MICROWAVE DEVICES, CIRCUITS AND SUBSYSTEMS FOR COMMUNICATIONS ENGINEERING Edited by I. A. Glover, S. R. Pennock and P. R. Shepherd All of Department of Electronic and Electrical Engineering University of Bath, UK Copyright © 2005 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. 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This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production. Preface xvii Preface This text originated from a Master’s degree in RF Communications Engineering offered since the mid-1980s at the University of Bradford in the UK. The (one-year) degree, which has now graduated several hundred students, was divided into essentially three parts: Part 1 – RF devices and subsystems Part 2 – RF communications systems Part 3 – Dissertation project. Part 1 was delivered principally in Semester 1 (October to mid-February), Part 2 in Semester 2 (mid-February to June) and Part 3 during the undergraduate summer vacation (July to September). Parts 1 and 2 comprised the taught component of the degree consisting of lectures, tutorials, laboratory work and design exercises. Part 3 comprised an indi- vidual and substantial project drawing on skills acquired in Parts 1 and 2 for its successful completion. In the mid-1990s it was decided that a distance-learning version of the degree should be offered which would allow practising scientists and technologists to retrain as RF and microwave communications engineers. (At that time there was a European shortage of such engineers and the perception was that a significant market existed for the conversion of numerate graduates from other disciplines, e.g. physics and maths, and the retraining of existing engineers from other specialisations, e.g. digital electronics and software design.) In order to broaden the market yet further, it was intended that the University of Bradford would collaborate with other European universities running similar degree programmes so that the text could be expanded for use in all. The final list of collaborating institu- tions was: University of Bradford, UK University of Cantabria, Spain University of Bologna, Italy Telecommunications Systems Institute/Technical University of Crete, Greece Microwave Devices, Circuits and Subsystems for Communications Engineering is a result of this collaboration and contains the material delivered in Part 1 of the Bradford degree plus additional material required to match courses delivered at the other institutions. xviii Preface In addition to benefiting students studying the relevant degrees in the collaborating insti- tutions, it is hoped that the book will prove useful to both the wider student population and to the practising engineer looking for a refresher or conversion text. A companion website containing a sample chapter, solutions to selected problems and figures in electronic form (for the use of instructors adopting the book as a course text) is available at ftp://ftp.wiley.co.uk/pub/books/glover. Contents v Contents List of Contributors xv Preface xvii 1 Overview 1 I. A. Glover, S. R. Pennock and P. R. Shepherd 1.1 Introduction 1 1.2 RF Devices 2 1.3 Signal Transmission and Network Methods 4 1.4 Amplifiers 5 1.5 Mixers 6 1.6 Filters 7 1.7 Oscillators and Frequency Synthesisers 7 2 RF Devices: Characteristics and Modelling 9 A. Suarez and T. Fernandez 2.1 Introduction 9 2.2 Semiconductor Properties 10 2.2.1 Intrinsic Semiconductors 10 2.2.2 Doped Semiconductors 13 2.2.2.1 N-type doping 13 2.2.2.2 P-type doping 14 2.2.3 Band Model for Semiconductors 14 2.2.4 Carrier Continuity Equation 17 2.3 P-N Junction 18 2.3.1 Thermal Equilibrium 18 2.3.2 Reverse Bias 21 2.3.3 Forward Bias 23 2.3.4 Diode Model 24 2.3.5 Manufacturing 25 2.3.6 Applications of P-N Diodes at Microwave Frequencies 26 2.3.6.1 Amplitude modulators 28 2.3.6.2 Phase shifters 29 2.3.6.3 Frequency multipliers 30 2.4 The Schottky Diode 32 2.4.1 Thermal Equilibrium 32 2.4.2 Reverse Bias 34 vi Contents 2.4.3 Forward Bias 35 2.4.4 Electric Model 36 2.4.5 Manufacturing 37 2.4.6 Applications 37 2.4.6.1 Detectors 38 2.4.6.2 Mixers 39 2.5 PIN Diodes 40 2.5.1 Thermal Equilibrium 40 2.5.2 Reverse Bias 40 2.5.3 Forward Bias 41 2.5.4 Equivalent Circuit 43 2.5.5 Manufacturing 44 2.5.6 Applications 45 2.5.6.1 Switching 45 2.5.6.2 Phase shifting 47 2.5.6.3 Variable attenuation 50 2.5.6.4 Power limiting 50 2.6 Step-Recovery Diodes 51 2.7 Gunn Diodes 52 2.7.1 Self-Oscillations 54 2.7.2 Operating Modes 55 2.7.2.1 Accumulation layer mode 56 2.7.2.2 Transit-time dipole layer mode 56 2.7.2.3 Quenched dipole layer mode 56 2.7.2.4 Limited-space-charge accumulation (LSA) mode 57 2.7.3 Equivalent Circuit 57 2.7.4 Applications 58 2.7.4.1 Negative resistance amplifiers 58 2.7.4.2 Oscillators 59 2.8 IMPATT Diodes 59 2.8.1 Doping Profiles 60 2.8.2 Principle of Operation 60 2.8.3 Device Equations 62 2.8.4 Equivalent Circuit 63 2.9 Transistors 65 2.9.1 Some Preliminary Comments on Transistor Modelling 65 2.9.1.1 Model types 65 2.9.1.2 Small and large signal behaviour 65 2.9.2 GaAs MESFETs 66 2.9.2.1 Current-voltage characteristics 68 2.9.2.2 Capacitance-voltage characteristics 70 2.9.2.3 Small signal equivalent circuit 71 2.9.2.4 Large signal equivalent circuit 74 2.9.2.5 Curtice model 74 2.9.3 HEMTs 75 2.9.3.1 Current-voltage characteristics 76 2.9.3.2 Capacitance-voltage characteristics 78 2.9.3.3 Small signal equivalent circuit 78 2.9.3.4 Large signal equivalent circuit 78 Contents vii 2.9.4 HBTs 80 2.9.4.1 Current-voltage characteristics 84 2.9.4.2 Capacitance-voltage characteristics 84 2.9.4.3 Small signal equivalent circuit 86 2.9.4.4 Large signal equivalent circuit 87 2.10 Problems 88 References 89 3 Signal Transmission, Network Methods and Impedance Matching 91 N. J. McEwan, T. C. Edwards, D. Dernikas and I. A. Glover 3.1 Introduction 91 3.2 Transmission Lines: General Considerations 92 3.2.1 Structural Classification 92 3.2.2 Mode Classes 94 3.3 The Two-Conductor Transmission Line: Revision of Distributed Circuit Theory 95 3.3.1 The Differential Equations and Wave Solutions 96 3.3.2 Characteristic Impedance 98 3.4 Loss, Dispersion, Phase and Group Velocity 99 3.4.1 Phase Velocity 100 3.4.2 Loss 100 3.4.3 Dispersion 101 3.4.4 Group Velocity 102 3.4.5 Frequency Dependence of Line Parameters 105 3.4.5.1 Frequency dependence of G 108 3.4.6 High Frequency Operation 109 3.4.6.1 Lossless approximation 111 3.4.6.2 The telegrapher’s equation and the wave equation 111 3.5 Field Theory Method for Ideal TEM Case 113 3.5.1 Principles of Electromagnetism: Revision 114 3.5.2 The TEM Line 117 3.5.3 The Static Solutions 117 3.5.4 Validity of the Time Varying Solution 119 3.5.5 Features of the TEM Mode 121 3.5.5.1 A useful relationship 122 3.5.6 Picturing the Wave Physically 123 3.6 Microstrip 126 3.6.1 Quasi-TEM Mode and Quasi-Static Parameters 128 3.6.1.1 Fields and static TEM design parameters 128 3.6.1.2 Design aims 129 3.6.1.3 Calculation of microstrip physical width 130 3.6.2 Dispersion and its Accommodation in Design Approaches 132 3.6.3 Frequency Limitations: Surface Waves and Transverse Resonance 135 3.6.4 Loss Mechanisms 137 3.6.5 Discontinuity Models 139 3.6.5.1 The foreshortened open end 139 3.6.5.2 Microstrip vias 141 3.6.5.3 Mitred bends 142 3.6.5.4 The microstrip T-junction 142 viii Contents 3.6.6 Introduction to Filter Construction Using Microstrip 145 3.6.6.1 Microstrip low-pass filters 145 3.6.6.2 Example of low-pass filter design 148 3.7 Coupled Microstrip Lines 148 3.7.1 Theory Using Even and Odd Modes 150 3.7.1.1 Determination of coupled region physical length 156 3.7.1.2 Frequency response of the coupled region 157 3.7.1.3 Coupler directivity 158 3.7.1.4 Coupler compensation by means of lumped capacitors 159 3.7.2 Special Couplers: Lange Couplers, Hybrids and Branch-Line Directional Couplers 161 3.8 Network Methods 163 3.8.1 Revision of z, y, h and ABCD Matrices 164 3.8.2 Definition of Scattering Parameters 166 3.8.3 S-Parameters for One- and Two-Port Networks 168 3.8.4 Advantages of S-Parameters 171 3.8.5 Conversion of S-Parameters into Z-Parameters 171 3.8.6 Non-Equal Complex Source and Load Impedance 174 3.9 Impedance Matching 176 3.9.1 The Smith Chart 176 3.9.2 Matching Using the Smith Chart 182 3.9.2.1 Lumped element matching 182 3.9.2.2 Distributed element matching 187 3.9.2.3 Single stub matching 187 3.9.2.4 Double stub matching 189 3.9.3 Introduction to Broadband Matching 191 3.9.4 Matching Using the Quarter Wavelength Line Transformer 194 3.9.5 Matching Using the Single Section Transformer 194 3.10 Network Analysers 195 3.10.1 Principle of Operation 196 3.10.1.1 The signal source 197 3.10.1.2 The two-port test set 197 3.10.1.3 The receiver 198 3.10.2 Calibration Kits and Principles of Error Correction 198 3.10.3 Transistor Mountings 202 3.10.4 Calibration Approaches 206 3.11 Summary 207 References 208 4 Amplifier Design 209 N. J. McEwan and D. Dernikas 4.1 Introduction 209 4.2 Amplifier Gain Definitions 209 4.2.1 The Transducer Gain 211 4.2.2 The Available Power Gain 212 4.2.3 The Operating Power Gain 213 4.2.4 Is There a Fourth Definition? 213 4.2.5 The Maximum Power Transfer Theorem 213 4.2.6 Effect of Load on Input Impedance 216 4.2.7 The Expression for Transducer Gain 218 Contents ix 4.2.8 The Origin of Circle Mappings 221 4.2.9 Gain Circles 222 4.3 Stability 223 4.3.1 Oscillation Conditions 224 4.3.2 Production of Negative Resistance 227 4.3.3 Conditional and Unconditional Stability 228 4.3.4 Stability Circles 229 4.3.5 Numerical Tests for Stability 230 4.3.6 Gain Circles and Further Gain Definitions 231 4.3.7 Design Strategies 237 4.4 Broadband Amplifier Design 239 4.4.1 Compensated Matching Example 240 4.4.2 Fano’s Limits 241 4.4.3 Negative Feedback 243 4.4.4 Balanced Amplifiers 244 4.4.4.1 Principle of operation 245 4.4.4.2 Comments 245 4.4.4.3 Balanced amplifier advantages 246 4.4.4.4 Balanced amplifier disadvantages 246 4.5 Low Noise Amplifier Design 246 4.5.1 Revision of Thermal Noise 246 4.5.2 Noise Temperature and Noise Figure 248 4.5.3 Two-Port Noise as a Four Parameter System 250 4.5.4 The Dependence on Source Impedance 251 4.5.5 Noise Figures Circles 254 4.5.6 Minimum Noise Design 255 4.6 Practical Circuit Considerations 256 4.6.1 High Frequencies Components 256 4.6.1.1 Resistors 256 4.6.1.2 Capacitors 259 4.6.1.3 Capacitor types 261 4.6.1.4 Inductors 263 4.6.2 Small Signal Amplifier Design 267 4.6.2.1 Low-noise amplifier design using CAD software 268 4.6.2.2 Example 269 4.6.3 Design of DC Biasing Circuit for Microwave Bipolar Transistors 272 4.6.3.1 Passive biasing circuits 272 4.6.3.2 Active biasing circuits 274 4.6.4 Design of Biasing Circuits for GaAs FET Transistors 277 4.6.4.1 Passive biasing circuits 277 4.6.4.2 Active biasing circuits 279 4.6.5 Introduction of the Biasing Circuit 279 4.6.5.1 Implementation of the RFC in the bias network 282 4.6.5.2 Low frequency stability 287 4.6.5.3 Source grounding techniques 288 4.7 Computer Aided Design (CAD) 290 4.7.1 The RF CAD Approach 291 4.7.2 Modelling 293 4.7.3 Analysis 296 4.7.3.1 Linear frequency domain analysis 296 x Contents 4.7.3.2 Non-linear time domain transient analysis 297 4.7.3.3 Non-linear convolution analysis 297 4.7.3.4 Harmonic balance analysis 297 4.7.3.5 Electromagnetic analysis 298 4.7.3.6 Planar electromagnetic simulation 298 4.7.4 Optimisation 298 4.7.4.1 Optimisation search methods 299 4.7.4.2 Error function formulation 300 4.7.5 Further Features of RF CAD Tools 302 4.7.5.1 Schematic capture of circuits 302 4.7.5.2 Layout-based design 302 4.7.5.3 Statistical design of RF circuits 303 Appendix I 306 Appendix II 306 References 310 5 Mixers: Theory and Design 311 L. de la Fuente and A. Tazon 5.1 Introduction 311 5.2 General Properties 311 5.3 Devices for Mixers 313 5.3.1 The Schottky-Barrier Diode 313 5.3.1.1 Non-linear equivalent circuit 313 5.3.1.2 Linear equivalent circuit at an operating point 314 5.3.1.3 Experimental characterization of Schottky diodes 317 5.3.2 Bipolar Transistors 319 5.3.3 Field-Effect Transistors 321 5.4 Non-Linear Analysis 322 5.4.1 Intermodulation Products 323 5.4.2 Application to the Schottky-Barrier Diode 327 5.4.3 Intermodulation Power 327 5.4.4 Linear Approximation 329 5.5 Diode Mixer Theory 331 5.5.1 Linear Analysis: Conversion Matrices 332 5.5.1.1 Conversion matrix of a non-linear resistance/conductance 333 5.5.1.2 Conversion matrix of a non-linear capacitance 335 5.5.1.3 Conversion matrix of a linear resistance 336 5.5.1.4 Conversion matrix of the complete diode 337 5.5.1.5 Conversion matrix of a mixer circuit 337 5.5.1.6 Conversion gain and input/output impedances 338 5.5.2 Large Signal Analysis: Harmonic Balance Simulation 339 5.6 FET Mixers 341 5.6.1 Single-Ended FET Mixers 341 5.6.1.1 Simplified analysis of a single-gate FET mixer 341 5.6.1.2 Large-signal and small-signal analysis of single-gate FET mixers 343 5.6.1.3 Other topologies 346 5.7 Double–Gate FET Mixers 349 5.7.1 IF Amplifier 354 5.7.2 Final Design 355 5.7.3 Mixer Measurements 356