CRYSTAL OSCILLATOR

DESIGN AND

TEMPERATURE COMPENSATION

Marvin E.Frerking

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CRYSTAL OSCILLATOR

DESIGN AND

TEMPERATURE COMPENSATION

The author assumes no responsibility for the use of any circuitry, program, or technique contained in this publication nor is any patent license implied.

Van Nostrand Reinhold Company Regional Offices: New York Cincinnati Atlanta Dallas San Francisco

Van Nostrand Reinhold Company International Offices: London Toronto Melbourne

Copyright © 1978 by Litton Educational Publishing, Inc. Softcover reprint of the hardcover 1st edition 1978 Library of Congress Catalog Card Number: 77-17876 ISBN-13: 978-94-011-6058-2 e-ISBN-13: 978-94-011-6056-8 DOl: 10.1007/978-94-011-6056-8

All rights reserved. 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, or information storage and retrieval systems-without permission of the publisher.

Manufactured in the United States of America

Published by Van Nostrand Reinhold Company 135 West 50th Street, New York, N.Y. 10019 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 Data

Frerking, Marvin E Crystal oscillator design and temperature compensation.

Includes bibliographical references and index. 1. Oscillators, Crystal. 2. Oscillators, Transistor.

3. Frequency stability. 4. Temperature control. I. Title. TK7862.07F73 621.3815'33 77-17876 ISBN-13: 978-94-011-6058-2

Foreword

Crystal oscillators have been in use now for well over SO years-one of the first was built by W. G. Cady in 1921. Today, millions of them are made every year, covering a range of frequencies from a few Kilohertz to several hundred Mega­hertz and a range of stabilities from a fraction of one percent to a few parts in ten to the thirteenth, with most of them, by far, still in the range of several tens of parts per million.Their major application has long been the stabilization of fre­quencies in transmitters and receivers, and indeed, the utilization of the frequency spectrum would be in utter chaos, and the communication systems as we know them today unthinkable,'without crystal oscillators.

With the need to accommodate ever increasing numbers of users in a limited spectrum space, this traditional application will continue to grow for the fore­seeable future, and ever tighter tolerances will have to be met by an ever larger percentage of these devices.

Narrowing the channel spacing-with its concomitant requirements for in­creasingly more stable carrier frequencies-is but one of the alternatives to in­crease the number of potential users of the frequency spectrum. Subdividing the time during which a group of users has access to a given channel is another; and many modern radio transmission systems make use of this principle. Here again, the crystal oscillator plays a dominant role; not to control the carrier frequency, but to keep the time slots for the various users coordinated, that is, to serve as the clock rate generator of the systems clocks in transmitters and receivers. The demands on oscillator performance are often even more stringent in this applica­tion than for carrier stabilization alone.

The use of crystal oscillators as clock rate generators has seen a rate of growth in the recent past that is nothing short of explosive, with no end in sight yet, in applications that are quite unrelated to the communications field, such as in the quartz wrist watch and in the microprocessor. Other uses include reference stan­dards in frequency counters and time interval meters, gauges for temperature and pressure, and instruments for the measurement of mass changes for scientific and environmental sensing purposes, to name just a few.

In short, the crystal oscillator is now more in demand than ever, and the need for improved performance in mass producible devices becomes more urgent with

v

vi Foreword

nearly every new application. An increasing number of engineers, therefore, find themselves confronted with the challenge of designing crystal oscillators with near optimum performance, as tailored to a specific application. Those new in the field are bound to discover very soon that there is no substitute for a consid­erable amount of hands-on experience. Rarely can a circuit reported on in the literature be used without modifications, and details, not discussed fully in the descriptions provided, are often found to be significant.

The possible combinations of circuit elements that make a viable oscillator are nearly limitless, and while most experienced designers have gravitated toward a few basic configurations, no one circuit, or even small group of circuits, has as yet evolved that is, in all details, universally suitable. Nor does it appear likely that this will happen in the foreseeable future, if for no other reason than be­cause new active devices are continually being brought to market, with often sig­nificant advantages for use in oscillator circuits, but requiring different condi­tions for proper operation. The general principles of crystal oscillator design, however, remain.

The basic building blocks of a crystal oscillator are the feedback circuit con­taining the crystal unit; the amplifier containing one or more active devices; and circuitry or devices such as needed for modulation, temperature compensation or control, etc.

What is needed most by the circuit designer is a clear approach to understand­ing the interrelationship'of the various circuit elements within each of these build­ing blocks and of the blocks with one another. And this holds true whether the goal is an oscillator, hand-tailored in small quantities to achieve the highest performance possible, or mass produced and capable of meeting the specified requirements under worst case conditions. While such approaches do exist, their exposition in the literature is scarce. It is to ftll this void that Mr. Frerking has written this book.

M. E. Frerking is surely one of the most accomplished and innovative practi­tioners of the art of crystal oscillator design, with extensive experience in the development of high performance oscillators for high volume use. In his book he shares with the reader the design techniques that he has found most useful and conveys a wealth of practical information that will be of immediate use to en­gineers who are faced with the challenge of designing a crystal oscillator for today1s more demanding applications.

Mr. Frerking's book is a timely, and most welcome, major addition to the literature on crystal oscillators.

Erich Hafner. PHD. Supervisory Research Physicist US Army Electronics Technology & Devices Laboratory Fort Monmouth,NJ

Acknowledgments

The author wishes to express his sincere appreciation to the Collins Telecommunications Products Division of Rockwell International whose support and facilities made this work possible, and to those engineers working in the field of frequency control whose contribu­tions have resulted in many of the techniques described in this book.

The author would also like to acknowledge the assistance rendered by Dr. John Robinson and Mr. H. Paul Brower for their suggestions and assistance in preparing the manuscript.

vii

Symbol

bf b j

bo

by Co C1

fa fL fs

List of Symbols

Description

forward transfer susceptance input susceptance output susceptance reverse transfer susceptance shunt capacity across crystal motional arm capacitance antiresonant frequency frequency at load capacitance CL

series resonant frequency forward transfer conductance gf

gf(min) minimum forward transfer conductance required for oscillation

gj input conductance gm forward transfer conductance (transconductance) go output conductance gy reverse transfer conductance hf forward current transfer ratio hi input impedance K Boltzman's constant 1.38 X 10-23 J tK L 1 motional arm inductance Pc power dissipated in crystal ppm parts per million q electron charge 1.602 X 10-19 C R 1 motional arm resistance Re equivalent resistance of crystal Rin parallel input resistance R L extemalload resistance Rmax maximum resistance crystal oscillator is capable of

handling

ix

x List of Symbols

R T total resistive component of collector load WT angular frequency at which the common emitter current

gain has decreased to unity Xe equivalent reactance of crystal Y, forward transfer admittance Y j input admittance Yo output admittance Y r reverse transfer admittance Z, forward transfer impedance Zj input impedance Zo output impedance Zr reverse transfer impedance

Contents

Foreword, Erich Hafner / v List of Symbols / ix

1. INTRODUCTION / 1

2. BASIC OSCILLATOR THEORY / 3

3. METHODS OF DESIGN / 4

3.1. Experimental Method of Design /4 3.2. Y-Parameter Method of Design /5 3.3. Power Gain Method of Design / 7 3.4. Nonlinear Modifications /11

4. OSCILLATOR FREQUENCY STABILITY /14

4.1. Temperature Effects of Frequency / 14 4.1.1. Temperature Control/IS 4.1.2. Temperature Compensation /16

4.2. Long-Term Frequency Drift /16 4.3. Short-Term Frequency Stability / 17

5. QUARTZ CRYSTAL RESONATORS / 20

5.1. Load Capacitance / 25 5.2. Pin-To-Pin Capacitance /25 5.3. Resistance / 26 5.4. Rated or Test Drive Leve1/26 5.5. Frequency Stability / 26 5.6. Finishing or Calibration Tolerance /28 5.7. Crystal Aging /29 5.8. Q and Stiffness of Crystals /29 5.9. Mechanical Overtone Crystals / 30 5.10. Spurious or Unwanted Modes /31 5.11. Vibration, Shock, and Acceleration / 34 5.12. Standard Military Crystals /34 5.13. Specifications and Standards /39

xi

xii Contents

6. DISCUSSION OF TRANSISTORS /40

6.1. Transistor Equivalent Circuits /41 6.2. Y-Parameter Model /42 6.3. Hybrid 'IT Equivalent Circuit /44 6.4. Nonlinear Models /46

6.4.1. Intrinsic Transistor Model /47 6.4.2. Nonlinear Model with Emitter Degeneration / 52

7. OSCILLATOR CIRCUITS / S6

7.1. Pierce, Colpitts, and Clapp Oscillators / 56 7.2. Pierce Oscillator / 58

7.2.1. Small-Signal Analysis / 58 7.2.2. Large-Signal Analysis /63 7.2.3. 1- to 3-MHz Pierce Oscillator / 66 7.2.4. 1- to 10-MHz Pierce Oscillator / 67 7.2.5. 10- to 20-MHz Pierce Oscillator / 69 7.2.6. Overtone Pierce Oscillator / 70 7.2.7. 25-MHz Pierce Oscillator / 71 7.2.8. Impedance-Inverting Pierce Oscillator / 72 7.2.9. 25-MHz Impedance-Inverting Pierce Oscillator / 74 7.2.10. 50-MHz Impedance-Inverting Pierce Oscillator / 75 7.2.11. 7S-MHz Impedance-Inverting Pierce Oscillator / 75

7.3. Colpitts Oscillator / 76 7.3.1. 3- to 10-MHz Colpitts Oscillator / 82 7.3.2. 10- to 20-MHz Colpitts Oscillator / 83

7.4. Clapp Oscillator / 85 7.4.1. 3- to 20-MHz Clapp Oscillator Circuit / 88

7.5. Grounded-Base Oscillator / 89 7.5.1. 2S-MHz Grounded-Base Oscillator / 9S 7.5.2. SO-MHz Grounded-Base Oscillator / 96 7.5.3. 7S-MHz Grounded-Base Oscillator / 98 7.5.4. 110-MHz Grounded-Base Oscillator / 99

7.6. Gate Oscillators / 100 7.6.1. Single-Gate Oscillators /100 7.6.2. Multiple-Gate Oscillators / 106

7.7. Integrated- Circuit Oscillators / 110

8. PREPRODUCTION TESTS FOR CRYSTAL OSCILLATORS /119

9. OTHER TOPICS /121

9.1. Crystal Switches / 121 9.2. Pullable Oscillators / 122

9.3 . Crystal Ovens / 126 9.4. Squegging, Squelching, or Motorboating /127 9.5. Spurious Oscillations / 128

10. TEMPERATURE COMPENSATION /130

10.1. Analog Temperature Compensation / 131 10.2. Hybrid Analog-Digital Compensation / 146 10.3. Digital Temperature Compensation /152

Contents xiii

10.4. Temperature Compensation with Microprocessors /157

Appendix A Derivation of the Complex Equation for Oscillation / 177 Appendix B Derivation of V-Parameter Equations for the Pierce Oscillator / 180 Appendix C Derivation of Y -Parameter Equations for the Grounded-Base

Oscillator / 188 Appendix D Derivation of Approximate Equations for the Clapp

Oscillator / 193 Appendix E Derivation of Approximate Equations for the Pierce

Oscillator Analysis / 195 Appendix F Derivation of Approximate Equations for the Colpitts

Oscillator / 197 Appendix G Large-Signal Transistor Parameters / 199 Appendix H Large-Signal Transistor Parameters with Emitter

Degeneration / 209 Appendix I Nonlinear Analysis of the Colpitts Oscillator Based on the

Principle of Harmonic Balance / 216 Appendix J Mathematical Development of the Sideband Level versus

Phase Deviation Equation / 224 Appendix K Derivation of Crystal Equations / 226 Appendix L Sample Crystal Specification / 231

Bibliography / 235

INDEX / 239

CRYSTAL OSCILLATOR

DESIGN AND

TEMPERATURE COMPENSATION