Microwave Devices and Circuit Design Ganesh Prasad Srivastava Vijay Laxmi Gupta
MICROWAVE DEVICES and CIRCUIT DESIGN GANESH PRASAD SRIVASTAVA Professor (Retired) Department of Electronic Science University of Delhi VIJAY LAXMI GUPTA Reader Department of Electronic Science University of Delhi
MICROWAVE DEVICES AND CIRCUIT DESIGN Ganesh Prasad Srivastava and Vijay Laxmi Gupta 2006 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN-978-81-203-2195-3 The export rights of this book are vested solely with the publisher. Fifth Printing November, 2013 Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi-110092 and Printed by Syndicate Binders, A-20, Hosiery Complex, Noida, Phase-II Extension, Noida-201305 (N.C.R. Delhi).
Contents Preface ix 1. INTRODUCTION 1 6 1.1 Microwave Engineering 1 1.2 Microwave Frequencies 1 1.3 An Overview of Applications of Microwaves 2 1.3.1 Bandwidth 3 1.3.2 Electromagnetic Noise 3 1.3.3 Antenna Size and Reflection from Targets 3 1.3.4 Microwave Interaction with Materials 3 1.3.5 Stable Oscillation Frequencies 3 1.4 Microwave Circuits 3 1.5 Microwave Matching Networks 4 1.6 Historical Landmarks 4 1.6.1 First Experiments in Radio Communications 4 1.6.2 Electromagnetic Theory of Radiation 4 1.6.3 First Waveguide 4 1.6.4 Development of Microwave Tubes 5 1.6.5 Ferrite Devices 5 1.6.6 Satellite Communication 5 1.6.7 Solid State Devices 5 1.6.8 Microwave Transistors 5 1.7 In This Text 5 Suggested Further Reading 6 2. TRANSMISSION LINES 7 53 2.1 Introduction 7 2.2 Circuit Model of a Transmission Line 7 2.2.1 Wave Propagation Constant 11 2.2.2 Characteristics Impedance, Z 0 12 iii
iv CONTENTS 2.3 Physical Significance of Propagation Constant Equations 14 2.4 Propagation Factor and Characteristic Impedance of Transmission Line 15 2.4.1 Ideal or Lossless Line 16 2.4.2 Line with Low Losses 17 2.5 Waveform Distortions 19 2.5.1 The Open Two-wire Line 20 2.5.2 The Coaxial Line 21 2.6 Transmission Line at High Frequencies 28 2.7 Impedance and Admittance of Short-circuited and Open-circuited Lines 29 2.7.1 Short-circuited Line 29 2.7.2 Open-circuited Line 30 2.8 Q(Quality Factor) of Resonant Lines 31 2.9 Quarter-wave Line 33 2.10 Impedance Matching by Stubbing 35 2.11 Impedance Measurement Using Transmission Lines 37 2.12 Solved Examples 42 Questions 51 Suggested Further Reading 53 3. PLANAR TRANSMISSION LINES 54 86 3.1 Introduction 54 3.2 The Symmetrical Strip Transmission Lines 54 3.2.1 Geometry of Special Planar Transmission Lines 55 3.2.2 Characteristics of Transmission Lines 56 3.2.3 Electrostatic Solution 57 3.2.4 Design Formulas 61 3.2.5 Substrate Materials 63 3.2.6 Criteria for Substrate Selection 64 3.3 The Stripline 73 3.4 The Coplanar Waveguide 74 3.5 The Slot Line 77 3.6 Fin Lines 82 Questions 84 References 85 4. THE SCATTERING MATRIX 87 148 4.1 Introduction 87 4.2 Network Representation 87 4.2.1 Impedance Representation 88 4.2.2 Admittance Representation 89 4.2.3 Hybrid Representation 90 4.2.4 G-Parameter Representation 90 4.2.5 ABCD-Parameter Representation 91 4.2.6 Inverse Chain Parameters 92 4.3 Parameter Conversion 93
CONTENTS v 4.4 Scattering Parameters 94 4.4.1 Conversion of S-Parameters into Other Network Parameters 100 4.4.2 General Properties of Scattering Matrices of Linear Lossless Microwave Devices 106 4.4.3 Application of Scattering Matrix Concepts to Tees 108 4.4.4 Magic or Hybrid Tee 110 4.4.5 Alternative Microstrip Realization of Hybrid Junction (Magic Tee) 117 4.5 Translation of Reference Planes 118 4.6 Scattering Matrix of Some Simple Microwave Devices 119 4.7 Additional Examples 121 4.8 Flow Graphs of Two-port Devices 123 4.9 Signal Flow Graph for Three- and Four-port Devices 130 4.9.1 Three-port Devices 130 4.9.2 Four-port Devices 133 4.10 Crossing 137 4.11 Some Aspects of a Two-port Junction Scattering Matrix 137 4.11.1 Shunt Susceptance jb 139 4.11.2 Series Reactance jx 139 4.12 Scattering Transfer Parameters 140 Questions 143 References 147 Suggested Further Reading 148 5. SMITH CHART AND IMPEDANCE MATCHING 149 220 5.1 Introduction 149 5.1.1 Decibels and Nepers 150 5.1.2 Derivation of Reflection Coefficient (Expression Based on Simple Transmission Line Equations) 151 5.2 The Smith Transmission Line Chart 152 5.3 Application of Smith Chart 157 5.3.1 Determination of Unknown Impedance 159 5.4 Impedance Matching 166 5.4.1 Quarter-wave Transformer 167 5.4.2 Quarter-wave Transformers with Extended Bandwidth 171 5.4.3 Stub-matching Using Smith Chart 173 5.4.4 Matching with Three Stubs 186 5.5 Compressed Smith Chart 187 5.6 The Normalized Impedance and Admittance Smith Chart 189 5.6.1 The Normalized Z Y Smith Chart 190 5.7 Impedance Matching Using Lumped Elements 190 5.7.1 Impedance Matching Networks 197 5.7.2 Microstrip Matching Networks 203 Questions 214 References 220 Suggested Further Reading 220
vi CONTENTS 6. WAVEGUIDES, CAVITIES AND RESONATORS 221 259 6.1 Introduction 221 6.2 Rectangular Waveguides 221 6.3 Solution of Wave Equations 222 6.3.1 Transverse Electric (E z = 0) Mode 225 6.3.2 Transverse Magnetic (H z = 0) Mode 230 6.3.3 Power Flow in Rectangular Waveguides 233 6.4 Circular Waveguides 235 6.4.1 TM Wave Equation 236 6.4.2 TE Modes in Circular Waveguides 240 6.5 Resonant Cavities 244 6.5.1 Rectangular Cavity 244 6.5.2 Cylindrical Cavity 247 6.5.3 Quality Factor of a Cavity 249 6.6 Dielectric Resonators (DRs) 252 6.6.1 Material Properties 252 6.6.2 Modes of Operation 253 Questions 257 Suggested Further Reading 258 7. SOLID STATE MICROWAVE DEVICES 260 316 7.1 Introduction 260 7.1.1 Bipolar Transistor 260 7.1.2 Microwave Transistor 261 7.1.3 Cut-off Frequency 262 7.1.4 Microwave Characterization 263 7.1.5 Device Geometry and Performance 267 7.2 Field Effect Transistors 269 7.2.1 MESFET 270 7.2.2 Construction and Operation 270 7.2.3 Transconductance and Output Resistance 272 7.2.4 Capacitance Voltage Characteristics 274 7.2.5 Second-order Effects 276 7.3 Biasing a Microwave Transistor 277 7.3.1 DC Biasing of a Microwave GaAs MESFET 278 7.4 DC-Biasing Circuits for Microwave Silicon Transistor 279 7.4.1 Biasing Circuit Design 280 7.5 HEMT Devices 282 7.5.1 Current Voltage Characteristics 283 7.6 Small Signal Device Model 285 7.6.1 Parasitic Inductances L S, L D, and L G 286 7.6.2 Parasitic Resistances R S, R D, and R G 286 7.6.3 Capacitances C GS, C GD, and C DS 286 7.6.4 Transconductance, g m 286 7.6.5 Output Conductance, g DS 286
CONTENTS vii 7.7 Microwave Semiconductor Diodes 287 7.7.1 PIN Diodes 287 7.7.2 PIN Diode Parameters 289 7.7.3 PIN Diode Switches 290 7.7.4 PIN Diode as a Phase Shifter 292 7.8 IMPATT and Related Avalanche Transit Time Devices 294 7.8.1 The Physics of IMPATT Diodes 294 7.8.2 Avalanche Multiplication 294 7.8.3 Output Power and Quality Factor 297 7.8.4 Equivalent Circuit of IMPATT Diodes 297 7.8.5 IMPATT Diode Oscillators and Amplifiers 298 7.8.6 IMPATT Diode Power Combiners 299 7.9 Gunn Diode 300 7.9.1 Operating Principle 300 7.9.2 Electron Dynamics in Negative Differential Mobility Medium 303 7.9.3 Domain Formation 305 7.9.4 Gunn Oscillation Mode 307 7.9.5 LSA Diodes 312 7.9.6 Practical Gunn Oscillators 312 Questions 314 References 315 Suggested Further Reading 316 8. MICROWAVE COMPONENTS 317 389 8.1 Introduction 317 8.2 Lumped Elements for Microwave Integrated Circuits (MICs) 317 8.2.1 Capacitive Elements 318 8.2.2 Inductive Elements 320 8.2.3 Resistive Elements 323 8.3 Directional Coupler 323 8.3.1 Waveguide Directional Couplers 327 8.3.2 The Quadrature Hybrid 339 8.3.3 Coupled-line Directional Coupler 340 8.3.4 The Lange Coupler 351 8.4 The Power Divider 352 8.4.1 Resistive Divider 355 8.4.2 Wilkinson Power Divider 356 8.4.3 Frequency Behaviour 362 8.5 Variable Power Dividers 362 8.6 Some Waveguide Components 363 8.6.1 Waveguide Variable Attenuation 363 8.6.2 Dielectric Phase Shifter 365 8.6.3 Quarter-wave Plate 367 8.6.4 Half-wave Plate 369 8.6.5 Precision Phase Shifter and Precision Attenuator 371
viii CONTENTS 8.7 Ferrite Non-reciprocal Devices 374 8.7.1 Faraday Rotation 377 8.7.2 Microwave Ferrite Devices 379 8.7.3 Circulator 383 Questions 386 References 388 9. MICROWAVE AMPLIFIERS AND OSCILLATORS 390 464 9.1 Introduction 390 9.2 Signal Flow Graph and Its Application to Microwave Circuit Design 390 9.2.1 Applications 394 9.3 Amplifier Stability 400 9.3.1 Unconditional Stability 406 9.4 Contant Gain Circles Unilateral Operation 418 9.4.1 Unconditionally Stable Case S ii < 1 419 9.4.2 Potentially Unstable Case ( S ii > 1) 422 9.4.3 Figure of Merit (Unilateral Case) 426 9.5 Simultaneous Conjugate Matching (Bilateral Case) 427 9.6 Noise in Microwave Amplifiers 440 9.7 Broadband Transistor Amplifier Design 447 9.7.1 Balanced Amplifier 447 9.8 Oscillator Design 449 9.8.1 One-port Negative Resistance Oscillator 451 9.8.2 Transistor Oscillator 452 9.8.3 Dielectric Resonator Oscillator 455 9.8.4 Some Common Facts 458 Questions 460 References 463 INDEX 465 470
Preface A thorough knowledge of microwave engineering is necessary for B.Tech. students pursuing courses in Electronics and Communication Engineering and M.Sc. students pursuing courses in Electronics Science. Though there are many good books covering Maxwell s equations and their application to analysis and synthesis of microwave circuits, the authors have endeavoured to write a textbook that particularly emphasizes two areas: (1) Scattering parameters and their relationships with other parameters like impedance, admittance, hybrid and ABCD, as during the analysis of microwave circuits, very often we have to switch from one system to another; (2) Smith chart, a design tool for microwave engineers, used in one form or the other for analyzing and synthesizing all microwave circuits. The concept of Smith chart is somewhat difficult to grasp, therefore, an attempt is made to clarify these concepts by solving several problems. As microwave engineering predominantly involves circuit analysis and design, the emphasis in this book is also on solving Maxwell s equations for different types of microwave transmission lines, like microstrip, stripline, coplanar, fin lines, and H-guides. In order to understand which type of line is to be used for a particular problem, the basic concepts of transmission lines are comprehensively explained. The bulky waveguide is gradually giving way to new types of transmission lines which have less weight and are smaller in size and therefore for many applications the waveguide circuits are being increasingly replaced. Earlier, the study of waveguides and microwave components was based on the field theory concept and solution of Maxwell s equations, but modern microwave engineering consists of study of planar components, monolithic integrated circuits, network analysis and active circuit design. Thus there is a need to study new tools and techniques to analyze these devices and circuits. For example, earlier, the open-circuit stubs were not used for tuning purposes because of spurious radiation, but now for miniature components the open-circuit configuration is often used. Many new active devices like bipolar and field effect transistors, and lumped microwave components are being widely used for the design of microwave amplifier and oscillator circuits. Dielectric resonators and low noise amplifiers are finding wide applications, hence their study has also been duly emphasized in this textbook. For high power and high frequency applications the microwave tubes are still used, but for low to moderate power applications the semiconductor devices are more suitable. Therefore, greater emphasis is placed in this text on the study of performance and geometry of microwave semiconductor devices. ix
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