**Functional Circuits and Oscillators** – For many years the field of electronics was concerned mainly with the use

of electronic devices in the generation, amplification, and control of sinu-

soidal and modulated waves. More recently, the rapidly growing fields of

instrumentation, control, and computing have placed great emphasis upon

electronic circuits that generate or employ pulses and nonsinusoidal waves.

The principal portion of this book deals with the analysis, characteristics,

and applications of circuits of this type. The last 22 sections treat sine-

wave oscillators, the basic principles of many of which are closely related

to those of circuits discussed in earlier sections.

A knowledge of the basic principles and characteristics of the circuits

treated throughout this book should enable the reader to synthesize circuits

to meet specific requirements. Of even greater potential value as a discipline

is the mathematical and phenomenological analysis of the circuits. For this

reason, greater emphasis has been placed upon the analysis and charac-

teristics of the basic circuits than upon specific circuits that meet individual

requirements. Where convenient, numerical values of circuit elements have

been provided in the examples of tube and transistor circuits.

Problems are numbered according to sections, and reference is made to

the problems at points where their solution should be helpful to an under-

standing of the theory. Many of the problems consist of outlines of details

of analysis that can be profitably performed by the reader, and that would

take up considerable space if included in complete form in the body of the

text. The reader is urged tb work at least a substantial portion of the

problems.

Table of Contents

## Functional Circuits and Oscillators Edited by

HERBERT J. REICH

Dunham Laboratory, Yale School of Engineering

Sheingold, Abraham — Fundamentals of Radio Communications

King, Donald D. — Measurements at Centimeter Wavelength

Reich, H. J., Ordnung, P. F., Krauss, H. L., Skalnik, J. G. Microwave

Theory and Techniques

Reich, H. J., Skalnik, J. G., Ordnung, P. F., Krauss, H. L. — Microwave

Principles

Murphy, Gordon J. — Basic Automatic Control Theory

Murphy, Gordon J. — Control Engineering

Hutter, Rudolf G. E. — Beam and Wave Electronics in Microwave Tubes

Fitchen, Franklin C. — Transistor Circuit Analysis and Design

Moon, Parry, and Spencer, Domina E. — Foundations of Electrodynamics

Moon, Parry, and Spencer, Domina E. — Field Theory for Engineers

Gartner, Wolfgang W. — Transistors; Principles, Design, and Applications

Reich, H. J. — Functional Circuits and Oscillators

Ku, Y. H. — Transient Circuit Analysis Functional Circuits and Oscillators

A series of text and reference books in electronics and communications.

Additional titles will be listed and announced as published.

FUNCTIONAL CIRCUITS

AND OSCILLATORS

HERBERT J. REICH

Department of Electrical Engineering

Yale University

D. VAN NOSTRAND COMPANY, INC.

PRINCETON, NEW JERSEY

TORONTO LONDON

NEW YORK

D. VAN NOSTRAND COMPANY, INC.

120 Alexander St., Princeton, New Jersey [Princi’pal office)

24 West 40 Street, New York 18, New York

D. Van Nostrand Company, Ltd.

358, Kensington High Street, London, W.14, England

D. Van Nostrand Company (Canada), Ltd.

25 Hollinger Road, Toronto 16, Canada

Copyright <§) 1961, by

D. VAN NOSTRAND COMPANY, Inc.

Published simultaneously in Canada by

D. Van Nostrand Company (Canada), Ltd.

No reproduction in any form of this book, in whole or in

part {except for brief quotation in critical articles or reviews),

may be made without written authorization from the publishers.

PRINTED IN THE UNITED STATES OP AMERICA

This Book Is Dedicated

TO All Who Have Participated in Its Preparation

## PREFACE – Functional Circuits and Oscillators

A large portion of this book deals with the theory, characteristics, and

applications of negative-resistance circuits and with the theory and char-

acteristics of sine-wave oscillators. The book might have been restricted to

these subjects and entitled, “Oscillators and Negative-Resistance Devices.”

Because many negative-resistance devices find their principal applications as

counters, memory devices, and generators of pulses and nonsinusoidal waves,

it seemed desirable to extend the coverage to other functional circuits, in-

cluding summing circuits, differential amplifiers, differentiators, integrators,

clippers, gates, and nonlinear-circuit simulators.

Much has been written on the subject of ‘negative-resistance circuits and

their applications. No previous attempt appears to have been made, how-

ever, to analyze generalized basic negative-resistance circuits and to derive

principles and criteria that can be conveniently used in the synthesis of

almost all presently-known practical negative-resistance circuits and devices

and the bistable, astable, monostable, and sine-wave-oscillator circuits based

upon them. When these principles and criteria are understood, it is a simple

matter to synthesize negative-resistance circuits using any type of active

element and to determine the ports at which the circuits have voltage-stable

current-voltage characteristics, and those at which they have current-stable

characteristics. The circuit elements that must be added in order to convert

a particular negative-resistance circuit into a bistable, astable, monostable,

or sine-wave-oscillator circuit can then be readily determined.

It is advantageous to consider all feedback oscillators from the point of

view of a basic generalized circuit consisting of a broadband amplifier and a

frequency-selective feedback network. In this manner a criterion for steady-

state oscillation of all feedback oscillators may be derived in terms of the

y and z parameters of two-port networks. The criterion may be readily

applied to the analysis of almost all commonly-used feedback oscillators

incorporating tubes, transistors, or other active elements. This approach

affords an insight into the causes of frequency instability and suggests

ways of increasing stability. It is also helpful in the synthesis of new or

modified circuits. Another important aspect of oscillator theory treated in

this book is the mechanism of amplitude stabilization by the use of circuit

nonlinearities.

The desire to minimize the space devoted to routine mathematical deriva-

vii

Vlll

### PREFACE

tions may tempt an author to rely unduly upon the statement, “It may be

readily shown that . . . when, in truth, the proper procedure is obvious

only after the analysis in question has been performed. In order to eliminate

mathematical details without straining the ingenuity of the reader unneces-

sarily, many proofs and derivations throughout the book have been presented

in the form of problems in which a general method of procedure is outlined.

It is hoped that this book may find application both as a text and as a

reference and that it will prove useful in the synthesis of new circuits to serve

specific functions. Although the author has attempted to make the book

up-to-date at the time of publication and to include pertinent recent refer-

ences, anyone working in any branch of the electronics field will be aware

of the difficulty faced by a single author in achieving this goal at the present

time of very rapid growth.

H. J. R.

New Haven, Conn.

April 1, 1961

CONTENTS

PREFACE vii

INTRODUCTION 1

- CIRCUITS FOR THE ADDITION OF VOLTAGES 1

Summing Amplifiers, 1; Tubes or Transistors with Common

Load, 3

- CIRCUITS FOR THE SUBTRACTION OF VOLTAGES . 4

The Differential Amplifier, 4; Differential-Amplifier Balance, 6;

Current Output of Differential Amplifier, 7; Differential Ampli-

fier with Single-Sided Output, 8; Transistor Differential Am-

plifiers, 10

- DIFFERENTIATING AND INTEGRATING CIRCUITS 11

Resistance-Capacitance Differentiating Circuit, 11; Effect of

Source Resistance and Load Capacitance, 13; Use of Inverse-

Feedback Amplifier, 15

- INTEGRATING CIRCUITS 18

Resistance-Capacitance Circuits, 18; Miller and Bootstrap Cir-

cuits, 20

- STABILIZED D-C AMPLIFIER FOR ADDING, DIFFER-

ENTIATING, AND INTEGRATING CIRCUITS . , , 21

Need for High Stability, 21; Basic Circuit, 22; Practical Cir-

cuit, 24

- CHARACTERISTICS OF DIODES 24

Thermionic Diodes, 24; Semiconductor Diodes, 25; Breakdown

Diodes, 27; Capacitor Diodes, 29; Transient Response of Semi-

conductor Diodes, 29

- CLIPPERS (AMPLITUDE COMPARATORS) . . . . 32

Diode Circuits, 32; The Use of Clippers in Rectangular-Wave

Generation, 34; Variants of the Basic Diode Circuits, 35; Clip-

ping by Single Triodes or Pentodes, 36 ; Transistor Clippers, 37 ;

The Cathode-Coupled Clipper, 37 ; Input Ratio of the Cathode-

Coupled Clipper, 38 ; Speed of Response of the Cathode-Coupled

Clipper, 39

IX

X

CONTENTS

- CLAMPING CIRCUITS .

Operation of Clamping Circuits, 40; Distortion by Clamping

Circuits, 42; Example of Clamper Application, 43

- PULSE SHARPENERS AND STRETCHERS

Resonant-Circuit Pulse Sharpener, 44; Diode Pulse Stretcher,

45; Transmission-Line Pulse Stretcher, 45; Monostable Circuits,

47

- ELECTRONIC SWITCHES (GATES)

Desirable Features of Electronic Switches, 47 ; Diode Gates, 47 ;

Not Circuits, 49; Full-Wave Diode Circuits, 49; Effect of Load

Capacitance and Conductance, 51

- VACUUM TRIODE AND PENTODE GATES

Full-Wave Triode Gate, 51; Cathode-Follower Gate, 52; Pen-

tode Gates, 53

- BEAM-TUBE GATES

Gated-Beam Tube, 54; Beam-Deflection Tube, 55; Secondary-

Emission Beam Tube, 56

- TRANSISTOR SWITCHES

Complete Collector Characteristic Curves, 58; Common-Emitter

Switch, 60; Common-Collector Switch, 61; Power Dissipation

in Transistor Switches, 62 ; Two-Transistor Circuits, 62 ; Com-

pensation for Unbalance, 63; Modified Circuits, 64; Transient

Effects in Transistor Switches, 64; Use of Transistor Switches as

Choppers, 65

- OR CIRCUITS, AND (COINCIDENCE) CIRCUITS, AND

NOT (ANTICOINCIDENCE) CIRCUITS

Or Circuits, 66; And Circuits, 66; Not Circuits, 68

- NEGATIVE-RESISTANCE CIRCUITS

Definition of Negative Resistance, 69; Example of a Negative-

Resistance Circuit, 70 ; Another Example of a Negative-Resist-

ance Circuit, 71

- SOME CHARACTERISTICS OF VOLTAGE-STABLE AND

CURRENT-STABLE CIRCUITS

Effect of Gain Parameters Upon Current-Voltage Curves, 72;

Criteria for Voltage-Stable and Current-Stable Ports, 73

- THE BASIC NEGATIVE-RESISTANCE CIRCUITS

Pi and Tee Circuits, 75 ; Effect of Reactive Elements, 77

CONTENTS

XI

- VACUUM-TUBE NEGATIVE-RESISTANCE CIRCUITS 7*9

Pentode Circuits, 79; Common-Cathode, Common-Cathode

Two-Tube Circuit, 81; Common-Grid, Common-Plate Two-

Tube Circuit, 84

- TRANSISTOR NEGATIVE-RESISTANCE CIRCUITS 85

Criteria for Negative Resistance in Transistor Circuits, 85;

Avalanche, Point-Contact, and P-N-P-N Transistors, 86 ;

P-V-P-V-Transistor Base Characteristics, 87; P-iV-P-V-

Transistor Emitter and Collector Characteristics, 89; Two-

Transistor and Three-Transistor Circuits, 90

- THE UNIJUNCTION TRANSISTOR 91

Structure of the Unijunction Transistor, 91

21 . DIODE NEGATIVE-RESISTANCE CIRCUITS …. 93

The Use of Transistors as Negative-Resistance Diodes, 93 ;

Current- Voltage Characteristics of-P-V-P-V Diodes, 94 ; Ef-

fect of Temperature and Illumination Upon P-V-P-V-Diode

Characteristics, 95 ; The Esaki Diode, 96

- GLOW AND ARC TUBES 97

Glow-Diode Current- Voltage Characteristics, 97 ; Arc-Diode

Current- Voltage Characteristics, 98; Current-Voltage Charac-

teristics of Grid-Controlled Arc Tubes, 99

- MULTISTABLE CIRCUITS 99

Definition of Multistable Circuit, 99; Graphical Explanation of

Bistability, 100

- STABILITY OF EQUILIBRIUM POINTS 101

Voltage-Stable Characteristic, 101 ; Current-Stable Character-

istic, 103 ; Criteria for Bistability, 104

- TRANSITION BETAVEEN STATES OF EQUILIBRIUM . 105

Change of Supply Voltage and Resistance, 105; Speed of Transi-

tion, 106; Triggering by Rectangular Pulse, 107; Triggering by

Exponential Pulse, 109

- TUBE AND TRANSISTOR BISTABLE CIRCUITS . Ill

Synthesis of Bistable Circuits, 111 ; Criteria for Bistability, 111 ;

Switching Diodes and Triodes; Thyratron, 113; Fully Con-

trollable Switching Devices, 114

- THE ECCLES-JORDAN CIRCUIT 116

Basic Circuit, 116; Transistor Eccles-Jordan Circuit, 117; Need

for Coupling Capacitors, 118; Use of Breakdown Diodes for

CONTENTS

Page

Coupling, 119; Variants of the Eccles-Jordan Circuit, 119;

Cathode-Coupled Eccles-Jordan Circuit, 121

- TRIGGERING OF THE ECCLES-JORDAN CIRCUITS 121

Methods of Triggering, 121 ; Comparison of Negative and Posi-

tive Triggering, 122

- COMMUTATION OF THE ECCLES-JORDAN CIRCUIT 122

Commutation by Coupling Capacitors, 122; Use of Diodes to

Aid Commutation, 124; Use of Breakdown Diodes to Aid Com-

mutation, 126; Commutation of Suppressor-Coupled Circuit, 127

- ANALYSIS OF THE ECCLES-JORDAN CIRCUIT AS AN

AMPLIFIER 127

Use of Voltage Transfer Characteristics, 127; Triggering by

Voltage Increment, 129; Speed of Transition, 130

- SPEED OF TRANSITION OF TUBE ECCLES-JORDAN

CIRCUITS 131

Equivalent Circuit During Transition, 131 ; Analysis for Rec-

tangular Triggering Pulse, 132; Analysis for Exponential Trig-

gering Pulse, 133; Settling Speed, 134

- SPEED OF TRANSITION OF TRANSISTOR ECCLES-

JORDAN CIRCUITS 136

Analysis of Equivalent Circuit, 136; Use of Breakdown Diodes

to Reduce Carrier-Storage Effects, 139

- STATIC STABILITY OF VACUUM-TUBE AND TRAN-

SISTOR-TUBE ECCLES-JORDAN CIRCUITS . .140

Method of Analysis of Tube Circuits, 140; Stability Criteria

for Tube Circuits, 140; Use of the Stability Criteria for Tube

Circuits, 141; Static Stability of the Transistor Eccles-Jordan

Circuit, 142; Requirements for Static Stability of Transistor

Circuits, 144 ; Stability of Diode-Coupled Transistor Circuit, 145

- MULTISTABLE CIRCUITS 145

Tristable Eccles-Jordan Circuit, 145; Triggering of Tristable

Circuit, 146; Current-Voltage Characteristic of Tristable Cir-

cuit, 147; Use of Nonlinear Load Resistance, 148; Use of Break-

down Diodes to Provide Nonlinear Load, 149; Multiple-Tube

Eccles-Jordan Circuit, 151

- THE USE OF MULTISTABLE CIRCUITS TO CONTROL

GATED AMPLIFIERS 153

CONTENTS

xiii

- BINARY AND TERNARY COUNTING CIRCUITS . . 155

Eccles- Jordan Binary Counter, 155; Addition and Subtraction

of Counts, 157

- DECADE COUNTERS 158

Conversion of Binary Circuit to Decade Circuit, 158 ; Alternate

Forms of Vacuum-Tube Circuit, 159; Transistor Decade Circuit,

160; Decade Circuit Incorporating Electronic Switch, 162; Cir-

cuits for Other Number Systems, 162

- COUNT INDICATORS FOR COUNTING CIRCUITS . 163

Indicators for Binary Counters, 163; Indicators for Decade

Counters, 164

- DECADE RING COUNTING CIRCUITS 166

Basic Ring Circuit, 166; Control of Direction of Commutation,

166; Another Type of Ring Circuit, 168

- GLOW-DIODE COUNTING CIRCUITS 170

Glow-Tube Binary Stage, 170; Glow-Tube Decade Counter, 171;

Semiconductor-Diode Circuits, 173

- COUNTER CIRCUITS USING STARTING-ANODE GLOW

TUBES, THYRATRONS, AND SWITCHING TRANSISTORS 173

Circuits Using Starting-Anode Glow Tubes, 173; Ring Circuit

Using Starting-Anode Tubes, 175; Thyratron and Switching-

Transistor Circuits, 176

- MULTIPLE-ELECTRODE GLOW COUNTING TUBES . . 176

Tubes with Two Sets of Transfer Electrodes, 176; Generation

of Triggering Pulses for Glow-Tube Circuits, 179; The Use of

Directional Cathodes to Insure Commutation, 180; Performance

of Directional-Cathode Tubes, 182

- MULTISTABLE MAGNETRONS 183

Negative-Resistance Magnetrons, 183; Magnetron Decade

Switching Tube, 185; Modifications of Magnetron Switching

Tube, 189; Mechanism of Switching, 189; Triggering Grids, 191

- MULTISTABLE ELECTROSTATIC-DEFLECTION TUBE . 192

Current- Voltage Characteristic, 192; Mechanism of Commuta-

tion, 194; Practical Tube, 196

- ANALYSIS OF NEGATIVE-RESISTANCE CIRCUITS

CONTAINING BOTH L AND C 197

Generalized Equivalent Circuits, 197; Analysis of Equivalent

Circuit Having Voltage-Stable Element, 198; Analysis of

XIV

CONTENTS

Page

Equivalent Circuit Having Current-Stable Element, 201 ; Oscil-

latory, Multistable, Astable, and Monostable Operation, 203

- GRAPHICAL ANALYSIS OF ASTABLE AND MONO-

STABLE CIRCUITS 204

Path of Operation, 204; Choice of Supply Voltage and Resist-

ance for Astable Operation, 205

- TYPICAL PATHS OF OPERATION FOR ASTABLE CIR-

CUITS BASED UPON CURRENT-STABLE ELEMENTS . 206

Analysis of Path of Operation, 206; Effect of Change of C/L

Ratio, 208; Useful Properties of Astable Circuits, 210

- PATHS OF OPERATION FOR ASTABLE CIRCUITS

BASED UPON VOLTAGE-STABLE ELEMENTS .210

Duality of Current-Stable and Voltage-Stable Circuits, 210;

Effect of Change of L/C Ratio, 212

- SOME GENERAL OBSERVATIONS CONCERNING

ASTABLE CIRCUITS 212

Synthesis of Astable Circuits, 212; Conversion of Bistable Cir-

cuits into Astable Circuits, 213; Choice of Supply Voltage and

Resistance for Astable Operation, 213; Advantages of Current-

Stable Circuits, 214

- PRACTICAL ASTABLE CIRCUITS 214

Pentode Relaxation Oscillator, 214; Phenomenological Explana-

tion of the Operation of the Pentode Circuit, 215; Cathode-

Coupled Relaxation Oscillator, 216; P-V-P-iV-Transistor Re-

laxation Oscillator, 217; Unijunction-Transistor Relaxation

Oscillator, 218

- THE MULTIVIBRATOR 220

Basic Circuit, 220; Analysis of Multivibrator Operation, 222;

Waveforms of Multivibrator Voltages and Currents, 223;

Screen-Coupled Pentode Multivibrator, 225; Cathode-Loaded

Multivibrator, 226

- STABILIZATION OF AIULTIVIBRATOR FREQUENCY . 227

Importance of Frequency Stability, 227; Period of Oscillation,

227; Frequency Instability of Vacuum-Tube Multivibrators,

229; Frequency Stability for Negative Grid Supply Voltage,

230; Frequency Stability of Transistor Multivibrator, 231;

Stabilization of Frequency Against Noise, 231; Stabilization

Against Variation of Load, 231

CONTENTS

XV

- TUNING OF THE MULTIVIBRATOR 232

Frequency of Oscillation, 232; Limits of Frequency of Oscilla-

tion, 233; Voltage Tuning of the Multivibrator, 234; Lineariza-

tion of Tuning, 234; Transistor Circuit, 236

- SYNCHRONIZATION OF RELAXATION OSCILLATORS . 236

Use of Relaxation Oscillators in Frequency Transformation,

236; Mechanism of Synchronization, 238; Synchronization by

Periodic Pulses, 239; Control by Resonant Circuits, 240

- MONOSTABLE CIRCUITS 240

Theory of Operation, 240; Conversion of Astable Circuits into

Monostable Circuits, 242; Analysis of One-Shot Multivibrator,

242; Causes of Nonrectangular Pulse Form, 245; Transistor

One-Shot Multivibrators, 247; Nonsaturating Transistor Cir-

cuit, 248; High-Current Transistor Circuit, 249; Monostable

Unijunction-Transistor Circuit, 250;. Use of Monostable Circuits

as Delay Circuits, 251

- PRECISION PULSE GENERATORS 251

Use of Miller Integrator for Timing, 251 ; The Phantastron, 252;

Modified Phantastron, 254

- SAWTOOTH-VOLTAGE GENERATORS 255

Types of Sawtooth-Voltage Generators, 255; Analysis of Astable

Sawtooth- Voltage Generators, 255; Frequency of Oscillation

of Astable Circuit, 257; Effect of Changes of Resistance and

Capacitance, 259; Choice of Supply Voltage and Resistance,

260; Monostable Operation, 260; Synchronization, 260

- PRACTICAL FORMS OF ASTABLE SAWTOOTH-

VOLTAGE GENERATORS 261

Glow-Tube Circuit, 261; Thyratron Circuit, 261; P-N-P-N-

Transistor Circuit, 263; Eccles-Jordan Circuit, 263

- SWITCH-TYPE SAWTOOTH-VOLTAGE GENERATORS . 264

Basic Circuit, 264; Bootstrap Circuit, 265; Miller Circuit, 267;

Suppressor-Controlled Miller Circuit, 269; Triangular-Wave

Circuit, 270; Pentode-Triode Circuit, 271

- SAWTOOTH-CURRENT GENERATORS 272
- BLOCKING-OSCILLATOR PULSE GENERATOR . .274

Principle of Operation, 274; Use of Resistor and Capacitor to

Control Pulse Length, 275; Modes of Operation, 275; Blocking-

Oscillator Transformers, 276

XVI

CONTENTS

Page

- ANALYSIS OF THE VACUUM-TUBE BLOCKING

OSCILLATOR 277

Analysis During Switching Periods, 277 ; Analysis During

Settling Periods, 279

- TRANSISTOR BLOCKING OSCILLATORS 280

Transistor Blocking-Oscillator Circuits, 280; Simplified Anal-

ysis, 281 ; Transition Time, 283

- LINEAR ANALYSIS OF TRANSITION OF TRANSISTOR

BLOCKING OSCILLATORS 284

Transition to the High-Current State, 284 ; Solution of Approxi-

mate Characteristic Equations, 287 ; Graphical Solution of Char-

acteristic Equations, 289; Effect of Loading, 289; Method of

Triggering, 289

- LINEAR ANALYSIS OF TRANSISTOR BLOCKING

OSCILLATORS DURING CONDUCTION 290

Analysis of Equivalent Circuit, 290; Use of R-C Timing Circuit,

292 ; Transition to Low-Current State, 293

- NONSATURATING TRANSISTOR BLOCKING

OSCILLATORS 293

Use of Diodes to Reduce Saturation, 293; Behavior Following

Transition to the High-Current State, 295; Conduction Period,

296

- NONLINEAR-CIRCUIT SIMULATORS 297

Advantages of Diode Circuits, 297 ; Characteristics of Multiple-

Branch Circuits, 298; Basic Diode Circuits, 298; Parallel and

Series Circuits, 300; Synthesis of Circuits Having Desired Char-

acteristics, 302 ; The Photoformer, 304

- PULSE AMPLIFIERS 306

Requirements of Pulse Amplifiers; Step Response, 306; Com-

pensation of Shunt Capacitance by Inductance, 307; Use of

Cathode-Follower Coupling Stages Between Pentodes, 310; Re-

sponse of Stages in Tandem, 310; Determination of Step-Voltage

Response, 310; Transistor Pulse Amplifiers, 311

- DISTRIBUTED AMPLIFIERS 311

Principle of Operation, 311; Number of Tubes Required, 313;

Attainable Bandwidth, 313

- GAIN CONTROLS FOR PULSE AMPLIFIERS . . . . 313

CONTENTS

xvii

- ONE-PORT AND TWO-PORT SINE-WAVE OSCILLATORS 314
- SINE-WAVE OSCILLATOR CHARACTERISTICS . .315

Desirable Features of Sine-Wave Oscillators, 315; Power Out-

put of Oscillators, 315; Harmonic Content, 316; Frequency

Stability, 316; Amplitude Stability, 317; Constancy and Accu-

racy of Calibration, 317

- NEGATIVE-RESISTANCE (ONE-PORT) OSCILLATORS . 317

Analysis of One-Port Oscillators, 317; Determination of Nega-

tive Resistance, 320; Type of Resonator Required, 321; Dy-

namic-Negative-Resistance Circuits, 321; Shunt and Series

Equivalent Circuits, 322

- AMPLITUDE AND FREQUENCY STABILIZATION OF

PARALLEL-RESONATOR NEGATIVE-RESISTANCE

OSCILLATORS

Amplitude Diagrams, 323; Amplitude Hysteresis, 325; Mini-

mization of Harmonic Content, 326; Amplitude Stabilization,

326; Frequency Stabilization, 328; Stabilization of Series-

Resonator Negative-Resistance Oscillators, 329

- ADMITTANCE DIAGRAMS FOR NEGATIVE-RESIST-

ANCE OSCILLATORS

Theory of Admittance Diagrams, 329; Analysis of an Admit-

tance Diagram, 331; Oscillation at More than One Frequency,

332 ; Use of Admittance Diagrams, 333

- PRACTICAL NEGATIVE-RESISTANCE OSCILLATORS

Choice of Circuits, 335; Pentode Negative-Resistance Oscil-

lators, 336; Balanced Negative-Resistance Oscillators, 337;

Cathode-Coupled and Emitter-Coupled Oscillators, 339; Nega-

tive-Resistance-Diode Oscillators, 339; Stabilization of Tran-

sistor Oscillators Against Changes of Temperature, 340

- ELECTRONIC TUNING AND MODULATION OF

NEGATIVE-RESISTANCE OSCILLATORS

Tuning by Direct Variation of Susceptance, 340; Tuning by

Variable-Admittance Tube and Transistor Circuits, 341

- FEEDBACK (TWO-PORT) OSCILLATORS

Choice of Amplifier, 342; Analysis of Generalized Feedback

Oscillator, 342 ; Analysis of Circuits in Which Amplifier Input

and Reverse Transfei; Admittance Are Small, 344; Analysis by

Differential Equations, 346

323

329

335

340

342

CONTENTS

- ADMITTANCE DIAGRAMS FOR FEEDBACK

OSCILLATORS , . a..

Justification for Admittance Diagrams, 346 ; Example of an Ad-

mittance Diagram for a Feedback Oscillator, 347; Klystron

Admittance Diagram, 348

- PARALLEL-RESONATOR FEEDBACK OSCILLATORS

Tuned-Output, Tuned-Input, Hartley, and Colpitts Circuits,

348; Choice Between Types, 350; Doubly Tuned and Push-Pull

Feedback Oscillators, 351; Methods of Obtaining Bias, 351

Page

346

348

- ANALYSIS OF PARALLEL-RESONATOR FEEDBACK

OSCILLATORS ^ ^ x

Methods of Analysis, 352; Analysis of Tuned-Plate Oscillator

by Differential Equations, 353; Analysis of Tuned-Plate Oscil-

lator by Two-Port-Network Equations, 354; Effects of Transit

Time, 355

- GENERALIZED ANALYSIS OF TUNED-OUTPUT

CIRCUITS .

Derivation of Expressions for Frequency and Criterion lor

Oscillation, 356; Tuned-Collector Oscillator, 359; Effect of Car-

rier Transit Time, 360; Other Tuned-Output Oscillators, 360;

Tuned-Input, Colpitts, and Hartley Analysis, 360

- AMPLITUDE LIMITATION IN PARALLEL-RESONATOR

FEEDBACK OSCILLATORS

Amplitude Diagrams for Vacuum-Tube Feedback Oscillators,

361; Capacitor-Gridleak Bias, 363; Design of Biasing Circuit;

Squegging, 365; Amplitude Limitation by Temperature-Con-

trolled Resistance, 366; Amplitude Stability, 366; Amplitude

Limitation in Transistor Feedback Oscillators, 368

- FREQUENCY STABILIZATION OF PARALLEL-

RESONATOR FEEDBACK OSCILLATORS

Stabilization Against Changes of Load, 370; Dependence of

Frequency upon Supply Voltage, 371 ; Stabilization of Frequency

Against Changes of Voltage, 373; Clapp-Gouriet Oscillator, 373;

Resistance Stabilization, 374; Reactance Stabilization, 375;

Stabilization of Frequency of Transistor Oscillators Against

Change of Temperature, 376; Use of Common-Collector and

Common-Base Coupling Stages, 377; Electronic Tuning and

Modulation of Feedback Oscillators, 377

CONTENTS

XIX

Page

- NULL-NETWORK OSCILLATORS 377

Desirable Features of Null-Network Oscillators, 377 ; Paral-

lel-Resonator Bridge Oscillator, 379; Bridged-Tee Feedback

Oscillators, 381; Parallel-Tee, Resistance-Capacitance-Tuned

Oscillator, 382

- WIEN-BRIDGE OSCILLATOR 384

Analysis of General Form of Circuit, 384; Vacuum-Tube Wien-

Bridge Oscillator, 384; Transistor Wien-Bridge Oscillator, 387;

Desirable Features of AVien-Bridge Oscillators, 389

- DOUBLE-FEEDBACK NULL-NETWORK OSCILLATORS . 391
- PHASE-SHIFT (LADDER-NETAVORK) OSCILLATORS . 391

Vacuum-Tube Phase-Shift Oscillators, 391 ; Stability of

Vacuum-Tube Phase-Shift Oscillator, 393; Use of Modified

Ladder Networks, 394; Tuning of Phase-Shift Oscillators, 397;

Transistor Phase-Shift Oscillators, 398; Two-Section Phase-

Shift Oscillator, 399; Other Types of Phase-Shift Oscillators,

400; Frequency-Modulation of Phase-Shift Oscillators, 401

- SUM- AND DIFFERENCE-CIRCUIT OSCILLATORS , . 406

“Seven-League” Oscillator, 406; De Lange Circuit, 407; Villard-

Holman Oscillators, 409

- CRYSTAL-CONTROLLED OSCILLATORS 412

Principle of Operation, 412; Use of Crystals in Negative-Re-

sistance Circuits, 413; Crystal-Controlled Feedback Oscillators,

414; Crystal-Controlled Null-Network Oscillator, 414

- MAGNETOSTRICTION OSCILLATORS 415
- BEAT-FREQUENCY (HETERODYNE) OSCILLATORS 416
- MICROAVAVE OSCILLATORS 418

APPENDIX 420

PROBLEMS 422

ADDENDUM 450

LETTER SYMBOLS 452

AUTHOR INDEX 455

SUBJECT INDEX . 459

### Introduction – Functional Circuits and Oscillators

For many years the field of electronics was concerned mainly with the use

of electronic devices in the generation, amplification, and control of sinu-

soidal and modulated waves. More recently, the rapidly growing fields of

instrumentation, control, and computing have placed great emphasis upon

electronic circuits that generate or employ pulses and nonsinusoidal waves.

The principal portion of this book deals with the analysis, characteristics,

and applications of circuits of this type. The last 22 sections treat sine-

wave oscillators, the basic principles of many of which are closely related

to those of circuits discussed in earlier sections.

A knowledge of the basic principles and characteristics of the circuits

treated throughout this book should enable the reader to synthesize circuits

to meet specific requirements. Of even greater potential value as a discipline

is the mathematical and phenomenological analysis of the circuits. For this

reason, greater emphasis has been placed upon the analysis and charac-

teristics of the basic circuits than upon specific circuits that meet individual

requirements. Where convenient, numerical values of circuit elements have

been provided in the examples of tube and transistor circuits.

Problems are numbered according to sections, and reference is made to

the problems at points where their solution should be helpful to an under-

standing of the theory. Many of the problems consist of outlines of details

of analysis that can be profitably performed by the reader, and that would

take up considerable space if included in complete form in the body of the

text. The reader is urged tb work at least a substantial portion of the

problems.