Modern Microwave Circuits DISCLAIMER OF WARRANTY The technical descriptions, procedures, and computer programs in this book have been developed with the greatest of care and they have been useful to the author in a broad range of applications; however, they are provided as is, without warranty of any kind Artech House, Inc., and the authors of the book titled Modern Microwave Circuits make no warranties, expressed or implied, that the equations, programs, and procedures in this book or its associated software are free of error, or are consistent with any particular standard of merchantability, or will meet your requirements for any particular application They should not be relied upon for solving a problem whose incorrect solution could result in injury to a person or loss of property Any use of the programs or procedures in such a manner is at the user’s own risk The editors, author, and publisher disclaim all liability for direct, incidental, or consequent damages resulting from use of the programs or procedures in this book or the associated software For a listing of recent titles in the Artech House Microwave Library, turn to the back of this book Modern Microwave Circuits Noyan Kinayman M I Aksun artechhouse.com Library of Congress Cataloging-in-Publication Data A catalog record of this book is available from the Library of Congress British Library Cataloguing in Publication Data Kinayman, Noyan Modern microwave circuits.—(Artech House microwave library) Microwave circuits I Title II Aksun, M I 621.3’813 ISBN 1-58053-725-1 Cover design by Igor Valdman Cover image is courtesy of Cascade Microtech, Inc The Smith Chart is a registered trademark of Analog Instruments Co., P.O Box 950, New Providence, NJ 07974 The Smith Chart on page 82 has been reproduced with the courtesy of Analog Instruments Co © 2005 ARTECH HOUSE, INC 685 Canton Street Norwood, MA 02062 All rights reserved Printed and bound in the United States of America No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized Artech House cannot attest to the accuracy of this information Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark International Standard Book Number: 1-58053-725-1 10 Contents xi Preface xiii Acknowledgments Chapter Microwave Network Theory 1.1 Review of Electromagnetic Theory 1.1.1 Maxwell’s Equations: Time-Dependent Forms 1.1.2 Maxwell’s Equations: Time-Harmonic Forms 1.1.3 Fields in Material Media: Constitutive Relations 1.1.4 The Wave Equation 1.1.5 Boundary Conditions 1.1.6 Energy Flow and the Poynting Vector 1.2 Plane Electromagnetic Waves 1.2.1 General Uniform Plane Waves 1.2.2 Plane Waves in Lossy Media 1.3 Transmission Lines 1.3.1 Field Analysis of General Cylindrical Waveguides 1.3.2 Transmission Line Equations Via Field Analysis 1.3.3 Transmission Line Equations Via Circuit Analysis 1.3.4 Analysis of General Transmission Line Circuits 1.3.5 Analysis of Terminated Transmission Line Circuits 1.4 Circuit Parameters 1.4.1 Scattering Parameters 1.4.2 Transfer Parameters 1.4.3 Z- and Y-Parameters 1.4.4 ABCD-Parameters 1.5 Circuit Parameters of Various Simple Networks 1.5.1 TEM Transmission Line 1.5.2 Pi-Network 1.5.3 T-Network 1.6 Equivalent Circuit of a Short Transmission Line 1.7 Signal Flowgraphs v 13 19 26 29 30 34 37 38 43 46 48 55 58 58 64 65 67 69 69 71 72 73 75 vi Modern Microwave Circuits 1.7.1 Nontouching Loop Rule 1.7.2 Signal Flowgraphs of Some Microwave Components 1.8 Power Gain 1.9 The Smith Chart 1.10 Impedance Matching 1.10.1 Single-Stub Matching 1.10.2 Double-Stub Matching 1.10.3 Matching with Lumped Elements 1.11 Network Analyzers 1.12 Calibration of Network Analyzers 1.12.1 SOLT Calibration 1.12.2 TRL Calibration 1.12.3 Multiline TRL 1.12.4 Two-Tier and One-Tier Calibration 1.13 Lumped Resonator Circuits 1.14 Transmission Line Resonators 1.15 Tapped Transmission Line Resonators 1.16 Synthesis of Matching Networks 1.16.1 Positive Real Functions 1.16.2 Foster’s Reactance Theorem 1.16.3 Darlington’s Method 1.16.4 Matching a Resistive Generator to an RLC Load References Chapter Microwave Printed Circuits 2.1 History of Microwave Printed Circuits 2.2 Microstrip Lines 2.2.1 Characteristic Impedance 2.2.2 Conductor Losses 2.2.3 Dielectric Losses 2.2.4 Radiation Losses 2.2.5 Higher-Order Modes and Dispersion 2.2.6 Surface Waves 2.3 Striplines 2.3.1 Characteristic Impedance 2.3.2 Conductor Losses 2.3.3 Dielectric Losses 2.3.4 Higher-Order Modes 2.4 Coplanar Waveguides 2.4.1 Characteristic Impedance 2.4.2 Higher-Order Modes 2.5 Microstrip Discontinuities 2.5.1 Microstrip Open End 2.5.2 Microstrip Series Gap 76 77 79 81 84 84 88 89 91 94 100 103 110 113 114 118 122 124 125 127 129 134 136 141 141 144 148 156 160 160 161 164 164 166 167 168 168 169 171 171 172 173 175 Contents vii 2.5.3 Change in Microstrip Width 2.5.4 Microstrip Bend 2.5.5 Microstrip T-Junction 2.6 Substrates for Microwave Printed Circuits 2.6.1 Laminates 2.6.2 Ceramics 2.7 Manufacturing Techniques for Printed Circuits 2.7.1 Multilayer Printed Circuits 2.8 Measurement of Substrate Materials 2.8.1 Dielectric Properties of Materials 2.8.2 Transmission/Reflection Method 2.8.3 Split-Cylinder Resonator Method References 176 176 177 178 181 183 184 186 188 191 195 202 204 Chapter Full-Wave Analysis of Printed Circuits 3.1 Review of Analysis Techniques for Printed Circuits 3.2 General Review of Green’s Functions 3.2.1 Green’s Function of Scalar Wave Equation 3.2.2 Green’s Function of Vector Wave Equation 3.3 Point Sources and Their Spectral Representations 3.3.1 Impulse Function Representations of Point Sources 3.3.2 Scalar Green’s Function for a Line Source 3.3.3 Scalar Green’s Function for a Point Source 3.4 Analysis of Planar Multilayer Media 3.4.1 Fresnel’s Reflection and Transmission Coefficients 3.4.2 Generalized Reflection and Transmission Coefficients 3.4.3 Green’s Functions in Planar Multilayer Media 3.5 Application of MoM to Printed Circuits 3.5.1 Integral Equations 3.5.2 Method of Moments References 211 211 214 216 219 224 225 227 237 244 253 260 265 278 278 282 287 Chapter Microstrip Patch Antennas 4.1 Design of Microstrip Patch Antennas 4.1.1 Quality Factor 4.1.2 Resonance Frequency 4.1.3 Radiation Resistance 4.1.4 Bandwidth 4.1.5 Radiation Pattern 4.1.6 Surface Waves 4.2 Analysis Techniques for Patch Antennas 4.2.1 Transmission Line Model 4.2.2 Cavity Model 4.2.3 Full-Wave Analysis Methods 291 292 293 296 298 299 300 304 304 305 306 310 viii Modern Microwave Circuits 4.3 Proximity-Coupled Microstrip Patch Antennas 4.4 Aperture-Coupled Microstrip Patch Antennas 4.5 Stacked Microstrip Patch Antennas 4.6 Microstrip Patch Antennas with Parasitic Elements 4.7 Inset-Fed Microstrip Patch Antennas 4.8 Circularly Polarized Microstrip Patch Antennas 4.9 Coupling Between Microstrip Patch Antennas References 321 324 328 332 336 340 346 351 Chapter Microstrip Coupled Lines 5.1 Analysis of Coupled TEM Lines 5.1.1 Analysis of Symmetrical Coupled TEM Lines 5.1.2 Analysis of Asymmetrical Coupled TEM Lines 5.2 The MTL Formulation 5.2.1 Lossless Lines in Homogenous Medium 5.2.2 Lossless Lines in Inhomogeneous Medium 5.3 Z-Parameters of Coupled-Line Sections 5.4 Coupled Microstrip Lines 5.4.1 Microstrip Directional Couplers 5.5 Coupled Striplines 5.5.1 Edge-Coupled Striplines 5.5.2 Broadside-Coupled Striplines 5.6 Wide-Bandwidth Directional Couplers 5.7 Hybrid Couplers References 357 358 359 364 369 375 376 378 381 386 392 392 394 396 400 411 Chapter Microstrip Filters 6.1 Basic Filter Theory 6.1.1 Filter Transformations 6.1.2 Norton’s Transformations 6.1.3 Darlington’s Method 6.1.4 Impedance Inverters 6.2 Richard’s Transformation 6.3 Stepped-Impedance Microstrip Filters 6.4 Coupled-Line Microstrip Filters 6.5 Bandstop Filters 6.6 Filter Design by Coupling 6.7 Interdigital Filters 6.8 Hairpin Filters 6.9 Cross-Coupled Filters 6.10 Cascade Quadruplets and Triplets 6.11 Filter Synthesis by Optimization 6.12 DC-Block Circuits References 415 416 429 442 446 449 453 460 464 475 481 494 497 502 514 521 524 527 ... in modeling passive microwave circuits Chapter sets the stage for microwave printed circuits, which is the main theme of the book xi xii Modern Microwave Circuits Microstrip circuits and their... British Library Cataloguing in Publication Data Kinayman, Noyan Modern microwave circuits. —(Artech House microwave library) Microwave circuits I Title II Aksun, M I 621.3’813 ISBN 1-58053-725-1 Cover... success in microwave circuit design This is especially important in microwave printed circuits (i.e., microstrip circuits) where quasi-static or empirical solutions are not accurate enough at microwave-