Rf circuit design theory and applications

Horton Associate Editor: Alice Dworkin Editorial Assistant: William Opaluch Marketing Manager: Tim Galllgan Managing Editor: Scott Disanno Production Liaison: Rose Keman Senior Operation

RF CIRCUIT DESIGN

REINHOLD LUDWIG GENE BOGDANOV

RF Circuit Design:

Theory and Applications

Reinhold Ludwig

Worcester Polytechnic Institute

Gene Bogdanov

Worcester Polytechnic Institute

PI A R) O N

Upper Saddle River, NJ 07458

Ludwig, Reinhold.

RF circuit design : theory and applications / Reinhold Ludwig, Gene Bogdanov,

p cm.

Includes bibliographical references and index.

ISBN 0-13-147137-6 (hardcover)

1 Radio circuits-D esign and construction 2 Radio frequency I Bogdanov, Gene II Title.

TK6553.L823 2007

621.384'12-dc22

2007040036

Library of Congress Cataloging-in-Publlcation Data

Vice President and Editorial Director, ECS: Marcia J Horton

Associate Editor: Alice Dworkin

Editorial Assistant: William Opaluch

Marketing Manager: Tim Galllgan

Managing Editor: Scott Disanno

Production Liaison: Rose Keman

Senior Operations Supervisor: Alexis Heydt-Long

Operations Specialist: Lisa McDowell

Cover Design: Jayne Conte Director, Image Resource Center: Melinda Patelli Manager, Rights and Permissions: Zina Arabia Manager, Visual Research: Beth Brenzel Manager, Cover Visual Research & Permissions: Karen Sanatar Image Permission Coordinator John Ferreri

Composition/Full-Service Project Management: Laserwords Printer/Binder: LSC Communications

MATLAB and SIMULINK are registered trademarks of The Math Works, 3 Apple Hill Drive, Natick, MA

Copyright © 2009 by Pearson Education, Inc., Upper Saddle River, New Jersey, 07458 Pearson Prendc&Hall All rights reserved

Printed in the United States of America This publication is protected by Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department.

Pearson Prentice Hall™ is a trademark of Pearson Education, Inc.

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Prentice Hall® is a registered trademark of Pearson Education, Inc.

Pearson Education Ltd., London Pearson Education North Asia, Ltd., Hong Kong

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Pearson Education, Canada, Inc Pearson Education Malaysia, Pte Ltd.

Pearson Education-Japan Pearson Education, Upper Saddle River, New Jersey

Pearson Education Australia PTY, Limited

15 17

ISBN-13: ^ 7 0 - 0 - 1 3 - 1 4 7 1 3 7 - 5

I S B N - 1 0 : 0 - 1 3 - 1 4 7 1 37-b

26 2020

To our families and the memory of my father F Ludwig

Library of Congress Cataloging-in-Publication Data

Ludwig, Reinhold.

RF circuit design : theory and applications / Reinhold Ludwig, Gene Bogdanov,

p cm.

Includes bibliographical references and index.

ISBN 0-13-147137-6 (hardcover)

1 Radio circuits-D esign and construction 2 Radio frequency I Bogdanov, Gene II Title.

TK6553.L823 2007

621.384'12-dc22

2007040036

Vice President and Editorial Director, ECS: Marcia J Horton

Associate Editor: Alice Dworkin

Editorial Assistant: William Opaluch

Marketing Manager: Tim Galligan

Managing Editor: Scott Disanno

Production Liaison: Rose Keman

Senior Operations Supervisor: Alexis Heydt-Long

Operations Specialist: Lisa McDowell

Cover Design: Jayne Conte Director, Image Resource Center: Melinda Patelli Manager, Rights and Permissions: Zina Arabia Manager, Visual Research: Beth Brenzel Manager, Cover Visual Research & Permissions: Karen Sanatar Image Permission Coordinator John Ferreri

Composition/Full-Service Project Management: Laserwords Printer/Binder: LSC Communications

MATLAB and SIMULINK are registered trademarks of The Math Works, 3 Apple Hill Drive, Natick, MA

Copyright © 2009 by Pearson Education, Inc., Upper Saddle River, New Jersey, 074S8 Pearson Prentice Hall All rights reserved

Printed in the United States of America This publication is protected by Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department.

Pearson Prentice Hall™ is a trademark of Pearson Education, Inc.

Pearson® is a registered trademark of Pearson pic

Prentice Hall® is a registered trademark of Pearson Education, Inc.

Pearson Education Ltd., London

Pearson Education Singapore, Pte Ltd

Pearson Education, Canada, Inc.

Pearson Education-Japan

Pearson Education Australia PTY, Limited

Pearson Education North Asia, Ltd., Hong Kong Pearson Educación de Mexico, S.A de C.V.

Pearson Education Malaysia, Pte Ltd.

Pearson Education, Upper Saddle River, New Jersey

15 17

I SBN-13: T 7 Ô - 0 - 1 3 - 1 4 7 1 3 7 - 5

I SBN-1D: 0 - 1 3 - 1 4 7 1 3 7 -b

2 6 20 2 0

Chapter 1 Introduction 1 1.1 Importance of Radio Frequency Design 2 1.2 Dimensions and Units 6

1.3 Frequency Spectrum 9 1.4 RF Behavior of Passive Components 10 1.4.1 Resistors at High Frequency 16 1.4.2 Capacitors at High Frequency 19 1.4.3 Inductors at High Frequency 22 1.5 Chip Components and Circuit Board Considerations 25 1.5.1 Chip Resistors 25 1.5.2 Chip Capacitors 27 1.5.3 Surface-Mounted Inductors 28 1.6 RF Circuit Manufacturing Processes 29 1.7 Summary 32

Chapter 2 Transmission Line Analysis 41 2.1 Why Transmission Line Theory? 42 2.2 Examples of Transmission Lines 45 2.2.1 Two-Wire Lines 45 2.2.2 Coaxial Line 46 2.2.3 Microstrip Lines 47 2.3 Equivalent Circuit Representation 49

2.4 Theoretical Foundation 52 2.4.1 Basic Laws 52 2.5 Circuit Parameters for a Parallel-Plate Transmission Line 57 2.6 Summary of Different Line Configurations 61 2.7 General Transmission Line Equation 62 2.7.1 Kirchhoff Voltage and Current Law Representations 62 -2.7.2 Traveling Voltage and Current Waves 66

2.7.3 Characteristic Impedance 67 2.7.4 Lossless Transmission Line Model 67 2.8 Microstrip Transmission Lines 68

2.9 Terminated Lossless Transmission Line 73 2.9.1 Voltage Reflection Coefficient 73 2.9.2 Propagation Constant and Phase Velocity 74 2.9.3 Standing Waves - 75 2.10 Special Termination Conditions 78 2.10.1 Input Impedance of Terminated Lossless Line 78 2.10.2 Short-Circuit Terminated Transmission Line 79 2.10.3 Open-Circuited Transmission Line 82 2.10.4 Quarter-Wave Transmission Line 83 2.11 Sourced and Loaded Transmission Line 87 2.11.1 Phasor Representation of Source 87 2.11.2 Power Considerations for a Transmission Line 88

2.11.3 Input Impedance Matching 91

2 f 1.4 Return Loss and Insertion Loss 92 2.12 Summary 95

3.1 From Reflection Coefficient to Load Impedance 104 3.1.1 Reflection Coefficient in Phasor Form 104 3.1.2 Normalized Impedance Equation 106 3.1.3 Parametric Reflection Coefficient Equation 108 3.1.4 Graphical Representation 110 3.2 Impedance Transformation 112 3.2.1 Impedance Transformation for General Load " 112 3.2.2 Standing Wave Ratio 113 3.2.3 Special Transformation Conditions 116 3.2.4 Computer Simulations 120

3.3 Admittance Transformation 123 3.3.1 Parametric Admittance Equation 123 3.3.2 Additional Graphical Displays 126 3.4 Parallel and Series Connections 127 3.4.1 Parallel Connection of R and L Elements 127 3.4.2 Parallel Connection of R and C Elements 128 3.4.3 Series Connection of R and L Elements 129 3.4.4 Series Connection of R and C Elements 129 3.4.5 Example of a T-Network 131 3.5 Summary 135

Chapter 4 Single- and Multiport Networks 145 4.1 Basic Definitions 146 4.2 Interconnecting Networks - - 154 4.2.1 Series Connection of Networks 154 4.2.2 Parallel Connection of Networks 156 4.2.3 Cascading Networks 157 4.2.4 Summary of ABCD Network Representations 158 4.3 Network Properties and Applications 163 4.3.1 Interrelations between Parameter Sets 163 4.3.2 Analysis of Microwave Amplifier 166 4.4 Scattering Parameters 169 4.4.1 Definition of Scattering Parameters 169 4.4.2 Meaning of 5-Parameters 172 4.4.3 Chain Scattering Matrix 175 4.4.4 Conversion between Z-and 5-Parameters 177 4.4.5 Signal Flowgraph Modeling 178 4.4.6 Generalization of 5-Parameters 184 4.4.7 Practical Measurements of 5-Parameters 188 4.5 Summary 195

'Chapter 5 An Overview of RF Filter Design 205 5.1 Basic Resonator and Filter Configurations 206 5.1.1 Filter Types and Parameters 206 5.1.2 Low-Pass Filter 210 5.1.3 High-Pass Filter 213 5.1.4 Bandpass and Bandstop Filters 214 5.1.5 Insertion Loss 221

5.2 Special Filter Realizations 224

6.4.3 Frequency Response 338 6.4.4 Limiting Values 3 3 9

6.5 Metal Oxide Semiconductor Transistors 3 39

6.5.1 Construction 340 6.5.2 Functionality 341 6.6 High Electron Mobility Transistors 342 6.6.1 Construction 343

6.6.2 Functionality 343

6.6.3 Frequency Response 346 6.7 Semiconductor Technology Trends 347 6.8 Summary 352

Clapter 7 Active RF Component Modeling 361 7.1 Diode Models 362 7.1.1 Nonlinear Diode Model 362 7.1.2 Linear Diode Model 364 7.2 Transistor Models 367 7.2.1 Large-Signal BJT Models 367 7.2.2 Small-Signal BJT Models 376 7.2.3 Large-Signal FET Models 388 7.2.4 Small-Signal FET Models 391

7.2.5 Transistor Amplifier Topologies 395

7.3 Measurement of Active Devices 397

7.3.1 DC Characterization of Bipolar Transistor 397

7.3.2 Measurements of AC Parameters of Bipolar Transistors 398 7.3.3 Measurements of Field Effect Transistor Parameters 403

7.4 Scattering Parameter Device Characterization 404 7.5 Summary 413

Ciapter 8 Matching and Biasing Networks 421 8.1 Impedance Matching Using Discrete Components 422 8.1.1 Two-Component Matching Networks 422

8.1.2 Forbidden Regions, Frequency Response, and Quality Factoi 431

8.1.3 T and Pi Matching Networks 442 8.2 Microstrip Line Matching Networks 446 8.2.1 From Discrete Components to Microstrip Lines 446 8.2.2 Single-Stub Matching Networks 450 8.2.3 Double-Stub Matching Networks 454

8.3 Amplifier Classes of Operation and Biasing Networks 458 8.3.1 Classes of Operation and Efficiency of Amplifiers 458 8.3.2 Bipolar Transistor Biasing Networks 463 8.3.3 Field Effect Transistor Biasing Networks 469 8.4 Summary 478

Chapter 9 RF Transistor Amplifier Design 48S 9.1 Characteristics of Amplifiers 486 9.2 Amplifier Power Relations 487 9.2.1 RF Source 487 9.2.2 Transducer Power Gain 488 9.2.3 Additional Power Relations 489 9.3 Stability Considerations 492 9.3.1 Stability Circles 492 9.3.2 Unconditional Stability 494 9.3.3 Stabilization Methods 501 9.4 Constant Gain 504 9.4.1 Unilateral Design 504 9.4.2 Unilateral Figure of Merit 510 9.4.3 Bilateral Design 512 9.4.4 Operating and Available Power Gain Circles 515 9.5 Noise Figure Circles 521 9.6 Constant VSWR Circles 525 9.7 Broadband, High-Power, and Multistage Amplifiers 529 9.7.1 Broadband Amplifiers 529 9.7.2 High-Power Amplifiers 540 9.7.3 Multistage Amplifiers 543 9.8 Summary 550

Chapter 10 Oscillators and Mixers 559 10.1 Basic Oscillator Models 560 10.1.1 Feedback Oscillator 560 10.1.2 Negative Resistance Oscillator 562 10.1.3 Oscillator Phase Noise 574 10.1.4 Feedback Oscillator Design 578 10.1.5 Design Steps 581 10.1.6 Quartz Oscillators 585

10.2 High-Frequency Oscillator Configuration 587 10.2.1 Fixed-Frequency Oscillators 591 10.2.2 Dielectric Resonator Oscillators 598 10.2.3 YIG-Tuned Oscillator 603 10.2.4 Voltage-Controlled Oscillator 604 10.2.5 Gunn Element Oscillator 608 10.3 Basic Characteristics of Mixers 609 10.3.1 Basic Concepts 610 10.3.2 Frequency Domain Considerations 612 10.3.3 Single-Ended Mixer Design 614 10.3.4 Single-Balanced Mixer 622 10.3.5 Double-Balanced Mixer 623 10.3.6 Integrated Active Mixers 624 10.3.7 Image Reject Mixer 628 10.4 Summary 641

Appendix A Useful Physical Quantities and Units 647

Appendix B Skin Equation for a Cylindrical Conductor 653

Appendix C Complex Numbers 657

C 1 Basic Definition 657 C.2 Magnitude Computations 657 C.3 Circle Equation 658

Appendix D Matrix Conversions 659

Appendix E Physical Parameters of Semiconductors 663

Appendix F Long and Short Diode Models 665

F 1 Long Diode 6 6 6

F.2 Short Diode 6 6 6

Appendix G Couplers 669

G 1 Wilkinson Divider 669 G.2 Branch Line Coupler 672 G.3 Lange Coupler 676

Appendix H Noise Analysis 677

H 1 Basic Definitions 677 H.2 Noisy Two-Port Networks 679

xll Contents

H.3 Noise Figure for Two-Port Network 682 H.4 Noise Figure for Cascaded Multiport Network 685

Appendix I Introduction to M a tl a b 689 1.1 Background 689 1.2 Brief Example of Stability Evaluation 691 1.3 Simulation Software 693 1.3.1 Overview 693 1.3.2 File Organization 693