanced transformerBTF B-receiver transmission forwardBW bandwidthCMRR common mode rejection ratioCPW coplanar waveguideCSV comma separated valuesDANL displayed average noise leveldBc dB relative to the carrierDDS direct-digital synthesizerDFT discrete Fourier transformDUT device under testDUTRNPI DUT relative noise power incidentEcal electronic-calibrationEM electromagneticENR excess noise ratioERC enhanced response calibrationEVM error vector magnitudeFBAR film bulk acoustic resonatorFCA frequency-converter applicationFN fractional-NFOM frequency offset modeFPGA field-programmable gate arrayGCA gain compression applicationGPIO general-purpose input/output

xxii List of Acronyms

GUI graphical user interfaceIBIS input output buffer information specificationIDFT inverse discrete Fourier transformIF intermediate frequencyIFFT inverse fast Fourier transformIFT inverse Fourier transformIIP input intercept pointIM intermodulationIMD intermodulation distortionIM3 third-order IM productIP3 third-order intercept pointIMD intermodulation distortionIPwr input powerKB Kaiser-betaLNA low-noise amplifierLO local oscillatorLTCC low-temperature cofired-ceramicLVDS low voltage differential signalingMMIC monolithic microwave integrated circuitMUT mixer under testNF noise figureNFA noise figure analyzerNOP normal operating pointNVNA non-linear vector network analyzerOPwr output powerPAE power added efficiencyPCB printed circuit boardPIM passive intermodulationPMAR power-meter-as-receiverQSOLT quick short open load thruRBW resolution bandwidthRRF reference-receiver forwardRMS root-mean-squareRNPI relative noise power incidentRTF reference transmission forwardSA spectrum analyzerSAW surface acoustic waveSCF source calibration factorSE single-endedSMC scalar mixer calibrationSMT surface mount technologySMU source measurement unitSNA scalar network analyzerSOLR short open load reciprocalSOLT short open load thruSRF self-resonant frequency

List of Acronyms xxiii

SRL structural return lossSSB single sidebandSSPA solid-state power amplifierSTF source transmission forwardSYSRNPI system relative noise power incidentTD time domainTDR time-domain reflectometerTDT time-domain transmissionTEM transverse-electromagneticTOI third-order intermodulationTR transmission/reflectionTRL thru reflect lineTRM thru reflect matchTVAC thermal vacuumTWT traveling wave tubeUT unknown thruVCO voltage-controlled oscillatorVMC vector mixer/converterVNA vector network analyzerVSA vector signal analyzerVSWR voltage standing wave ratioYIG yttrium-iron-garnetYTO YIG-tuned-oscillator

1Introduction to MicrowaveMeasurements

“To measure is to know.”1 This is a text on the art and science of measurement of microwavecomponents. While this work is based entirely on science, there is some art in the process,and the terms “skilled-in-the-art” and “state-of-the-art” take on particular significance whenviewing the task of measuring microwave components. The goal of this work is to providethe latest, state-of-the-art methods and techniques for acquiring the optimum measurementsof the myriad of microwave components. This goal naturally leads to the use of the vectornetwork analyzer (VNA) as the principal test equipment, supported by the use of power meters,spectrum analyzers, signal sources and noise sources, impedance tuners and other accessories.

Note here the careful use of the word ‘optimum’; this implies that there are tradeoffs betweenthe cost and complexity of the measurement system, the time or duration of the measurement,the analytically computed uncertainty and traceability, and some previously unknown intangi-bles that all affect the overall measurement. For the best possible measurement, ignoring anyconsequence of time or cost, one can often go to national standards laboratories to find thesebest methods, but they would not suit a practical or commercial application. Thus here theattempt is to strike an optimum balance between minimal errors in the measurement and prac-tical consequences of the measurement techniques. The true value of this book is in providinginsight into the wide range of issues and troubles that one encounters in trying to carefullyand correctly ascertain the characteristics of one’s microwave component. The details herehave been gathered from decades of experience in hundreds of direct interactions with actualmeasurements; some problems are obvious and common while others are subtle and rare. It ishoped that the reader will be able to use this handbook to avoid many hours of unproductivetest time.

For the most part, the mathematical derivations in this text are intended to provide thereader with a straightforward connection between the derived values and the underlyingcharacteristics. In some cases, the derivation will be provided in full if it is not accessiblefrom existing literature; in other cases a reference to the derivation will be provided. There

1 Lord Kelvin, “On Measurement”.

Handbook of Microwave Component Measurements: With Advanced VNA Techniques, First Edition. Joel P. Dunsmore.© 2012 John Wiley & Sons, Ltd. Published 2012 by John Wiley & Sons, Ltd.

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are extensive tables and figures, with key sections providing many of the important formulas.The mathematical level of this handbook is geared to a college senior or working engineerwith the intention of providing the most useful formulas in a very approachable way. So, sumswill be preferred to integrals, finite differences to derivatives, and divs, grads and curls will beentirely eschewed.

The chapters are intended to self-standing for the most part. In many cases, there willbe common material to many measurement types, such as the mathematical derivation ofthe parameters or the calibration and error-correction methods, and these will be gatheredin the introductory chapters, though well referenced in the measurement chapters. In somecases, older methods of historical interest are given (there are many volumes on these oldertechniques), but by and large only the most modern techniques are presented. The focus hereis on the practical microwave engineer facing modern, practical problems.

1.1 Modern Measurement Process

Throughout the discussion of measurements a six-step procedure will be followed that appliesto most measurement problems. When approaching a measurement these steps are:

� Pretest: This important first step is often ignored, resulting in meaningless measurementsand wasted time. During the pretest, measurements of the device under test (DUT) areperformed to coarsely determine some of its attributes. During pretest, it is also determinedif the DUT is plugged in, turned on and operating as expected. Many times the gain, matchor power handling is discovered to be different than expected, and much time and effort canbe saved by finding this out early.

� Optimize: Once the coarse attributes of the device have been determined, the measurementparameters and measurement system can be optimized to give the best results for thatparticular device. This might include adding an attenuator to the measurement receiversor adding booster amplifiers to the source, or just changing the number of points in ameasurement to capture the true response of the DUT. Depending upon the device’s particularcharacteristic response relative to the system errors, different choices for calibration methodsor calibration standards might be required.

� Calibrate: Many users will skip to this step, only to find that something in the setup doesnot provide the necessary conditions and they must go back to step one, retest and optimizebefore recalibration. Calibration is the process of characterizing the measurement system sothat systematic errors can be removed from the measurement result. This is not the same asobtaining a calibration sticker for an instrument, but really is the first step, the acquisitionstep of the error correction process that enables improved measurement results.

� Measure: Finally, some stimulus is applied to the DUT and its response to the stimulus ismeasured. During the measurement, many aspects of the stimulus must be considered, aswell as the order of testing and other testing conditions. These include not only the specifictest conditions, but also preconditions such as previous power states to account for non-linearresponses of the DUT.

� Analyze: Once the raw data is taken, error correction factors (the application step of errorcorrection) are applied to produce a corrected result. Further mathematical manipulationson the measurement result can be performed to create more useful figures-of-merit, and the

Introduction to Microwave Measurements 3

data from one set of conditions can be correlated with other conditions to provide usefulinsight into the DUT.

� Save data: The final step is saving the results in a useful form. Sometimes this can be assimple as capturing a screen dump, but often it means saving results in such a way that theycan be used in follow-up simulations and analysis.

1.2 A Practical Measurement Focus

The techniques used for component measurements in the microware world change dramaticallydepending upon the attributes of the components; thus, the first step in describing the optimummeasurement methods is understanding the expected behavior of the DUT. In describingthe attributes and measurements of microwave components it is tempting to go back to firstprinciples and derive all the underlying mathematics for each component and measurementdescribed, but such an endeavor would require several volumes to complete. One could literallywrite a book on the all the attributes of almost any single component, so for this book the focuswill be on only those final results useful for describing practical attributes of the components tobe characterized, and then quote and reference many results without the underlying derivation.

There have been examples of books on microwave measurements that have focused onthe metrology kind of measurements [1] made in national laboratories such as the NationalInstitute for Standards and Technology (NIST, USA), or the National Physical Laboratory(NPL, UK), but the methods used there don’t transfer well – or at all – to the commercialmarket. For the most part, the focus of this book will be on practical measurement examples ofcomponents found in commercial and aerospace/defense industries. The measurements focuswill be commercial characterization rather than the kinds of metrology found in standards labs.

Also, while there has been a great deal written about components in general or ideal terms, aswell as much academic analysis of these idealized components, in practice these componentscontain significant parasitic effects that cause their behavior to differ dramatically from thatdescribed in many textbooks. And, unfortunately, these effects are often not well understood,or are difficult to consider in an analytic sense, and so are only revealed during an actualmeasurement of a physical devices. In this chapter, the idealized analysis of many componentsis described, but the descriptions are extended to some of the real-world detriments that causethese components’ behavior to vary from the expected analytical response.

1.3 Definition of Microwave Parameters

In this section, many of the relevant parameters used in microwave components are derivedfrom the fundamental measurements of voltage and current on the ports. For simplicity, thederivations will focus on measurements made under the conditions of termination in real-valuedimpedances, with the goal of providing mathematical derivations that are straightforward tofollow and readily applicable to practical cases.

In microwave measurements, the fundamental parameter of measurement is power. One ofthe key goals of microwave circuit design is to optimize the power transfer from one circuitto another, such as from an amplifier to an antenna. In the microwave world, power is almostalways referred to as either an incident power or a reflected power, in the context of powertraveling along a transmission structure. The concept of traveling waves is of fundamental

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importance to understanding microwave measurements, and to engineers who haven’t had acourse on transmission lines and traveling waves – and even to some who have – the conceptof power flow and traveling waves can be confusing.

1.3.1 S-Parameter Primer

S-parameters have been developed in the context of microwave measurements, but have aclear relationship to voltages and currents that are the common reference for most electricalengineers. This section will develop the definition of traveling waves, and from that the defini-tion of S-parameters, in a way that is both rigorous and hopefully intuitive. The developmentwill be incremental, rather than just quoting results, in hopes of engendering an intuitiveunderstanding.

This signal traveling along a transmission line is known as a traveling wave [2], and hasa forward component and a reverse component. Figure 1.1 shows the schematic a two-wiretransmission structure with a source and a load.

If the voltage from the source is sinusoidal, it is represented by the phasor notation

vs(t) = Re(|Vs| e j(ωt+φ)

), or Vs = |Vs| e j(ωt+φ) (1.1)

The voltage and current at the load are

VL = |VL| e jφVL , IL = |IL| e jφI

L (1.2)

The voltage along the line is defined as V(z) and the current at each point is I(z). Theimpedance of the transmission line is as described in Section 1.2.1, Eqs. (1.3), (1.4) and (1.5),provides for a relationship between the voltage and the current. At the reference point, thetotal voltage is V(0), and is equal to V1; the total current is I(0). The power delivered to theload can be described as

PL = PF − PR (1.3)

Where PF is called the forward power and PR is called the reverse power. To put this in termsof voltage and current of Figure 1.1, the total voltage at the port can be defined as the sum ofthe forward voltage wave traveling into the port and the reverse voltage wave emerging fromthe port

V1 = VF + VR (1.4)

Figure 1.1 Voltage source and two-wire system.