Microwave Semiconductor Engineering Van Nostrand Reinhold Electrical/Computer Science and Engineering Series Sanjit Mitra, Series Editor

HANDBOOK OF ELECTRONIC DESIGN AND ANALYSIS PROCEDURES USING PROGRAMMABLE CALCULATORS, by Bruce K. Murdock

COMPI LER DESIGN AND CONSTRUCTION, by Arthur B. Pyster

SINUSOIDAL ANALYSIS AND MODELING OF WEAKLY NONLINEAR CIRCUITS, by Donald D. Weiner and John F. Spina

APPLIED MULTIDIMENSIONAL SYSTEMS THEORY, by N. K. Bose

MICROWAVE SEMICONDUCTOR ENGINEERING, by Joseph F. White Microwave Semiconductor Engineering

c [

Joseph F. White, Ph. D. Vice President Technical Director Semiconductor Devices MICROWAVE ASSOCIATES, INC. ~ Burlington, Massachusetts II A MIA-COM Company

Van Nostrand Reinhold Electrical/Computer Science and Engineering Series

InimI VAN NOSTRAND REINHOLD COMPANY ~ NEW YORK CINCINNATI TORONTO LONDON MELBOURNE Van Nostrand Reinhold Company Regional Offices: New York Cincinnati

Van Nostrand Reinhold Company International Offices: London Toronto Melbourne

Copyright e 1982 by Van Nostrand Reinhold Company Softcoyer reprinl of the hardcover 1st edit ion 1982

Library of Congress Catalog Card Number: 81·10498

ISBN 978·94-011 ·7067·3 ISBN 978·94-01 1·7065·9 (eBook) DOl 10.1 007/978·94-011·7065·9

All rights reserved. Originally copyrighted CI 1977 by Artech House under the title, SEMICONDUCTOR CONTROL. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means - graphic, electronic, or mechanical, including photocopying, recording, taping, OJ information storage and retrieyal systems - without permission of the publisher.

Manufactured in the United States of America

Published by Van Noslrand Reinhold Company 135 West 50th Street, New York, N.Y. 10020

'Published simultaneously in Canada by Van Nostrand Reinhold Ltd.

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Library of Congress Cataloging in Publication Dala

White, Joseph F., 1938- Microwave semiconductor engineering.

(Van Nostrand Reinhold electrical/computer science and engineering series) Bibliography ; p. Includes index. I. Microwaye devices - Design and construction. 2. SemicondUctors. I. Title. II. Series. TK7876.W49 621.381'33 81·10498 AACR2 To Christopher, Patricia Jeanne, Catherine, and Elizabeth Foreword Joseph F. White has studied, worked, and taught in all aspects of microwave semiconductor materials, control diodes, and circuit applications. He is thoroughly grounded in the physics and math• ematics of the field, but has primarily the engineer's viewpoint, combining basic knowledge with experience and ingenuity to gen• erate practical designs under constraints of required performance and costs of development and production. As a result of his teach• ing experience and numerous technical papers and oral presenta• tions, he has developed a clear, well-organized writing style that makes this book easy to use as a self-teaching text, a reference volume, and a design handbook. Dr. White believes that an engineer must have a good understand• ing of semiconductor physics, a thorough knowledge of microwave circuit theory, at least an elementary acquaintance with transistor drivers, and the ability to check and refine a microwave circuit on a computer terminal to be qualified for modern, creative design of microwave semiconductor control components. These subjects are well covered in approximately the first half of the book; the second half treats the general and specific design of switches, at• tenuators, limiters, duplexers, and phase shifters, with many ex• amples drawn from his experience and that of others. Especially important is the chapter Mathematical Techniques and Computer Aided Design; it should appeal to all who are concerned with microwave circuits, whether or not these circuits include semiconductor elements. In particular, engineers seeking a good introduction to computer programming will find this book serves the function well; typical books and instruction manuals on FORTRAN are too general, too complex, and too confusing for those who wish to learn the programming skills needed for com• puter aided design of microwave circuits. Dr. White provides the necessary information for time-shared FORTRAN IV work, start• ing with the fundamentals and covering integer, real, and complex variables; operation symbols; real and complex functions; sub• routines; simple READ, WRITE, and FORMAT statements; flow charts; and so on. He gives a number of program listings as exam• ples, starting with simple ones, then moves on to subroutines for vii lossy line immittance transformation, complex ABeD matrix multiplication, response calculation, and a final flow chart and listing of a general network analysis program for the cascaded two-port building blocks commonly found in microwave circuits. Also, he reproduces a number of printouts from his terminal which illustrate the effect of the WRITE and FORMAT state• ments, thereby making their meanings unambiguous. I believe that other microwave engineers will share my admiration for the broad value of this book, and will consult it frequently regarding various aspects of microwave circuits, either with or without semiconductors as elements.

Seymour B. Cohn Tarzana, California

viii Preface This book, initially entitled Semiconductor Control, was written to be a text and engineering reference for engineers who develop control devices at Microwave Associates, a purpose it continues to serve. Yet, whether one wishes to design a microwave control device, such as a switch or a phase shifter, or some other microwave solid-state device, such as a Gunn diode oscillator or an FET amplifier, the principles requisite for an understanding of the physics of semiconductors, the techniques used for microwave circuit design and analysis, and the computer-aided evaluative methods to be employed are the same. Several colleagues have suggested that, while this book's techniques are illustrated with semiconductor control devices, its utility extends throughout the semiconductor microwave engineering area - hence, the new title. A consideration was to revise the book to include other semi• conductor devices such as Gunn and avalanche diodes, bipolar and field-effect transistors, and so forth. But these are better treated in their own separate texts. To include these devices here with the same detail presently afforded to control components would result in too long a book. Alternatively, to reduce the control device treatment to allow for other devices would compromise the thorough control device coverage that is unique to this text. This book is useful for students and practicing engineers interested in semiconductor device use at microwave frequencies and who therefore must understand both semiconductor and circuit principles sufficiently to design, measure, and analyze their per• formance. The book represents a compendium of techniques, derivations, practical applications, formulas, and constants that I have collected over a 20-year period in my practice of semi• conductor microwave engineering. Included also are several detailed mathematical and theoretical treatments that the practicing engineer is likely to encounter and be curious about - such as how to define waveguide impedance absolutely and why backward wave couplers have match, isolation, and 90° phase split at all frequencies, how the Smith Chart is derived and why matrix theory is useful. The introduction to FORTRAN IV programming is especially designed for microwave circuit engineers. ix The book need not be read through, cover to cover. Each chapter, and within the chapters most of the sections, can be read on a stand-alone basis. In the Introduction that follows, I have high• lighted those elements of each chapter that are special. To derive most of the benefits from the book, one need but scan this intro• duction in sufficient detail that when an occasion for treating one of these topics arises, a ready reference can be made to the appro• priate sections. It is the reader who decides how effectively subjects have been chosen and covered. Accordingly, comments, suggestions for future revision and related text, and the noting of errors that are directed to me will be especially appreciated.

Joseph F. White Lexington, Massachusetts

x Introduction Microwave Semiconductor Engineering treats principles of semi• conductors emphasizing 1) the properties which predominate at microwave frequencies, 2) the mathematical and circuit design techniques required to utilize them at microwave frequencies, and 3) practical engineering applications for controlling microwave signals in amplitude and phase using semiconductors. The book is a useful addition to the personal library of the engineering student or practicing professional, whether specializing in microwave semiconductor applications or merely needing to make reference to these topics occasionally. A conversational format has been used to permit the reader to gain a qualitative perspective of the material on each subject, a perspec• tive that may itself suffice in many situations. The reader may be interested, for example, in determining just what it is that defines a semiconductor, how lifetime is specified and why it is important, and how it would affect circuit performance. From a circuit view• point, the reader may need to know how a simple filter can be designed to include the diode capacitance in a switch, or how a directional coupler works and what methods can be used to analyze it. At this general insight level, the reader may skim the book, obtaining only the introduction to and physical insight into a subject that the reader's interest may require. At the specific design level, the reader seeks more detailed and quantitative infor• mation regarding semiconductors and the design of the circuits utilized. For this reader, the most fundamental exposition of the subject is never too much, and for this purpose an in-depth coverage is provided. The book assumes only an introduction to electrical engineering, specifically to microwaves; it can be used in conjunction with or following a first course in microwaves, since most microwave analysis methods, even use of the Smith Chart, are derived directly in the text and the appendices. Chapters I-III introduce the semiconductors themselves, evolving the physical principles behind semiconductors, the PN junction, rectification, the PIN diode, and the characteristics that affect microwave performance. The concepts of doping, hole and elec- xi tron carriers, lifetime, mobility, charge, punchthrough, breakdown, depletion, C(V) law, dielectric relaxation frequency, microwave resistance determination through charge control modeling, transit time, microwave breakdown, parasitic reactances, and thermal time constant modeling are defined and illustrated with examples. This introductory treatment develops the physical reasoning and the measurement definitions and techniques behind semiconductor operation with which the designer must be familiar, concluding with data for typically available diodes. Intimately related areas, often overlooked in device treatments, receive special attention. Chapter IV is devoted to drivers for PIN devices, defining balanced and unbalanced TTL logic, showing how diode and driver are chosen for switching speed and describ• ing measurements, built-in fault detection (BITE), pulse leakage considerations, and complementary switching. The fundamental limits of control circuitry are derived, based upon the general properties of three-port networks, in Chapter V. Not only are the power handling and insertion loss relationships useful to control circuitry, their derivations demonstrate practical uses of complex variable theory and the impedance matrix to establish general circuit results of practical importance. No field is more open to mathematical analysis than microwaves. Prior to the last two decades, nearly all scientific calculations were performed by hand; today, nearly all are, or can be, done by computer. The former method imparts more understanding of the physical behavior, but the later can provide more speed, efficiency, and accuracy. The experienced scientist and engineer understands that reliance on both is necessary, and more important, that the effective mathematical approaches for each are different.

Chapter VI - Mathematical Techniques introduces, in terms readily assimilated by the electrical engineer or physicist, matrix algebra with definitions and a library of functions needed for most circuits; even and odd mode analyses demonstrated by an evalua• tion of the phenomenal "backward wave coupler;" FORTRAN IV programming, most practical for microwave engineering because of its capacity for direct complex number manipulation; and pro• cedures for generating interactive microwave analysis computer programs, including a complete program example capable of analyzing general two-port networks. This program is then used throughout the remainder of the book to analyze most of the circuit examples. xu The last three chapters describe the theory and practice of semi• conductor control circuit design. Chapter VII - Limiters and Duplexers describes nonlinear limiting in terms of microwave frequency and semiconductor diode properties. A detailed description of avalanche limiting using bulk semiconductors is also presented. Waveguide diode limiter circuit evaluation is performed in a manner that demonstrates how to use the wave• guide Green's functions. The bulk element analysis shows how the general three-port theory derived in Chapter V can be applied. Practical designs of actual limiters in coax, waveguide, and integrated circuit microstrip are given. These examples show tuning and its effectiveness using either fixed capacitance and inductance or distributed tuning to resonate the reactances of the diode and bulk semiconductor elements. Design data are pre• sented in universal curves for easy determination of ultimate device frequency, loss, and isolation limitations. Chapter VIII - Switches and Attenuators shows how semicon• ductor elements can be embedded within filters, thereby permit• ting a large body of filter theory to be usable for control circuit design. Practical results with an octave bandwidth, high-power switch demonstrate not only the filter approach, but also the effectiveness of "quarter wavelength spacing" and stagger series tuning of diodes for increased isolation bandwidth. Waveguide, stripline, coaxial, and micros trip circuit media operating from 0.5 to 18 GHz are covered within the demonstration of switching circuit techniques. Packaged beam lead individual diode chips as well as bulk effect window devices are used in the examples given to illustrate the different semiconductors that are possible. Chapter IX - Phase Shifters contains complete analysis of digital phase shifters using the switched line, loaded line, lumped element, and reflection circuits, with practical examples from 0.4 to 15 GHz. Techniques for increasing bandwidth and power handling capacity are shown. Continuous phase shifters are treated, including derivation of the maximum phase shift per decibel of loss, nonlinear power limits, and varactor selection. Appendices A-J include charts and computer programs to evaluate the characteristics of various transmission lines and couplers, the frequency response of bias blocks and returns, material properties, often-used constants and formulas, and a review of the basis and use of the Smith Chart.

X111 Acknowledgment

This book was begun at the suggestion of one of my most valued friends, Theodore Saad, President of Sage Laboratories, founder of Microwave Journal, and one who has contributed generously to the microwave field with his witful critiques, his sense of its history, and his willingness to work hard on many of the Institute of Electrical and Electronics Engineers committees to bring interesting symposia, papers, and reports to its members. Claire Alterio typed patiently, skillfully, and frequently most of the final pages of the manuscript and assisted Neal Vitale in its editing. Eleanor Walsh and Jan Beland typed the initial chapters. This book's publication, through the generous cooperation extended to me by Microwave Associated, Inc., especially by Dr. Frank Brand, now President, is a demonstration of the firm's commitment to professionalism. Many of my colleagues in MIA-COM, now the parent company, contributed to the material in the book as we developed ideas and methods together over 20 years. I've acknowledged specific contributions at the ends of the chapters, but to all I extend my appreciation both for the results as well as the enjoyment that accompanied the shared effort.

xiv Contents Foreword by Seymour B. Cohn vii Preface ix Introduction xi Chapter I The PN Junction A. The Need to Understand Low Frequency Diode Behavior 1 B. Silicon - The Semiconductor 3 C. The PN Depletion Zone 8 D. Junction Potential 13 E. Diffusion and Drift Currents 14 F. Rectification and the I-V Law 17 G. Depletion Zone Width Modulation - The Depletion C(V) Law 23 H. Reverse Voltage Breakdown 32 References 36 Questions 36 Chapter II PIN Diodes and the Theory of Microwave Operation A. The PIN Diode - An Extension of the PN Junction 39 B. Microwave Equivalent Circuit 48 C. High RF Power Limits 80 References 87 Questions 89 Chapter III Practical PIN Diodes A. Basic Parameters - I Region Thickness and Area 91 B. Table of Typically Available PIN Diodes 92 C. Definition of Characteristics 93 References 114 Questions 114 Chapter IV Binary State Transistor Drivers A. What The Driver Must Do 117 B. The Driver as a Logic Signal - Power Supply Buffer (TTL Compatibility) 118 C. Switching Speed 125 D. High Power Reverse Bias (Enhanced) Leakage Current Supply 135

xv E. Fault Detection Circuits 136 F. Complementary Drivers 140 References 140 Questions 141 Chapter V Fundamental Limits of Control Networks A. Introduction 143 B. The Simple Loss (or Isolation) Formula 144 C. The General Three-Port SPST Equivalent Circuit 147 D. Switching Limits 152 E. Duplexing Limits 160 F. Phase Shifting Limits 165 G. Summary 174 References 174 Questions 174 Chapter VI Mathematical Techniques and Computer Aided Design (CAD) A. Introduction 177 B. CAD Mathematical Analysis Approaches 182 C. FORTRAN Computer Programming 205 References 241 Questions 242 Chapter VII Limiters and Duplexers A. Introduction to Practical Circuit Designs 245 B. How Limiters Function 246 C. Coaxial Duplexers 258 D. High Frequency, Waveguide Limiters 267 E. Integrated Circuit Limiters 280 F. Bulk Limiters 290 References 311 Chapter VIII Switches and Attenuators A. Broadband Coaxial Switches 315 B. Coaxial High Power 350 C. Switched Duplexers 355 D. Waveguide Switches 358 E. Strip line Switches 360 F. Microstrip Switching 365 G. Bulk Effect Switching 375 References 387 xvi Chapter IX Phase Shifters and Time Delay Networks A. Introduction 389 B. Switched Path Circuits 391 C. Transmission Phase Shifters 400 D. Reflection Phase Shifters 437 E. Schiffman Phase Shifters 474 F. Continuous Phase Shifters 479 References 493 Answers 497 Appendices A. Constants and Formulas 501 B. Material Properties 506 C. Thermal Resistance Calculations 510 D. Coaxial Lines 515 E. Microstrip 521 F. Strip line 526 G. VVaveguide 530 H. Strip line Backward VVave Hybrid Coupler 531 I. Bias Blocks and Returns 534 J. The Smith Chart 537 References and Bibliography 550 Index 553

XVll