CRYSTAL RECTIFIERS
`
`By HENRY C. TORREY
`ASSOCIATE PROFESSOR OF PHYSICS
`RUTGERS UNIVERSITY
`
`And CHARLES A. WHITMER
`ASSOCIATE PROFESSOR OF PHYSICS
`RUTGERS UNIVERSITY
`
`EDITED BY
`
`8. A. GoupsmIt
`
`Leon B. Linrorp
`
`James L. Lawson
`
`Apsert M. Stone
`
`OFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT
`
`NATIONAL DEFENSE RESEARCH COMMITTEE
`
`First Epirion
`Sreconp IMPRESSION
`
`
`
`NEW YORK AND LONDON
`
`McGRAW-HILL BOOK COMPANY,
`
`INC.
`
`1948
`
`1
`
`APPLE ET AL. EXHIBIT 1016
`
`APPLE ET AL. EXHIBIT 1016
`
`1
`
`

`

`CRYSTAL RECTIFIERS
`
`Coprricut, 1948, BY THE
`McGraw-Hitt Book Compaxy, Inc.
`PRINTED IN THE UNITED STATES OF AMERICA
`
`All rights reserved. This book, or
`parts thereof, may not be reproduced
`im any form without permission of
`the publishers.
`
`
`Ee \NST. Tey |
`
`MAR 20 195°
`Linpsey-
`
`THE MAPLE PRESS COMPANY, YORK, PA.
`
`2
`
`

`

`Foreword
`
`
`HE tremendous research and development effort that went into the
`development of radar and related techniques during World WarII
`resulted not only in hundreds of radar sets for military (and some for
`possible peacetime) use but also in a great body of information and new
`techniques in the electronics and high-frequency fields. Because this
`basic material may be of great value to science and engineering,it seemed
`most important to publish it as soon as security permitted.
`The Radiation Laboratory of MIT, which operated under the super-
`vision of the National Defense Research Committee, undertook the great
`task of preparing these volumes. The work described herein, however,is
`the collective result of work done at many laboratories, Army, Navy,
`university, and industrial, both in this country and in England, Canada,
`and other Dominions.
`The Radiation Laboratory, once its proposals were approved and
`finances provided by the Office of Scientific Research and Development,
`chose Louis N. Ridenour as Editor-in-Chief to lead and direct the entire
`project. An editorial staff was then selected of those best qualified for
`this type of task. Finally the authors for the various volumesor chapters
`or sections were chosen from among those experts who were intimately
`familiar with the variousfields, and who wereable and willing to write
`the summaries of them. This entire staff agreed to remain at work at
`MITfor six months or more after the work of the Radiation Laboratory
`was complete. These volumes stand as a monumentto this group.
`These volumes serve as a memorial to the unnamed hundreds and
`thousands of other scientists, engineers, and others who actually carried
`on the research, development, and engineering work the results of which
`are herein described. There were so manyinvolvedin this work and they
`worked so closely together even though often in widely separated labora-
`tories that it is impossible to name or even to know those who contributed
`to a particular idea or development. Only certain ones whowrote reports
`or articles have even been mentioned. But to all those who contributed
`in any way to this great cooperative developmententerprise, both in this
`country and in England, these volumesare dedicated.
`L. A. DuBrince.
`
`Ae
`Aoee\
`
`i
`
`3
`
`3
`
`

`

`
`
`
`
`MRSAMIRctasERGiLesichatgeReinkeobeattentiaccsiSRORORTEReR
`
`4
`
`
`

`

`
`
`Preface
`
`
`1TH the development of microwave radar,
`the crystal rectifier,
`WShick had been little used since the invention of the vacuum tube
`several decades ago, again became important—as important as the magne-
`tron, klystron, or other microwave components.
`In the past five years crystal rectifiers have been manufactured,
`literally by the millions, for use primarily as microwave detectors. A
`correspondingly large amount of fundamental research and engineering
`development has taken place in the commercial and governmentallabora~-
`tories in the United States and in England. As a result the crystal-
`rectifier unit that has emerged is a compact, stable device whichis superior
`in many applications to the vacuum-tube diode.
`Its most extensive use
`up to now has been as a frequency converter in microwavereception,
`where its performance has not been equaled.
`It has also been used to a
`lesser extent as a low-level microwave detector.
`The recent development of germanium rectifiers capable of withstand-
`ing relatively high inverse voltages holds great promise for applications
`as second detectors in wideband receivers and in a variety of other cir-
`cuits where vacuum-tubediodes are ordinarily used.
`The purpose of this book is to present the fund of knowledge on crystal
`rectifiers that has accumulated during the course of World War II.
`Because of the need in radar systems for high-quality microwave con-
`verters, a large fraction of the work was expended for the develop-
`ment of crystal rectifiers for this application. A correspondingly large
`fraction of the book has, therefore, been devoted to the theory and proper-
`ties of the crystal converter. Other applications are discussed in Part III
`as Special Types.
`As in every other branch of microwave work, the development of
`measuring equipment and techniques has taken place simultaneously
`with that of the crystal rectifier itself. We have,
`therefore, included
`detailed discussions of methods of measurement of crystal properties
`and a description of standard test equipment for production and routine
`testing.
`The techniques for manufacturing converter crystals are discussed in
`Chap. 10. Special
`techniques required for the manufacture of other
`types are described in the appropriate chapters. The procedures pre-
`sented in detail are drawn largely from the work done at the MIT
`vu
`
`
`
`5
`
`

`

`
`
`Vill
`
`PREFACE
`
`Radiation Laboratory and by NDRCcontractees, but no attempt has
`been madetc include the details of all of the procedures that have been
`successfully employed.
`Because of the unique nature of war research and development, it
`is impossible to acknowledge adequately individual contributions to
`this subject. Much of the workis a result of the joint efforts of many
`individuals. At the present writing most of the available literature
`is in the form of reports that, for reasons of security, have not yet been
`published in scientific journals. Much of
`the literature referred to
`will undoubtedly appear later, however, in journal articles, or will be
`declassified and made available by the United States government.
`We have therefore given references to some of the more important of
`these documents.
`In England the chief contributors to crystal research and develop-
`ment were the General Electric Company, British Thompson-Houston,
`Ltd., Telecommunications Research Establishment, and Oxford Uni-
`versity;
`in this country they were the Bell Telephone Laboratories,
`Westinghouse Research Laboratory, General Electric Company, Sylvania
`Electric Products, Inc., and E. I. duPont de Nemours and Company.
`The crystal groups at the University of Pennsylvania and Purdue Uni-
`versity, who operated under NDRCcontracts, were responsible for much
`of the fundamental research and development work reported herein.
`DuPont and the Eagle-Picher Company developed manufacturing
`processes and produced in quantity highly purified silicon and germanium
`oxide, respectively, without which much of the improvement in crystal
`rectifiers would have been impossible.
`the Radiation
`We are particularly indebted to our colleagues at
`Laboratory whose contributions and stimulating discussions have been
`invaluable in writing this book.
`The preparation of
`this manuscript would have been impossible,
`finally, without the splendid aid of the editorial staff.
`In addition to
`those names listed as editors, we wish particularly to emphasize our
`gratitude to Barbara E. Myers, Marjorie 5. Tariot, and Natalie C.
`Tucker, editorial assistants.
`
`Henry C. Torrey.
`CHaRLes A. WHITMER.
`
`CamBripGe, Mass.
`June, 1946.
`
`||
`
`6
`
`

`

`Contents
`
`
`FOREWORDsy L. A. DuBnripce .
`
`PREFACE. .....
`
`Cuar.1.
`
`INTRODUCTION .. .
`
`vii
`
`THE PHENOMENON OF RECTIFICATION... ...
`1-1. The Nonlinear Element.....
`1-2. Detection.
`fo
`1-3. Frequency Conversion ae
`Tue NaTURE OF THE CRYSTAL RECTIFIER.
`.
`.
`1-4. The Discovery and Early Use of CrystalIRectifiers.
`1-5. Recent Developments . Ce ee
`
`aononPe
`
`PART I. GENERAL PROPERTIES
`
`Cuap.
`
`2,5 FUNDAMENTAL PROPERTIES OF THE CRYSTAL RECTI-
`FIER... 2...
`
`15
`
`15
`15
`18
`
`20
`20
`23
`
`25
`25
`33
`
`40
`
`45
`
`45
`
`51
`53
`
`64
`
`THE PRESENT CrysTAL CARTRIDGES.
`Lo ee ee
`2-1. Description of the Cartridge
`2-2. Stability and Handling Precautions. .......2.2.2..
`ELECTRICAL PROPERTIES.
`.
`
`.
`
`.
`
`.
`
`.
`
`2:3. The Voltage-current Characteristic
`2-4. The Equivalent Circuit.
`.
`.
`Mixer CrysTaAlts........
`
`.
`.
`2-5. Conversion Loss, Noise, and Noise Figure.
`2-6. Optimum Local-oscillator Level
`.
`.
`. an
`2-7. The R-f Impedanceof Crystal Rectifiers Loe
`2-8. The I-f Impedanceof Crystal Rectifiers
`
`.
`
`Cuap. 3. PROPERTIES OF SEMICONDUCTORS.
`
`Lo
`.
`3-1. Band Theory...
`3-2. Electron Distribution in1 Semiconduetors Loe
`3-3. Work Functions and Contact Potentials .
`3-4. Electrical Conductivity and. Hall Coefficient for Scmiconductors
`3-5. Characteristic Constants of Silicon and Germanium .
`3-6. Effect of Impurity Additions in Silicon and Germanium.
`ix
`
`7
`
`

`

`x
`
`CONTENTS
`
`Cuap. 4. THE SEMICONDUCTOR—METAL CONTACT ........ 68
`
`toe eee ee 68
`. 2. 2...
`4:1. Barrier-layer Rectification.
`4-2. Formation and Structure of the Barrier Layer. toe ee ee
`70
`4-3. Diffusion and Diode Theories of Rectification .
`. 2... .. ..
`WZ
`4.4. The D-c Characteristic.
`. 2. 2...) ee. 82
`4.5. Depletion Layers.
`.
`.
`. 0)
`4-6. Rectification at High Frequencies Poe ee ee ee OF
`
`PART II. THE CRYSTAL CONVERTER
`
`Cuap. 5. FREQUENCY CONVERSION. ................ 211
`5-1. Discussion of the General Problem.
`.
`. 2... ... 2.2... ‘114
`5-2. The Admittance Matrix. ....... coe ee ee ee ey TNE
`
`THe PHENOMENOLOGICAL THEORY OF CONVERSION... ....... . 119
`5:3. The Admittance Matrix in Terms of Measurable Parameters .
`. 119
`5-4, Transformation of the Matrix to New Variables...
`.
`.
`.
`.
`. 121
`5-5. Reciprocity. ....... Coe ee ee 184
`Conversion Loss anD MIXER ADMITTANCES.......... 2...
`. 128
`
`. 2... 128
`. 2.
`5-6. General Definition of Loss; Special Cases...
`5-7. Conversion Loss in the Broadband Case...
`.... . ... . 130
`5-8. General Expression for Conversion Loss.
`.
`2. ee. 186
`.
`.
`5-9. Effect of the Image Termination on Conversion Loss.
`. ew. 140
`5-10. Effect of Image Termination on I-f Impedance. ....... . 148
`Tue Puysican THEORY oF CONVERSION. ............... 152
`5-11. Matrix of a Nonlinear Resistance .
`.
`.
`woe ee. 158
`5-12. Effect of Parasitic Impedances on Conversion Loss. 2. ew.
`. 157
`5-13, Effect of a Variable Barrier Capacitance... ......... 168
`5-14. Harmonie Reinforcement... .. .
`. eee ee. 167
`5-15. Conversion with a Subharmonic Local Oscillator. wee ee ee 170
`5-16. Harmonic Generation...
`. 2... 2. ee ee ee 18
`5-17. Modulation. ©... 1 ee ee TS
`
`Cuar.6. NOISEGENERATION....................179
`THEoRY.......
`.
`See eee ee 19
`
`6-1. Shot and Thermal Noise inna CrystalRectifiers... 2... .. . 179
`6-2. Other Sources of Noise... 2... .
`to ee ee ee 186
`INTERMEDIATE-PREQUENCY AND Vipgeo NOISE. ............ . 187
`6-3. Dependence of Noise Temperature on Frequency. ....... 188
`6-4. Dependence on Temperature. ...........2.2.2. =. 104
`
`MicrowavE NoIsE..... 2... ee ee ee ew we 195
`6-5. The Crystal as a Microwave Noise Generator. ...... .
`. 195
`Cuar. 7. LOSS AND NOISE MEASUREMENTS. ..... we ew ee . 198
`Loss MEASUREMENTS .... . Ce ee ee ee we 198
`7-1, General Considerations.
`. 5...) 1 1 et ee ewe 198
`‘
`
`
`
`&
`:
`z
`i
`:
`c
`&
`i
`b
`:
`,
`e
`:
`
`i
`:
`
`:
`i
`
`:
`t
`‘
`
`
`
`pepeseparmemRef
`
`&
`‘
`4
`‘
`i
`|
`i
`4
`:
`
`:
`4
`:
`:
`
`:
`:
`é
`
`MERRIESAR,NITRBEIESI
`
`
`
`
`
`8
`
`

`

`. 200
`. Ce ee ee
`.
`7-2. The Heterodyne Method .
`202
`
`7-3. .2.....-....0-0080-2 204Impedance Methods...
`
`. 213
`7-4, The Incremental and Amplitude-modulation Mcthods .
`
`CONTENTS
`
`Xi
`
`NOISE-TEMPBRATURE MEASUREMENTS .
`7-5. General Considerations.
`.
`Loe
`7-6. The Roberts Coupling Cireuit.
`.
`.
`. 2...
`7-7. Narrow-band Coupling Circuit.
`7-8. Use of the Noise Diode in Noise-temperature Measurements.
`
`. 2...
`
`MEASUREMENT OF Loss, NoIsE, AND RECEIVER NOISE FIGURE .
`7-9. The Measurement of Receiver Noise Figure.
`7-10. The Measurement of Mixer-crystal Properties.
`7-11. Loss and Noise Temperature as a Function of R-f Tuning.
`
`Cuap.8. BURNOUT. .......
`
`8-1. General Considerations.
`8-2. Burnout Theory.
`Loe
`8-3. Burnout Theory.
`Lone
`8-4. Experiments on BurnoutLoe
`8-5. Burnout Limitations of Standard Crystal Units Lae
`
`Cuap. 9, TEST EQUIPMENT.....
`Stranparp Loss Tsst Sets.
`9-1. The Conversion-loss Set for the 39cm Band ......
`9-2. The Conversion-loss Set for the 10-cem Band. .... .
`9-3. The Conversion-loss Set for the l-cm Band .
`.
`9-4, The Mechanical Modulator. .......
`
`Stanparp Notss Test Sets .....
`
`9-5. The Noise Measuring Set for the 3-cm Band. ....... .
`9-6. The Noise Measuring Set for the 10-em Band. .......
`9-7. Noise-temperature Measurement of l-cm Rectifiers.
`.
`.
`
`BuRNovUr
`.
`. Loe
`9-8. Bpike Test
`9-9. Microsecond Pulse Test
`
`1 ee ee ee ee
`2 1.
`©
`Frevp TESTING.
`9-10. D-c Tests. 2. 6. we ee ee ee
`
`. 218
`. 218
`. 223
`. 225
`. 226
`
`. 227
`- 227
`. 230
`. 232
`
`. 236
`
`. 236
`. 239
`. 248
`. 256
`. 260
`
`. 264
`
`. 264
`. 265
`. 272
`. 276
`. 280
`
`. 283
`. 283
`. 289
`. 292
`
`. 293
`. 293
`. 296
`
`. 297
`. 297
`
`Cuap. 10. MANUFACTURING TECHNIQUES .....
`PREPARATION: OF SEMICONDUCTOR.
`.
`.
`.
`. 0-1)
`+ et ee ee
`10-1. Purification of the Semiconductor .
`.
`.
`10-2. Addition Agents.
`. :
`soe
`10-3. Preparation of the Ingot -Le
`10-4. Polishing, Heat-treatment, and Etchingre
`
`
`
`
`
`9
`
`

`

`xii
`
`CONTENTS
`
`Tue Cat WHISKER. ....
`Lone ae
`.
`10-5. Whisker Materials.
`10-6. Fabrication of the Whisker Coe
`ASSEMBLY AND ADJUSTMENT OF THE CARTRIDGE. .... .
`
`.
`
`10-7. The Ceramic Cartridge.
`10-8. The Coaxial Cartridge...
`
`.
`
`Some Design ConsiIpERATIONS AFFECTING ELECTRICAL PERFORMANCE.
`
`.
`
`10-9. R-fImpedance........ Coe ee
`10-10. Conversion Loss and Burnout. ...... .
`
`PART III. SPECIAL TYPES
`
`Cuar. 11. LOW-LEVEL DETECTION. .......
`
`PRoPERTIES OF CRYSTAL ReEcTIFIERS AT Low LEVELS .
`11-1. Reetification at Low Levels... 2...
`11-2. Equivalent-circuit Theory.
`.
`11-3. Effect of Bias on Low-level Properties
`11-4. Variation of Low-level Properties with Temperature...
`
`.
`
`.
`
`.
`
`. 316
`. 316
`. 318
`
`» 323
`. 323
`. 326
`
`. 328
`. 328
`. 329
`
`. 333
`
`. 333
`. 333
`. 385
`. 340
`. 342
`
`THeory OF LOW-LEVEL DETECTION...
`
`. 344
`. B44
`a
`11:5. The Figure of Merit of a Video Crystal.
`. 347
`11-6. Effect of D-c Bias on Figure of Merit. .. ... .
`11-7. The Effect of Temperature Variation on Crystal-video Receiver
`Performance. .....
`. 348
`
`.
`
`.
`
`MEASUREMENTS,
`
`11-8. R-f Equipment and Measurements.
`11-9. Equipment and Methods for Measuring Current Sensitivity, Video
`2... . 855
`Resistance, and Figure of Merit. ......
`
`. 349
`350
`
`seemnang
`
`SrrecIAL MANUFACTURING TECHNIQUES. .......
`
`.
`.
`.
`11-10, Stability Considerations.
`. Lo
`.
`.
`11-11. Processing the Silicon.
`.
`.:
`.
`.
`.
`11-12. Fabrication of the Whisker
`11:13. Adjustment of the Rectifying ContactLoe
`
`Cuap. 12, HIGH-INVERSE-VOLTAGE RECTIFIERS ..... .
`
`Tur HIGH-INVERSE-VOLTAGE RECTIFIER AND ITS APPLICATIONS .
`
`.
`
`.
`
`12:1. Preparation of the Ingot.........
`12-2. Etching and Surface Treatment ..... .
`12-3. Assembly and Adjustment of the Cartridge .
`12-4. Low-frequency Properties.
`Lo
`12-5. High-frequency Properties .
`Lo
`.
`Lo
`.
`12-6.
`Silicon High-inverse-voltage Rectifiers Lo
`12-7. Theory of the Negative-resistance Characteristics Lo
`12:8. Photoelectric Effects in Silicon and Germanium .
`
`.
`
`. 357
`. 358
`. 358,
`. 359
`. 359
`
`. 361
`
`. 361
`. 364
`. 369
`. 369
`. 372
`378
`. 389
`. 391
`. 392
`
`LSTET,
`
`10
`
`10
`
`

`

`CONTENTS
`
`xill
`
`Cuap. 13. WELDED-CONTACT GERMANIUM CRYSTALS. .... .
`
`. 398
`
`. 898
`. 2...
`13-1. Construction of Welded-contact Rectifiers... 2...
`13-2, General Properties.
`.
`2. 2... 0... ee ee e400
`13:3. Negative I-f Conductance. .. .
`. Soe ee ee ee ee 401
`13-4. Loss and Noise Measurements... .......2....,.. . 403
`13-5. Theory of Negative I-f Conductance and Conversion Amplification 406
`13-6. Applications... 2... ee 48
`
`APPENDIX A The Reciprocity Theorem of Dicke .
`
`.
`
`. ....... .
`
`. A417
`
`APPENDIX B Skin Effect at a Metal-semiconductor Contact... .. .
`
`APPENDIX C_ Spreading Resistance of an Elliptical Contact.
`
`APPENDIX D Crystal-rectifier Types and Specifications.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`. 421
`
`. 427
`
`.
`
`.
`
`.
`
`.
`
`. woe ee 429
`
`:
`
`j
`
`)
`
`
`
`INDEX... 2. ee. 485
`
`
`
`11
`
`11
`
`

`

`12
`
`12
`
`
`

`

`
`
`CHAPTER 1
`
`INTRODUCTION
`
`THE PHENOMENON OF RECTIFICATION
`
`The process of rectification and its applications are well known and
`extensively treated in the literature. However, within the last five
`years a wealth of new information on the crystal rectifier has accumulated
`as a result of its superior performance in microwavereceivers.
`In fact,
`the use of crystal rectifiers for frequency conversion occurredforthefirst
`time during World War II. The purpose of this book is to give an
`account of the present state of our knowledgeof the crystal rectifier and
`its applications. The applications with which weare chiefly concerned
`have to do with the use of the rectifier as a nonlinear device in the detec-
`tion and frequency conversion of r-f signals. As a background for the
`analysis of the crystal rectifier we shall begin with a brief review of the
`process of detection and frequency conversion.
`1-1. The Nonlinear Element.—Rectification may be defined as an
`operation on an a-c voltage to produce a unidirectional component. The
`vacuum-tube diode is a familiar example of a device that performs this
`function. The unidirectional component arises from the fact that the
`average resistance to current flow is less in one direction than in the other.
`In addition to the d-c component in the rectifier output there are also
`present harmonics of the input signal which arise because of the nonlinear
`character of the rectifying element. The relative amplitudes of
`the
`harmonics depend on the shape of the current-voltage characteristic
`curve in the operating region. The magnitude of the d-c component
`also depends on the shapeof the characteristic. For example, it is clear
`that a nonlinear element having the characteristic curve of Fig. 1-la,
`which is an odd function of the voltage about the origin, will have no
`output d-c component at all when operated at zero bias. However,if a
`d-c bias voltage is applied so that the operating point is at A, the applica-
`tion of a small a-c signal will result in a net increase in the direct current
`over that produced by the bias alone. This occurs because the average
`current will be greater for the positive swings of the a-c signal than for
`the negative ones.
`Rectifiers that are useful for detection purposes have characteristics
`similar to that shown in Fig. 1:1b. The shape of the characteristic will
`of course depend on the physical nature of the rectifier.
`In general, the
`
` | | | | ||\ |
`
`
`
`13
`
`13
`
`

`

`2
`
`INTRODUCTION
`
`[Skc. 1-2
`
`important features are a high back resistance and a relatively lowfor-
`ward resistance. At high frequencies other physical characteristics, such
`as capacitance of the rectifying element, transit time, etc., are important
`factors.
`In the vacuum-tube diode, for example, the resistance in the
`back direction is very high.
`In the forward direction the current is
`proportional to the three-halves power of the
`applied voltage when the voltages are small.
`For larger voltages there is a region that is ap-
`proximately linear. As we shall sce later, the
`shapeof the crystal-rectifier charactcristic may
`vary widely depending on the nature of the
`crystal and the wayin which it is constructed.
`Weshall postpone the discussion of the crystal-
`rectifier characteristic and the consideration of
`the other properties that are of importance in
`the microwaveregion.
`t
`
`
`
`Shaenactcesistrate
`
`
`hommeagempnntngenrts9:
`
`Sena
`
`(6)
`Fic. 1:1.—Nonlinear ele-
`ments.
`(a) Nonrectifying
`element
`at
`zero
`bias;
`(6)
`rectifying element.
`
`Fic.
`
`1-2,—Ideal
`characteristic,
`
`e
`rectifier
`
`1-2. Detection.—In the use of the rectifier for detection there are two
`classifications that are of particular interest to us:
`(1) linear and (2)
`square-law detection.
`Linear Detection.—In linear detection, the rectifier functions essen-
`tially asa switch. Let us assumethat therectifier characteristic is ideal—
`that is, that the resistance in the back direction is infinite, and in the for-
`ward direction is small and constant (see Fig. 1-2).
`It is well known
`that when a sinusoidal waveis impressed on the ideal rectifier the average
`current through this rectifier will be proportional to the amplitude of
`the input wave. The voltage across the rectifier load resistance will
`then be composed of a d-c component proportional to the amplitude of
`the input signal plus components of the input frequency and its even
`harmonics.
`Mostrectifiers will approximate this ideal performance if the input
`signal is large enough to make the region of curvature near the origin
`small compared with the substantially straight part of the characteristic
`over which the voltage varies. Furthermore, the load resistance is usu-
`
`
`
`14
`
`14
`
`

`

`
`
`Src. 1-2]
`
`DETECTION
`
`3
`
`ally chosen large compared with the rectifier resistance so that the effect
`on the output voltage of variation of the forward resistanceof therectifier
`is small.
`Theefficiency of rectification is defined as the ratio of the d-c voltage
`across the output load resistance to the peak amplitude of the input
`signal.
`It depends on the ratio of load resistance to the internal resis-
`ance of the rectifier and the amplitude of the input signal as noted above.
`In the detection of amplitude-modulated waves in radio reception a
`load consisting of a parallel RC combination is commonly used. With
`proper choice of the values of R and C the output voltage will, to a very
`close approximation, vary like the envelope of the amplitude-modulated
`wave. Under these conditions, the rectification efficiency of vacuum-
`tube diode rectifiers is normally about 70 to 90 per cent. A detailed
`analysis of linear detectors used in radio receivers may be found in stand-
`ard textbooks on radio engineering! and will not be given here. We will
`return to a discussion of the use of one of the crystal rectifier types as a
`linear detector in Chap. 12.
`‘Square-law Detectton.—The term square-law is applied to a detector
`in which the d-c, or rectified, output is proportional to the square of the
`amplitude of the input signal.
`It can readily be seen that such a response
`depends on the nonlinearity of the characteristic at the operating point,
`Over a limited range the current-voltage characteristic of a rectifier can
`be represented by a Taylor expansion terminating in the squared term
`2
`a)
`i= $0) = flee) + OF sert 5 5(60),
`where é, is the bias voltage determining the operating point, and 8¢ is the
`small input signal voltage. The derivatives are evaluated at the operat-
`ing point
`é@. Any rectifier will,
`therefore, function as a square-law
`rectifier when the applied signal is sufficiently small, provided that the
`second derivative of the characteristic does not vanish at the operating
`point. The linear term is, of course, of no importance asfar as rectifica-
`tion is concerned, since it is symmetrical about the operating point.
`By meansof Eq. (1) we can determine analytically the output of the
`rectifier for a given input signal. The analvsis can be summarized briefly
`as follows. Let us consider a signal consisting of a single sinusoidal wave,
`E sin wt.
`In addition to the frequency of the signal, the cutput will
`contain d-c and second-harmonic components with amplitudes propor-
`tional to E?.
`In general, if the signal is composed of a numberof sinu-
`soida] components the output will contain, in addition to the frequency
`components of the signal, the d-c component, second harmonics of each
`
`For example see F. . Terman, Radio Engineer's Handbook, McGraw-Hill, New
`York, 1943.
`
`
`
`15
`
`15
`
`

`

`4
`
`INTRODUCTION
`
`[Sxc. 1-3
`
`frequency component, and sum and difference frequencies formed by
`every possible combination of frequencies contained in the input signal.
`The amplituce of the d-c componentwill be proportional to the sum of the
`squares of the amplitudes of the signal components. The amplitude of
`each second-harmonic component will be proportional to the square of
`the amplitude of
`the corresponding signal component; the amplitude
`of the sum anddifference frequencies will be proportional to the product
`of the amplitude of the input components involved in the combination.
`As an example, let us consider the square-lawdetection of an ampli-
`tude-modulated wave given by the expression
`
`e = E,(1 + msin Bo) sin at.
`
`Se
`32
`age
`~ a
`3°43
`(a)
`
`E.
`53
`32
`3°
`
`faa
`
`°
`
`18atoeeesoe
`aNOMENINESCH
`
`
`
`«uRETSSRCRRpRNEgTOaieororieeemameers
`
`
`
`soeenmeatanysrtamgEe
`
`For purposesof analysis this wave may be represented bythree frequency
`components,
`the carrier and two sidebands, with angular frequencies
`w, (w — 8), and (w + 8), respectively.
`These are represented graphically in
`Fig. 1:3a. The relative amplitudes of
`the additional components in the out-
`put of the detector are shown in Fig.
`1-3b for the case where m = 0.5.
`The square-law detectoris a useful
`device for
`the measurement of
`the
`powerof an a-c signal because therec-
`tified output
`is proportional
`to the
`square of the input amplitude. As we
`shall see later, the crystal rectifier is
`often employed as a square-law de-
`tector in monitoring microwave power.
`&a 32 8 In fact, such a device is serviceable
`323 3 outside the square-lawregion provided
`Frequency
`it is calibrated.
`1)
`It is clear that the magnitude of
`Fic, 13.—Frequencies involved in
`the various components arising from
`(a) Frequencies in detector
`.
`detection.
`input.
`(modulation percentage = 50);
`the square term of Eq. (1) will be pro-
`(6) additional
`frequencies
`in the de-
`portional to the magnitudeof the sec-
`tector output.
`:
`:
`«ae
`ond derivative of the characteristic at
`the operating point. Maximum sensitivity will then be obtained by
`adjusting the d-c bias so that the operating point is also the point of max-
`imum curvature on the characteristic. Other factors of importancein the
`microwave region, such as capacitance, noise generation, etc., will be dis-
`cussed in Chap. 11.
`1.3. Frequency Conversion.—Heterodyne reception provides a means
`of converting the carrier frequency of a signal to a new value. This is
`
`epeprasempsognRecapPASTmeIRNSTere
`
`
`
`16
`
`16
`
`