MIT Radiaton Lab Series V24 Threshold Signals

8/8/2019 MIT Radiaton Lab Series V24 Threshold Signals

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MASSACHUSETTS INST ITUTE OF TECHNOKWYRADIATION LABORATORY SERIES

LouIs N. RIDENOUR, Ediior-in-Chief

THRESHOLD SIGNALS


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MASSACHUSETTS INSTITUTE OF TECHNOLOGYRADIATION LABORATORY SERIES

Board of EditorsLouIs N . RI DE~OUFt ,E&~or -in -Chie f

GE OIWI B. COLLX~S, Depu ly Ed it or -in -Ch iefBRITTONCHANCE,S. A. GOUDSMIT,R . G . HERB, HUBERT M. J AiUES ,J ULIANK. KN IFF ,J AMESL . LAWSON ,LEON B . L IN FORD,CAROL G . MONTGOMERY,C . NEWTON , ALBERTM. STONE , Lours A. TURNE FL GE OR GE E . VALLE Y, J R ., HE FiBE nT H. WH EATON

1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18,19.20.21.22,23.24.25,26.27.28.

RADAR SYSTEM ENGINEER INGRiden ou lRADAI i AIDS TO NAVIGATIONHa l lRADAR BEAcoIuRoberhLORANp&C63, McKenzie, and WoodwardPULSE GE NEF tATORS~l aS0 f3 a nd LebacqzMIC130WAvE MAGNETRONSCO/lin SKLYSTRONSAND MICROWAVETRIo DEsHam il lon, Knipp, and KuperP RINCIPLE SOF MICROWAVE Cmcu lTs -Mon@omer y , Dick e, an d Pu rcellMICROWAVETRANSMISSION(kwurr-&anWAVEGUIDEHANDBooKMarcuUilzTECH NIQUEOF MICROWAVEMEASUREMENTSMOn@Omf7~MICROWAVEANTENNATHEORY AND DESIGN&kTP ROP AGATIONOF SHORT RADIO WAvEsKemMICROWAVEDuPLExERsSmul l in and Mon tgomeryCRYSTAL RECTIFIE RST orrey an d Wh itm erMICROWAVEMIxERs-PoundCOMPONENTSH.4N~BooK-BlackburnVAIXJ UMTUBE AMPLIF IERSValley an d Wallm anWAvEFoRkis-Ghance, Hughes, Ma cNich ol, Sa yr e, a nd WilliamsELECTRONICTIME ,MEASUREMEY rscha?t ce, H u lsiz er, MacN ich ol,

an d William s13LECTRONIC NSTR UMENTs+?_ee n Iooo ci, Holdam , an d MacR aeCATHODERAY TUBE D1sPLAYsSo//e r , S t a r r , an d V alley _MICROWAVERECEIVERSVan V oorh zeTHRESHOLi )&GNALS-LaUISOn and Uh lenbeckTHNORYOF S EworwE ciiAxts~ s-J am es, N ichols, an d PhtllipsRADAR SCANNERSAND R A~o~E sCad y, Kareli[z, and Tu r n e rCOMP UTING\ ~ECH ANISMSAND L1xncEs-SuobodaINDExHenney

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THRESHO-LD SIGNALS

Edi[ed byJAMES L. LAWSON

RESEAACH ASSOCI.4TE , GENERAL ELECTliIC RESEARCH LAEOR .4TOIIYSCHENECTADY, NEW YORK

GEORGE E. UHLENBECK ,P ROFESSOR OF P HYSICS, UNIVERSITY OF MICHIGAN

OFF ICE OF SCIENTIF IC RESEARCH AND DEVELOPMENTN.4TIONAL DEFENSE RESEARCH COMMITTEE

lh ST EDITION

NEW YORK . TORONTO - LONDON


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,.:

THRESHOLD SIGNALSCOPYRIGHT, 1950, IIY THE

MCGRAW-HILL BooK COMPANY, IN(PRINTED IN THE LEiITED STATES OF AMERI(A

All righ ts r eserv ed . This book, 01parts thereo,f, may not ~~ revo~uceclin any jorm without perm ission oj

the publ ishers.

THE MAPLE PRESS COMPANY, YORK, PA.


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Foreword

T HE t remendous research and developmen t effor t that wen t in to thedevelopmen t of radar and rela ted techniques dur ing Wor ld War IIresu lted not on ly in hundreds of radar sets for military (and some forpossible peacet ime) use bu t a lso in a grea t body of informat ion and newtechniques in th e elect ron ics and h igh -frequency fields. Because th isbasic ma ter ia l may be of gr ea t valu e t o scien ce a nd en gin eer in g, it seem edmost impor tan t to publish it aa soon as eecu r ity permit ted.

The Radiat ion Laboratory of MIT, which opera t ed under the super-vision of t he Na tion al Defen se Reeea rch Commit tee, u nder took t he gr ea ttask of prepar ing these volumes. The work descr ibed herein , however ,is the collect ive resu lt of work done at many labora tor ies, Army, Navy,un iversity, and indust r ia l, both in th is coun t ry and in England, Canada,and oth er Domin ion s.

The Ftachat ion Labora tory, once it s proposa ls were approved andfin an ces pr ovided by t he Office of Scien tific Resea rch a nd Developmen t,chose Louis N. Ridenour aa Editor -in -Ch ief to lead and direct the en t ireproject . An editor ia l staff was then selected of those best qualMed forth is type of task. Finally th e au thors for the var ious volumes or chap-t ers or sect ions were chosen from among those exper t s who were in t i-mately familiar with the var ious fields, and who were able and willingto wr ite the summaries of them. This en t ir e staff agreed to remain atwork a t MIT for six months or more after the work of the Radiat ionLabora tory was complete. These volumes stand as a monument to th isgroup.

These volumes serve as a memoria l to the unnamed hundreds andt hou sa nds of ot her scien tists, en gin eer s, a nd ot her s wh o a ct ua lly ca rr iedon t he r esea rch , developm en t, and en gin eer in g wor k th e resu lt s of wh ichare h erein descr ibed. There were so many involved in th is work and th eywor ked so closely t oget her even t hou gh oft en in widely sepa ra ted la bor a-t or ies th at it is impossible t o n ame or even t o kn ow t hose wh o con tr ibu tedto a par t icu lar idea or developmen t . On ly cer ta in ones who w rotereports or a r t icles have even been men t ioned. Bu t to all t hose whocon tr ibu ted in a ny wa y t o t his gr ea t cooper at ive developmen t en ter pr ise,both in th is coun try and in England, these volumes are dedicted.

L. A. DUBRIDGE.v


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ContentsFOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VPREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiCKAP.1. INTRODUCTION. . . .. . . . . . . . , . . . . . 1

CEAP. 2. TYPES OF SIGNALS AND METHODS FOR THEIR RECEP-TION.. . . . . . 3CONTINUOUS-WAVESIGNALZ. . . . . . . . . . . 3

2.1 Un r n od u la t edCon t in u ou c-w a veSign ~l . . . . . . 32.2 Amp lit u d e Mod u la t ion . . . . . . . . . . . . . . . . . . . 5%3 F r equ en cy-m odu la k d Con t in u ou s-w a ve Sign a ls . . . . . . 132.4 P h a ce -m od u la t ed Con t in u ou s-w a ve Sign a lc . . . . . . . . . 17

P IJ ISXn &QNAIA . . . . . . . . . . . . . . . . . . . . . . . . ..13

2.51n fi1t a P u lce T r a in c, . . . . . . . . . . . . . . . . ...182.6 Finite Pulce Traine, . . . . . . . . . . . . . . . . ...192.7 Am p lit u d e -m od u la t ed P u fze T r a in e . . . . . . . . . . . . 242% Oth e r Typ e s of Mod u la t ion . , . . . . . . . . . 30

CHAP . 3. THEORETICAL INTRODUCTION . . . . . . . . . . 333.13.23.33.43.53.63.73.8

The Mathematica l Descr ipt ion of Noise . . . . 33Average Values . . . . . . . . . . . . . . . . . . . ...35The Relat ion between the Correla t ion Funct ion and tbe Spectrum 39Examplea of Spectra . . . . . . , .,,.........,42Some Proper t ies of the Gaucsian Dist r ibut ion . . . . . 46Tbe Random-wslk Problem. . MIThe Gauczian Random Procezc. . . . . . . . 53Spect rum after a Nonlinear Device . . . . 56

CEAP. 4. BASIC ORIGINS OF INTERNAL NOISE . . . . . . 64THEaMAL Noise . . . . . . . . . . . . . . . . . . . . . . . . ..64

4.1 Stat ist ical Deriva t ion of the Thermal Noice Spect rum . . . . 644.2 The Gauccian Character of Thermal Noise . . . 664.3 Kinet ic Deriva t ion of the Thermal Noise Spect rum . . . . . 694.4 Genera lizat ion8 . . . . . . . . . . . . . . . . . . . ...714.5 E xperimen ta l Confir rna t ionc . . . . . . . . . . . . . . 76

NOISE DDE TO D ISCRETENE SSO F TRE E LECTRON ICCHARGE . 794.6 Deriva t ion of the &hottky Formula . 79

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x CONTENTS4.7 Space Charge Depression of the Shot Noise. , 834.8 Exper imen tal Confirmat ions; the Upper Limit of the Shot-noise

Spect rum . . . . . . . . . . . . . . . . . . . ...894.9 Par t it ion Noise..,,.. .914.1o Transit -t ime Effect s in Tr iodes and Mu lt icollector Tubes; In du ced

Grid Noise.. 93ADDITIONALSOUFLCESOFNOISE . . . . . . . 95

4.11 Cur ren t Noise ;Flicker Effect ; P osit ive Ion Fluctuat ions 95(; HAP . 5. RECE IVER NOISE .. . . . . . . . . . . . . . . . . . ..98

5.1 In t r od u c t ion . . . . . . . . . . . . . . . . . . . . ...985.2 An t en n a Noise . . . . . . . . . . . . . . . . . . . ...1035,3 Con ver t e r Noise . . . . . . . . . . . . . . . . . . . ...1085.41.0ca l+sc illa t or Nod e ..... . . . . . . . . . . . ...1125.5 In t e r m ed ia t e -fr eq u en cy Noise . . 11556 Noise Ca n ce lla t ion Sch em es. . . . . 122

CHAP. 6. EXTERNAL NOISE SOURCES; CLUTTER. . 1246.1 Or igin and Descr ipt ion of Clut ter. 1246.2 Der ivat ion of the First Two Probability Dist r ibut ions 12563 The Probability Dist r ibut ions When a Constant Signal Is Present 1306.4 Exper imental Techniques for Clu t ter Measurements. 1326.5 Exper imental Rwults. 13766 Classifica t ion of In ter ference 1436.7 Simple Types of In ter ference 1446.8 Complex Types of In ter ference 145

CHAP . 7 . THE DETECTABILITY OF SIGNALS IN THE P RESENCE OFNOISE . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...149

THEORETICAL INmonucmoN. . . . . . . . 1497.1 Definit ion of the Signal Threshold. . . . 1497,2 Probability Dist r ibut ions and Spect ra 1517.3 Detectability Criter ia . 1617.4 What Is the Best Method for Detect ing a Radar Signal. 1657.5 Theory of the Ideal Obsemer . 1677.6 Mathemat ical Appendix . 173

CHAP. 8. PULSE TRAINS IN INTERNAL NOISE 1768.1 Standards for the Measurement of Signal Power . 1768.2 A (Synthet ic) System for Exper imenta l Purposes 1798.3 The Determinat ion of Threshold-signa l Set t ing 1858.4 System Parameters and Scaling 1938.5 In fluence of Trace Brightness, Average Noise Deflect ion , Sweep

Direct ion . . . . . . . . . . . . . . . . . . . . . ...1978.6 Dependence on the Product of I-f Bandwidth and Pulse Length 1998.7 Effects of Video Bandwidth; Sweep Speed, Focus . 2118.8 The Dependence upon Repet it ion Frequency 2228.9 The Influence Df the Signal Presenta t ion Time and of the Screen

Mater ia l . . . . . . . . . . . . . . . . . . . . . ...230


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CONTENTS xi8.10 The Dependence upon the Number and Spacing of Possible Signal

Posit ions and upon the At ten t ion In terva l . . 2328.11 The Influence of Video Mixing . . . . . . 236

CHAP. 9. PULSE TRAINS IN INTERNAL NOISE; OTHER METHODS OFPRESENTATION . . . . . . . . . . . . . . . . . . . . . . . ...238INTENSITY-MODULATED DISPJAY (PPI) . . . . . 238

9.1 Similar it ies tothe A-ecope. . . . . . 2389.2 The Influence of Scann ing. . . . . .2419.3 The Influence of Limit ing. . . . . . . . 2469.4 Video Mixing . . . . . . . . . . . . . . . . . . . . ...2489.5 Signal Fluctua t ions and Target Movement . . . . . . . . 249

AURAL .mm METEFI METHODS OF DETECTION . . . . . 2529.6 Theoret ica l Resu lts for the Signal Threshold . . . . . . . 2529.7 The Equivalence with the Visual Method of Detect ion . . . . . 254

CNAP. 10. MODULATED PULSE TRAINS. . . . . . . 25710.1 The Receiving System. . . . . . . . . . . .25710.2 Exper imen ta l Results . 26410.3 Theoret ica l Der iva t ion of the Boxcar Spect rum of Noke Alone 27310.4 Theoret ica l Der ivat ion of Signa l-modulat ion Threshold. 278

OTHEn METHODS OF MODULATION . . . . . . . . . . . . . . . . . .28810.5 Propeller Modula t ion . . . . . . . . . . . . . . . . . ..2W10.6 Theoret ica l Analysis of a Pulse-width Modula t ion System, . ..292

Cr rAP. 11. THRESHOLD PULSED SIGNALS IN CLUTTER. . . . . 297INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

11.1 Compar ison between $lut ter and Noise. . . . . . 29711.2 Threshold Signal in the Absence of Satu ra t ion. . . 29811.3 Threshold Signals in the Presence of Satura t ion . . 302

METHODS FORTHE REDUCTION OF CLUTP ER SATURATION. . . 30311.41n st a n t a n eou s AGC . . . . . . . . . . . . . . . . . . ..3o311.5 Loga r it hm ic I -f Amp lifie r . . . . . . . . . . . 30611.6 Vid eo Sa t u r a t ion . . . . . . . . . . . . . . . . . . . . . 30811.7 The T ime-var ied Gain Cont rol . . . . . . . . 31111.8 Efficiency of Circu it s Used for Reduct ion of Clut ter Satu ra t ion 313

MOVING TARGET INDICATION . . . . . . . . . . . . . . . . . . .. 32411.9 Gen e r a l Descr ip t ion . . . . . . . . . . . . . . . . . ,32411.10 Th r e sh old Sign a ls in t h e MTI Syst em . . . . . . . . . 329

CHAP . 12. THRESHOLD SIGNALS IN ELECTRONIC INTERFERENCE 335THRESH OLDS1m+me IN UNMODULATEDCONTINUOUS-WAVEINTERFE RENCE335

12.1 E ffec t of C -w In t e r fe r en ce . , , , , , . , . . . . . . . . .335


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xii CONTENTS12.2 Vid eo Over loa d in g . . . . . . . . . . . . . . . . . . . ..34 I12.3 In t e r m ed ia t e -fr equ en cy Over loa d in g. . . . . 34312.4 Dep en d en ce of Th r esh old Sign a l u p on C-w In t e r fe r en ce F r e -

q u en cy . . . . . . . . . . . . . . . . . . . . . . ...247THRESHOLDSIGNALSIN NOISE -MODULATEnCONTINUOUS-WAVEINTE RF ER -

ENCE . . . . . . . . . . . . . . . . . . . .35312.5 Cont inuous-wave Inter ference Amplitude Modulated by Noise 354

THRESHOLDSIGNAIAIN PUHED INTERFERENCE 35612.6 Descr ipt ion of Pulsed In ter ference. . . . 35612.7 Railing In ter ference. . . . . . . 35612.8 Randomly Spaced In ter ference Pulses . . . . . 365

CHAP. 13. THRESHOLD MODULATIONS FOR AMPLITUDE-MODU-LATED AND FREQUENCY-MODULATED CONTINUOUSLWAVESYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . ...367

13.1 In t r od u ct ion . . . . . . . . . . . . . . . . . . . . . .. 36713.2 Th e Min im um Det ect a b le h p li t u d e Mod u la t ion 36813.3 Th e Noise Sp ect r um for a n F -m Reee ive r . . . . . . 36913.4 Th e Sp ect r um of Sign a l P lu s Noise for an F -m Rece ive r . . 37413.5 Th e Min im um De t e ct a b le F r eq u en cy Mod u la t ion . . . . 380

LVDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385


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CHAPTER 1I INTRODUCTIONTh e fun dam en ta l process in th e r ecept ion of elect rom agn et ic sign als

is to make percept ible to the human observer cer t a in fea tu res of th ein coming elect r omagnet ic r adia t ion . Sin ce per cept ion is t he a cqu isit ionof in forma tion , t hese fea tu res m ay be ca lled in telligen ce or in forma -t ion . The elect romagnet ic wa ve may con ta in th is in format ion in manyways; th e par t icu lar method used to abst ract it and make it percept ibledepen ds u pon t he st ru ctu re of th e or igin al ra dia tion .

Antenna - Indicator HumanobserverFIG. l. l.The rece iving sys tem.

A book of th is length does not permit adequa te discussion of all t ypesof radia t ion . It is hoped, however , that most of the common types nowwidely u sedprin cip ally in t h e field s of r adio, t elevis ion , communica t ion s,and radarand the process. of recept ion applicable to each can bepresented.

b To change the character ist ics of the signal in to a form suitable forhuman per cept ion , severa l even ts must usually ta ke pla ce. Th e completesyst em in which th is t ra in of even t s occu r s can be conven ien t ly refer redto as th e receiving system and can be subdivided in to fou r fundamentalfunct iona l par t s aa shown in Fig. 1-1.

The Antennu .-The funct ion of th e an tenna is to conver t the elect ro-magnet ic energy fa lling upon it to elect r ic volt ages or cu rren ts, wh ichappear on th e inpu t terminals of the receiver . In some cases it is desir -able to consider the an tenna as a par t of the receiver , since some of thereceiver proper t ies a re determined by cer ta in proper t ies of the an tenna(rad ia t ion res is t ance , et c.).

The Receiver .Th e fun ct ion of t he r eceiver is t o select t he in com in gsignal r find to change it s elect r ica l form in such a way tha t the ou tpu t ofth e receiver con ta in s on ly the desir ed par t s of th e signal. In genera l,th ese par t s a re on ly those frequencies su itable for human percept ion .The frequencies percept ible t o the ear have become known as audiofr equ en cies, a nd t hose visu ally per cept ible a s video fr equ en cies. P er ha ps20 kc/see represen ts th e upper limit of audio frequencies, bu t videofrequencies may be as h igh as 10 or even 100 Me/see, depending upon theindicator. 1


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2 INTRODUCTIONIn addit ion to fr equency select ion and frequency changing, the

r eceiver m ust a lso pr ovide amplifica tion . The incoming radia t ion isordinar ily feeble and must be grea t ly amplified in order to actua te theindica tor . Th e tota l r equ ired power amplifica t ion in th e receiver may forsom e a pplica tion s be as h igh as 1015. N oise a nd in ter fer en ce lim it at ionspreven t it s being made as high as one pleases.The main purpose of this book is to discuss these fundamenta l

limitat ions and to det ermine the effect of the var ious pa rameters in ther eceivin g system on t he detect abilit y of signa ls.The incoming signa l may be of severa l types. It t herefore follows

tha t th e cha racter ist ics of th e r eceiver it self must be specia lized and a redet ermin ed by t he t ype of in forma tion r equ ir ed fr om t he in com in g signa l.Because of the genera l complexity of receivers, fu r thermore, ther e ar eusually severa l types which per form essent ia lly the same funct ion butwhich may differ in their limita t ions. The var ious r eceiver types aremost convenien t ly discussed in conjunct ion with the kinds of signa l forwh ich t hey a re design ed.

The Indica tor .-The outpu t of the r eceiver consists of voltages orcu rr en t s con ta in in g t hose desir ed fr equ en cies in t h e sigi~a l th at a r e su it ablefor human percept ion . The funct ion of the indica tor is t o conver t thesevoltages or cu r r en t s in to audio sound waves or perhaps light pa t ternstha t th e human obser ver can per ceive. Common forms of in dica tors a ret he lou dspeaker for radio r ecept ion and th e ca th ode-ray oscilloscope fort he r ecept ion of video sign als. There a re obviously many ways in whichth is indica t ion can be presen ted to the observer . Severa l a lt erna t ivemeth ods of indica t ion ar e men tion ed in Sec. 2.6.

The Human Obser ver .Human per cept ion of cer ta in sign al pr oper tiesdepends not on ly on what is presen ted to the observer on the indica torbut also on what use he makes of tha t informa t ion . Percept ion sensit iv-ity will t her efore depend on character ist ics of the human observer tha ta re not always flexible. The ear , eye, and brain a re subject t o cer ta inlimita tion s t ha t in ma ny ca ses r est rict t he assim ila tion of u sefu l in forma -t ion . The signal informat ion may, for example, be spread ou t over at ime so long tha t t he human observer cannot in tegra te the informat ion .His memory is limited; hence he can effect ively use informat ion on lywith in a limited t ime. The human observer must th er efor e be consider edas par t of the receiving system. It is even somet imes conven ient t oexpr es%human lim it at ion s in t erms of cer ta in in dica tor or r eceiver pa ram-eters. In the example just men t ioned the human memory t ime can berela ted to an equiva lent t ime constant or bandwidth in the receiver .Simila r ly, proper t ies of the ear , such as its bandwidth or frequencysen sit ivit y, will be sim ila r t o t he elect rica l pr oper ties of equ iva len t filt er sin t he r eceiver . .


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CHAPTER 2TYPES OF SIGNALS AND METHODS FOR THEIR RECEPTION

CONTINUOUS-WAVE SIGNALS2.1. Unmodula ted Con t inuous-wave Signal.-The simplest form of

sign al is t he so-ca lled u nmodu la ted con tin uou s wa ve. Thic io the namegiven an elect rom agnet ic wa ve in which th e ma gn itude of t he altern at ingelect ric field st ren gt h is con st an t in t im e; for example,

& = &oCos zr(fot + so). (1)I Both 80 a nd t he fr equ en cy f, are constan t . The constan t CXOefines theI sero of the t ime scale, so that1 & = .SOC0527rao at t ime t = O.

Th e ch ar act er ist ics of a c-w sign al a re t her efor e con st an t amplit ude, con -stan t frequency, and par t icu lar phase at t = O. These condit ions cannotbe met by any known elect romagnet ic radia t ion , since in such a case 80must have exist ed th roughou t all t ime. Lik ewise, if &O is not con st a nt ,t here will be more than a single frequency associa ted with the wave.This will be shown in Sec. 2.2. Therefore there is no such th ing as amonochromat ic c-w signal. If 80 is on ly slowly varying with t ime, how-ever , &will be ver y n ea rly monoch roma tic in fr equ en cy. It is conven ien tto refer to &O as the signal-car r ier amplitude. The car r ier frequency isessen tia lly mon och romat ic or , mor e specifica lly, will con ta in a fr equ en cyband small with r espect to t he lowest desir ed au dio or video frequ en cy.The in format ion that can be abst racted from th is c-w carr ier is verymeager . One can only inquire, does the car r ier exist or not? And tor obta in the answer even to th is quest ion may take a long time. To

improve the ra te at which informat ion can be t ransmit ted, some param-eter of the or iginal c-w signal is var ied with t ime or modulated. In theusual modula t ion of a c-w carr ier , either a var ia t ion of the amplitude(amplit ude modu la tion ), a va ria tion of t he fr equ en cy (fr equ en cy modu la -t ion ), or a var ia t ion of the phase off, (phase modula t ion) may be made.Th ese will be discu ssed in t he n ext sect ion . The modula t ing fr equenciesare, for conven ience, those wh ich u lt imately become the indica tor fre-quencies, that is, audio or video frequencies, since the human observermost ea sily a bst ra cts in forma tion fr om t hem .The modulat ing funct ion may be represen ted by F(t ). For audio

3


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4 TYPES OF S IGNALS AND THEIR RECEPTION [SEC.2.1m ovulat ions one wishes to make F(t ) cor respond to the instan taneouspr essu re of t he modu la ting sou nd wa ve. Sin ce t his pr essu re is n orma lly1 a tm in the absence of sound, it is necessary tha t F(t) be a constantdifferent from zero in the absence of modula t ion . The sound pressu remay vary upward or downward with audio modulat ion. For a singleaudio t one, t h er efor e, F(t) may be represen ted by

1 + c Cos 2T(pt + B),where ~ < 1.F or a complex audio sound, F(t) may be r epr esen ted

1+2C. cm 27(PJ + /3.),

,nwhere the va lues of the cs are such tha t F(t ) never becomes negat ive.If the or iginal sound wave is feeble, the fluctuat ing par t of F(t) may beamplified but must not be made so grea t that F(t) becomes n ega tive. IThis amplifica t ion is always desirable in pract ice, since one wishes tomake the par t of F(t) tha t conta ins the in telligence as la rge as possiblewith respect to the constant par t or ca r r ier that contains essent ia lly noinformat ion. For a single audio tone where

F(t) = 1 + c COS%@ + ~), (2)it is conven ient t o refer to e as the fract iona l modulation or to 100~ as themodulation percentage.If the modula t ing wa ve is to represent some ot her desired character -

ist ic, su ch a s ligh t in ten sit y for t elevision t ra nsm ission , a con st an t ca rr ieramplitude may not be necessary. Unlike the sound-wave case, wherewith in the wave it self the pressure can be less than tha t with no sound,the light in tensit ies reproduced by cur rent s in a photoelect r ic cell a renever less than those produced with no light . In other words, it is nevern ecessa ry t o modula te downward from the zero intensity case. ThusF(t) can represen t direct ly the light-intensity va lues when the photo-elect ric cell is sca nn ed over t he t elevised scen e. A car r ier is no longerrequired to ensure that the complete modula t ing funct ion be posit ive.In this case the terms fract iona l modula t ion and modulat ion per -centage are meaningless. The funct ion F(t) can be made as la rge asone pleases by amplificat ion , unt il the peak values exceed tha t whichca n be su pplied in t ra nsm ission .

LTh is r es tr ict ion is n eces s ar y b eca u s e, a z will b e s h own la ter in t h e t ext , d evicesde s igned fo r r ep roduc ing F(t) a c tu a l ly give t h e absolu te value of F(t); t he r efo re , in o rde rt o r ep r oduc e F(t) wit h ou t d is t or tion , it s s ign mu s t n e ver r ever s e.


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SEC. 2 .2] AMPLITUDE MODULATION 52.2. Amplit ude Modu la tion .-Th e in com in g wa ve maybe r epr esen ted

by t he equ at ion & = (t) Cos %r(jot + so), (3)wh er e t he car rier field st rengt h 80 and t he fr equency jo are constants.The funct ion F(t ) represen t s the modula t ing funct ion , and aO is a phaseconstant. Th e amplitude of the r -f wave is observed to be modula tedby F(t ). In genera l, & conta ins none of the frequencies in F(t)but con-sists of a band of frequencies in the neighborhood of fo. Ms band of

L_ LllLrequency & f-(a ) Modu la t in g fu n c tion (b ) Ra d io-fr eq u en c y s p ect rumFm. 2 .1 .-Sk le bands p roduc edby amp lit udem odu la t ion .frequencies will be spread over a frequency range just twice as large asthe modula t ing frequencies in F(t ). This can be easily shown in thefollowing way. Let [z,(t ) = 1 + 1% WE ~(p.t + (3.) ;n (4)[z=&ol+ 16. Cos %r(p.t + p.) Cos 2T(f0t + ~o) , (5)nand& = &, Cos *(jot + ao) + ; zC. COS% [(jOt + Pn)t + ~0 + 8.1n+ $ z. COS%[(jot p.)t + a, /%]. (6)nThe ca r r ier t erm, it should be noted, remains unchanged at frequency joand amplitude &o. There ar e no terms at the modula t ing frequencieszpn, but for each modula t ing frequency p. there a re two terms in qwhose frequencies are (jo f pJ , respect ive y. These a re commonlyr efer red to as sidebands about the ca r r ier of fr equency jo. Th e ampli-t ude of each sideband is i&t i..This condit ion is illust r ated in Fig. 21, wh er e a modula t ing fu nct ioncon t a in ing two fr equencies is a ssumed. Th e sideba nd spect rum is sim ila rto the spect rum of F(t ). For a single tone of 100 per cent modula t ion ,the sideband amplitude is ~&O. The two sidebands for a single tone,


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6 TYPES OF S IGNALS AND THEIR RECEPTION [SEC.2.2therefore, for any fract ional modu la t ion c con ta in a tota l power equal to{2/2 t im es t he ca rr ier power .A common example of the a-m wave is that u sed in ordinary broadcast

radio t ransmission . In th is case F(t ) is simply the audio or speech wave.The input to the receiver from the antenna is essen t ia lly an elect r icvolt age t% t ha t is lin ea rly pr opor tion al t o t he r adio-wa ve field st ren gt h &.Th e fu nct ion of t he r eceiver is t o r epr odu ce t he modu la tin g a udio fu nct ionF(t ) from the input voltage st i. Th e r epr odu ct ion ca n be a ccomplish ed

I!;in* Radio-frequency< Detector Audiooramplifier videoamplifier -GoutFIG. 2.2 .Elemen ts of a s ingle-detect ionreceiver .

in a var iety of ways. Th ree genera l types of receivers a re used for th ispurpose.

Singledetection Receiwer .In th is type the frequency changing isaccomplished by means of a detector. Th e essen tia l pa rt s of t he r eceivera re shown in Fig. 22.Th e r -f amplifier is u sed t o pr ovide su fficien t r -f sign al t o t he det ect or

for the la t ter to opera t e proper ly. The pu rpose of the detector is toreproduce the audio-modulat ion funct ion . It will, in general, provideoth er fr equencies that a re not wanted. The pu rpose of the audio or

(a) Carr ier (b)Modu lated-fwave (c) Modulat ingunctionFm. 2.3.Amplitude-modulatedwave.video amplifier is to reject all unwanted frequencies and to amplify thedesir ed fr equ en cies u nt il t h ey a r e of su fficien t size t o a ct u at e t h e in dica tor .A det ect or mu st be a n on lin ea r device; bu t as will be sh own , n on lin ea r-

ity is not a sufficien t condit ion for detect ion . A represen ta t ion of thea-m r-f wave is shown in Fig. 2.3, where for simplicity the modulat ingfunct ion F(t ) is assumed to be composed of a car r ier plus a single a-f tone.It has been shown tha t the analysis of an r-f wave of this type conta ins

on ly th ree frequencies: the car r ier r adio frequency and two sidebandssepara ted from the car r ier fr equency by the modulat ing frequency. Itdoes not , in genera l, con ta in the modulat ing frequent y itself; th is can beseen by noticing that the average va lue of the wave, averaged over t imescor respon din g t o t he modu la tin g fu nct ion , is essen tia lly zer o. If, h ow-ever , t he n ega tive r -f volt ages a re su ppr essed wit hou t a lt er in g t he posit ive

I


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SEC.2-2] AMPLITUDE MODULATION 7voltages, then th e average value of the wave will va ry according to themodu la tin g fu nct ion , a nd det ect ion will occu r. Det ect ion will t h er efor er esu lt fr om a n on lin ea r device t ha t amplifies n ega tive volt ages differ en tlyfrom posit ive volt ages. If the input and ou tpu t voltages of th is non -linea r device a re r epr esen ted by t he gen era l power ser ies

$&t . zn&?., (7)ndetect ion takes place on ly because of the presence of th e even terms;t ha tis, n =2,4,. The odd terms do not con t r ibu te to detect ion ,sin ce for t hese t erms n ega tive or posit ive in pu t volt ages pr odu ce n ega tiveor posit ive ou tpu t voltages, r espect ively. Thus a pu re cubic-lawn on lin ea r device will n ot be a det ect or .Perhaps th e simplest detector is th e s~called squardaw device in

which the ou tpu t voltage is propor t iona l to the square of th e inpu tvoltage; .% = ge. (8)As shown previously, ~ and F(t) may be generally represen ted by theequations

& = &oF (t ) Cos 2m (.fot+ so), (9)

[zF(t ) = 1 + 16. Cos 21r(p=t + l%) , (lo)nso t ha t

& = gwvt) c@J22djot + a,), (11)or [z 1[1 + Cos 4r(f0t + a,)&t= g&; 1+ c. Cos zr(pnt + /%) 2 1 7 (12)nfrom which=g[1+2znc0s%pn+~n)

+n Cn qCos 2T(pnt + /9.) Cos %(pIt + /%)11[ 1+ COSzWd + ao) . (13)

2The frequencies presen t in 8~, a re, therefore, zero (d-c term), p., 2Pfl,p. + pl, p pl, 2 j0 , 2 .fo f p., 2 f0 f 2p., 2 j0 + (p. + pi), and2 f0 + (p. pJ. The on ly terms of in t erest a re the p. terms and,inciden ta lly, the terms 2p~, pm + PI, and p. pt . Th ese fou r gen era l


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8 TYPES OF S IGNALS AND THEIR RECEPTION [SEC. 2 .2t erms (apar t from the d-c term) are the only ones tha t will fa ll in the passban d of t he a udio or video amplifier . They have amplitude funct ions a tt he ou tpu t of the squa re-law det ector given by g&~c.,g&~(c~/4), g&3(c.cJ4 ),and g&~(c~ct/4), respectively. Of these four terms the fir st is the desiredone, th e second represen ts second harmonic distor t ion, and the th ird andfour th represen t cross-modulation products. In genera l, detect ionproduces cross-modula t ion terms and harmonic distor t ion , but it will benot iced in the precedin g example that the amplitudes of these undesiredterms rela t ive to the desired one are usually quite small. If the coeffi-cien t s a re small (small modula t ion percentage), these terms may beneglected in comparison with the desired p. terms.In pr inciple the a-m wave can be det ect ed without producing dis-

t or tion s in t he modulat in g fu nct ion even wh en t he fra ct ion al modulat ionis high . This is accomplished by means of the so-called linear det ector ,wh ich pa sses or amplifies a ll volt ages of on e pola rit y lin ea rly bu t sh ows n ooutput at all for input voltages of the opposite polar ity. The averageoutput voltage is therefore linear ly propor t iona l to the envelope of ther -f wave, which , of course, is rela ted to the modula t ing funct ion F(t )it self. The envelope of the modula ted wave is not st r ict ly F(t ) butrepresents F(t) on ly if a sufficien t car r ier exists t o ensure tha t F(t ) isa lways a posit ive funct ion. The envelope, in genera l, represen ts theabsolute value of F(t). The significance of this will be brought out moreclear ly in la ter chapters, but this fact ult imately leads t o possibilit ies ofcr oss modula tion even wit h t he en velope det ect or .Even though this linear , or envelope, det ector reprodu ces F(t ) prop-

er ly, it s character ist ic curve is ext remely nonlinear at zero voltage. Atthis poin t the curva tu re is infin ite. Pract ica l detector s are limited int hk cu rva tu re; t her efor e t he r egion of small volt ages is n ot similar t o th atof an idea l linear detector . For th is reason pract ica l linear detectorsalways opera te a t high voltage levels and must ther efore be preceded byconsiderable r -f amplifica t ion. Examples of such det ectors a re diodedet ector s , in fin it e-impedance t r iodes , and h igh-level anode-bend det ector s .Beca use of limited cu rva tu re in ch ar act er ist ics, low-level det ect or s

are almost invar iably square law; examples are crysta l detectors, low-level diodes, etc. If desired, h igh-level det ectors can be made squarelaw, bu t or din ar ily lin ea r det ect or s a re pr efer red.Few receivers in common use are of the simple type shown in Fig. 2.3.

Th e difficu lt ies wit h t he sin gl~det ect ion r eceiver a re u su ally a ssocia tedwith the r -f amplificat ion. The r -f amplifier must genera lly be tunedto t he desired r -f sign al a nd h ave con sider able over -a ll ga in. It is usuallydifficu lt to const ruct a tuned r -f amplifier of severa l stages with txoDerst abilit y, select ivit y, a nd t un in g r an ge. In widespread ~se is ar eceiver , t he super het er odyn e, t ha t over comes t hese difficu lt ies. t ;pi of

q


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SEC.2.2] AMPLITUDE MODULATION 9Superhetemd~ Receiver .Th e essen tia l elem en ts of a su per het er o-

dyne receiver a re shown in Fig. 24. The r -f signal is fdd th rough an r -famplifier , wh ose fu nct ion will be sh or tly discu ssed, t o a m ixer , con ver ter ,or fir st det ector as it is somet imes ca lled. In to th is mixer is a lsoin ject ed t he u nmodu la ted ou tpu t of a loca l r -f oscilla tor , wh ose amplit udeat the mixer is made very la rge compared with tha t of the incoming r -fsignal. The mixer is a detect or of one of the two var iet ies ju st descr ibed,in whose ou tpu t will be found many frequencies. Besides the incoming

&i~ - f Mixeror l-f * 2nddetector+ Videooramph fier + 1st d et ect or+ amplifwr audio -8 wAILocaloscillator II I~G. 2.4 .Elements of a su perhe terodynerece iver ,

fr equencies jo, t h e modula t ion s id ebands , and th e loca l-oscilla t or fr equencyu , harmonics of th ese frequencies will be found and, most impor tan t ,cross terms between th e signal frequencies and u . Eith er th e fre-quency fO + u or Ijo COIan be set to a par t icu la r va lue by tun ing theloca l-oscilla tor fr equ en cy ~. Th us a ny in com in g r -f sign al wit h it s modu -la t ion sidebands can be conver t ed to a par t icu lar intermediate frequencywit h sim ila r modu la tion sideba nds. This i-f signal is then amplified asshown in Fig. 24 to a su itable level for proper detect ion ; then the audioor video frequencies a re ext ract ed as in th e case of the simpler receiverof F ig. 2.3.Beca use t he amplitu de of t he loca l oscilla tion s is la rge compa red wit h

th e signal oscilla t ion s a t th e mixer , t he am plitude con ver sion fr om ra diofrequ en cies t o in term ediat e fr equ en cies is essen tia lly linear . Th e signaloscilla t ions may be regarded as small per tu rba t ions on th e st rong localoscilla t ions. Modu la t ion sidebands are thus exact lv the same at thein termedia t e frequency as th ey are at the radio frequ en cy, since the sys-t em is essen tia lly lin ea r. F ur th ermor e, t he so-ca lled con ver sion ejicien qof the mixer from radio frequency to in termedia t e frequ en cy can be ver ygood because of the st rong loca l oscilla tor . A deta iled discussion of th esu per het er odyn e con ver ter a ppea rs in t he lit er at ur e. 1For a given local-oscilla tor fr equency u , th ere a re two possible radio

fr equ en cies t ha t will combin e wit h w t o form t he in termedia te fr ermen c~.To ~uppress on e of these possible r -f channels, it is customary to place infron t of the mixer a simple r -f amplifier tuned to the desir ed radio fr~1&e, for example,K. R. S tu r ley,Rad ioR ec&er DeaigrJ , P ar t 1, Ch ap. 5, Ch ap-man& Hall, London, 1943.


22/399

10 TYPES OF S IGNALS AND THEIR RECEPTION [SEC.2.2quency (see Fig. 2.4). This process is called radio-frequency preelection.F or some a pplica tion s, h owever , t his pr eca ut ion is n ot essen tia l.The pr incipal advantages of a superheterodyne receiver over the

simple t ype shown in Fig. 23 ar e t he following:1. Since most of the gain may be situated in the fixed i-f amplifier ,t he select ivit y a nd ga in of t he r eceiver a re essen tia lly in depen den tof the radio frequency. .

2. Th e tu nin g con tr ol (essen tia lly by t he loca l-oscilla tor fr equ en cy)is much simpler than for a gang-tuned ser ies of r -f amplifiers.

3. For the recept ion of very-high-frequency waves, h igh receivergain is much easier to obtain at the rela t ively low intermedia tefrequency.

It is possible t o exten d th e t r ea t ment t o r eceiver systems that conta insever al mixer s. Ea ch pr ocess of h et er odyn e det ect ion or con ver sion , t ha tis, on e in volvin g t he mixing of r -f sign al wit h a loca l oscilla tor , will yielda new i-f signal whose amplitude funct ion is linear ly pr opor t ion al t o t heamplitude funct ion of the or iginal r -f signal. Many superheterodyner eceiver s h ave been built in volvin g two h et er odyn e det ect or s. The r-fsign al is fir st con ver ted by mea ns of t he fir st loca l oscilla tor t o a r ela tivelyhigh first in termedia te frequency, which is la ter conver t ed to a secondlower intermedia te frequency by a second fixed-tuned lo~al oscilla torbefore final detect ion takes place. The advantages cla imed for thedou ble-su per het er odyn e r eceiver a re twofold. (1) Th e fir st in termedia tefrequency can be made high with the result tha t the r -f preelect ion (pre-ceding the first mixing) becomes much more effect ive. (2) The highover -a ll ga in in t he r eceiver ca n be divided between t he two in termedia tefrequencies; hence at no time is it necessary to const ruct an amplifier atone frequency of ext reme over-a ll gain . This process minimizes thedanger of feedback and instability in the amplifier . The pr incipal dis-advantage of the double-heterodyne receiver is, of course, it s rela t ivecomplexity.No mat ter how many heterodyne detector s t ir e used in a receiver ,however , the over-a ll conversion from r-f voltage to final i-f volt age islin ea r; if t he pa ss ba nd of t he r eceiver is gr ea t en ou gh , t he sign al amplifica -t ion will be independent of the modulat ing frequency. In other words,if th e or iginal r -f signal volta ge at th e input of t he receiver is r epresent edby

&h = &oF(t ) Cos 27r (jd + so), (14)wher e, a s befor e, F(t)is the modula t ing funct ion and ~0 is the radio fre-qu en cy, t he volt age in t he last i-f amplifier will be given by t he expr essior i

&i-fa &~.fF(t)OS%(hd + T), (15)


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SEC.2-2] AMPLITUDE MODULATION 11where ho is the last in termediat e frequency and Y is a phase constan tdet ermin ed by aO and the phases of th e local oscilla tors. Because of th iscomplet ely lin ea r r ela tion sh ip, a ll pr oblems en coun ter ed in a s up er h et er o-dyn e r eceiver ca n usually be t rea ted in t er ms of th e i-f amplifier a nd som esimple conver sion quan tity represen ta t ive of th e mixer it self. Forexample, in problems of noise th is quan tity, as will be shown in Chap. 5,has to do essen t ia lly with the conver sioneficiency of the mixer and the noise fig- ~-f

s

R-f Audiou re of t he i-f amplifier . input oscillator outputSuperregenerative Receiver .-A super-regenera t ive receiver is one in wh ich the Oscuaa.process of grea t amplifica t ion and theprocess of detect ion are accomplished switchwith in one vacuum tube. The main FIG. 2 .5 .Elem en ts of a su per-regenerat ive receiver.purpose, th erefore, is to provide a h igh-gain sensit ive receiver by the use of a min imum number of tubes. Thech ief drawbacks of such a receiver a re (1) the dificu lty of making andmain ta in ing proper adjustmen t and (2) nonlinear reproduct ion ordistortion.The method by which h igh gain and detect ion are accomplished is

shown in it s essen t ia l form in Fig. 2.5. The r-f input is connected to atube whose circu it s a re tuned to the desir ed signal frequency. Anoscilla tion con tr ol swit ch is u sed t o pu t t his t ube in to a n oscilla tin g con di-t ion . As soon as th is switch makes a connect ion . the condition foroscilla tion is est ablish ed, bu t t he oscilla tion s t hemselves a re n ot cr ea ted.They begin t o build up, however , from the in it ia l volt age found at theoscilla tor in pu t (sign al volt age in gen er al) a nd if a llowed t o pr oceed wou ldbuild up to a steady va lue determined by the power -ou tpu t capabilit iesof the oscilla tor tube. If the gain of the oscilla tor is constan t du r ing thebu ildu p (wh ich implies lin ea r amplifica tion ), t he oscilla tion bu ildu p willfollow a r ising exponen t ia l cu rve that will even tually fla t ten off a t th esa tu ra tion ou tpu t va lu e.In the super regenera t ive receiver , however , th e oscilla t ion con t rol

swit ch is usually tu rned off before the oscilla tor reaches a steady value.Th e final oscilla ting volta ge at t he ou tpu t of t he tu be depen ds, t her efor e,on the value of inpu t voltage (signal) and on the length of t ime theoscilla t ion con t rol swit ch is le ft connected. It is a lso clear tha t it depen dsu pon t he r egen er at ive ga in of t he oscilla tor t ube, t ha t is, t he r egen er at ivefeedback.As soon as th e oscilla tor con trol switch is tu rn ed off, t he oscilla t ionsin th e r -f input to th e oscilla tor die ou t exponen t ia lly unt il th ey reach the

va lue of volt age supplied by th e signal. At th is poin t it is possible tost ar t t he en tir e oper at ion a ga in . In pr act ice t he oscilla tion con tr ol swit ch{,;/


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12 TYPES OF S IGNALS AND THEIR RECEPTION ~Ec, 2 .2is tu rned on and off successively at a h igh ra t e called th e quenchor in t er rupt ion frequency. The con t rol switch is in actual pract ice aquench oscilla tor tha t con t rols the feedback in the r -f oscilla tor . Thequench ing ra t e must be h igh , since th e sampling of th e signa l volt ageat the st ar t of oscilla t ion buildup must be rapid compared with th emodula t ion frequency. The inpu t and ou tpu t voltages in the super -r egen er at ive r -f oscilla tor a re sh own dia gr amma tica lly in F ig. 26.

Inputvoltage

FIG. 2 .6 .Inpu t and ou tpu t vo lt age s in a superregenerativereceiver.In t he pr ecedin g descr ipt ion of t he su per regen er at ive r eceiver oscilla -

tor linear ity has been assumed, and under th ese condit ions no detect iontakes place. If the oscilla tor tube is opera ted in a non linear region ,however , th e average pla te cu r ren t being th erefore dependen t upon theoscilla tion , amplit ude det ect ion will occu r. Th e amplifica t ion possiblefrom the single tube can , in pr inciple, be increased withou t limit , since itdepends on ly on how far the oscilla t ions are a llowed to increase. Itis for th is reason , however , that when the tube is opera t ed at h igh ampli-fica tion , t he over -a ll ga in is ext rem ely sen sit ive t o t he cir cu it con dit ion s,such as r -f oscilla tor feedback or in ter rupt ion frequency. If thesecircu it condit ions are held constan t , however , the ou tpu t signa l will belinear ly propor t iona l to th e input signal. For th is reason it is common tor efer to th is method of su perregenera t ive opera t ion as the linear mode ofopera t ion . In th is case the buildup cu rve is a pu re exponen t ia l. Ingen er al, h owever , lin ea rit y is n ot obt ain ed, sin ce t he r -f feedba ck u su allyva ries du rin g t he bu ildu p pr ocess.The r -f oscilla tor may be opera t ed in a sligh t ly differen t fash ion to

a llevia te the cr it ica l gain adjustmen t . This is done by quench ing theoscilla tor a jt er it has reached a satu ra t ed value. The t ime necessa ry t or ea ch satu ra t ion clea rly depen ds on sign al size, h en ce th e ou tpu t volt agewill st ill con t a in signa l in t elligence. The opera t ion is illust ra ted in Fig.2.7. Opera t ion of th e tube in a non linear region will resu lt in detect ion ,yielding cu r ren t s conta in ing signal in telligence. The proper t ies of th is


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SEC. 2.3] FREQUENCY-MODULATED C-W S IGNALS 13method of superregenera t ive opera t ion and those of the previouslydescr ibed met hod a re somewh at differ en t, pa rt icu la rly wit h r ega rd t o t he~uest ion of non linear ity. In the type shown in Fig. 26 th e ou tpu tvolt age in cr ea ses essen tia lly lin ea rly wit h in pu t simal, wh er ea s in t he t v~show; in Fig. 27 the ou tpu t vol~age is e~nt i~ly propor t iona lloga rit hm of t he in pu t volt age.

2.3.

OutplliVoltageFIG.2.7 .Inpu t an d ontput voltages of a su perregenera t iverece iver .Frequency-modula ted C-w Signals.-In the t ransmission of

an f-m r -f signal the amplitude of the r -f signal is held constan t . t he radiofr equ en cy it -m lf bein g va r ied in a ccor dan ce-wit h s ome desir ed modu la tin gfunct ion F(t ). Such a signal may be represen ted by

/& = &, Cos > [1 + F(t )]j, dt . (16)f,There are two impor t an t parameters of fr equency modula t ion ,

n amely, t he fr equ en cies con ta in ed in F(t) it self and t he tota l frequ en cyexcu rs ion or devia t ion , f- f~.It should be noted that if F(t ) = O, the wave is represen ted by

& = E, Cos >(.fd + a,) (17)as before, bu t th is is a cor rect r epresen ta t ion on ly when the frequency isconstant. In genera l, t he phase angle of 8 will be propor t iona l to thet ime in tegral of the frequency, whether or not th e frequency it self isconstan t . The unit constan t pu t under th e in tegra l with F(t) plays t hesame role as that of the car r ier with amplitude modula t ion ; tha t is, itpermits downward as well as upward modula t ion . ;t is st illnecessary to make th e quant ity 1 + F(t) posit ive at a ll t imes. Forin ter ference-suppression pu rposes the frequency excu rsion , aa will beshown in Chap. 13, shou ld be la rge. The excu rsion must be small,h owever , com pa red with th e cen ter fr equ en cy f,, so th at sever al chan nels


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27/399

SEC.23] FREQUENCY-MODULATED C-W S IGNALS 15harmon ics of p. For a la rge index of modula t ion the impor tan t sidebandsa re th ose lyin g with in t he fr equ en cy excu rsion in terval; th e Bessel fun c-t ions of order h igher than the argumen t (modula t ion index) approachzero rapidly as the order becomes high . On th e other hand, for a lowindex of modula t ion few sidebands have an appreciable amplitude; th efir st (J , t er m) is, apa rt fr om th e ca rr ier (J O term ), th e on ly on e of a ppreci-able amplitude. These qualita t ive effects a re illust ra ted in Fig. 2%,

kfo ~=P(a ) Amp lit ude spect r a for f-m waves . The ve r tic a l line s rep resen t the re la t ive ampl i-tudes of th e carrier and s ideband componen t s ,

(b) Frequency-modu latedwave.~IG. 2.8 .Frequencym odula t ion; typica l waveform and spect ra ,

which shows amplitude spect r a for th ree typica l cases. In addit ion tothe effects ju st ment ioned it can be seen that for large index of modula -t ion , the density of sidebands is near ly un iform with in the excu rsionin terval. Fu r thermore th e car r ier , wh ich var ies wit h J o(k.fo/ p), canvanish for cer ta in values of th e modula t ion index; th is situat ion is qu itedifferen t from the a-m case. In Fig. 2.8 the sideband amplitudes a re allsh own wit h posit ive coefficien ts; t he dia gr ams in dica te t her efor e t he a bsmlu t e va lu es of sideband amplit udes. This is, of cou rse, the quant ity thatwou ld be measu red by a lin ear r eceiver of ba ndwidth su fficien t ly m ar rowt o con ta in on ly on e sideba nd.The funct ion of the receiver is to conver t th e f-m signal in to m a-msignal, where it may be conver t ed in t he usual manner to an audio orvideo signal. In addit ion to the frequen ry-to-amplitude conver t er th ere


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16 TYPES OF S IGNALS AND THEIR RECEPTION [SEC.23is a n amplit ude limiter th at r em oves amplitu de fa ding fr om t he in comin gsigna l; it is also h elpfu l in r edu cin g cer ta in kinds of exter na l in ter fer en cesu ch a s ign it ion or spa rk -gen er at ed in t er fer en ce.The frequency-to-amplitude conver t er ordinar ily consist s of a dis-

cr imina tor circu it whose output voltage changes linear ly not only withthe amplitude of the incoming signal but a lso with its frequency. Sinceamplitude var ia t ions, which may occur in t he incoming signa l becau se offadin g, a re essen tia lly r em oved by t he init ia l amplitu de limiter , t he on ly

Amplitude Frequency-b Amplitude8in- - -limiter amplitude modulation -V3Mconverter receiver~G. 2.9.Frequ eney-m0d u lationreeeiver.

Inputoltageas a functionof time

Voltageafter amplitudelimiter

Voltageafterfrequency-to-amplitudeilter, as a funtiton of timeFIG. 2 .10.Voltage waveforms in f-m receiver .

th ing tha t can produce amplitude var ia t ion of the ou tput signal is thefr equency var ia t ion of the incoming wave. Once the a-m wave is pro-duced, it is rect ified or detected in the usual fash ion. A block diagram ofan f-m receiver is shown in Fig. 29. Typica l volt age wa veforms occu r-r ing at var ious places in the receiver a re shown in Fig. 2.10. It will ben ot iced t ha t in ciden ta l sign al fa din g in amplit ude is vir tu ally elim in at ed.Product ion of the a-m wave will of cour se involve changes in radio fr~quency tha t will occupy a large frequency band. The a-m receiver mustt her efor e be a ble t o amplify t his la rge ba nd of fr equ en cies befor e det ect iontakes place; otherwise distor t ion will occur : The linear ity of over -a llr espon se is gover ned a lmost complet ely by t he lin ea rit y of t he fr equ en cy-to-amplitude con ver t er . This con ver t er , or slope filter as it is somet imesca lled, can be made very near ly linear .An idea l f-m r eceiver is t h er efor e essen tia lly in sen sit ive t o a n in com ing


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SEC. 2.4] PHASE-MODULA TED C-W S IGNALS 17a-m signal. Likewise an a-m r eceiver is insensit ive t o an f-m wa ve, exceptwhere the bandwidth of the a-m receiver is smaller than the frequencyexcursion of the f-m signal. In th is case, because of the slope of theresponse curve, the frequency funct ion is conver ted to an amplitudefunct ion, usually in a nonlinear fash ion , and the receiver will not bein sen sit ive t o t he f-m signa l.2.4. Phase-modulated C-w Signa ls. Phase modulat ion is in one

sen se mer ely a t ype of fr equ en cy modu la tion . The tota l phase angle of&is made to va ry in accordance with the modula t ing wave F(t ). A p-mwa ve can t her efor e be r epr esen ted by

8 = .5, Cos 27r~ot + a, + ml(f)], (20)wh er e m is a con st an t r epr esen tin g t he ch an ge in ph ase a ngle a ccompa ny-ing a unit change in F(t ). If F (t ) is expressible in a Four ier ser ies,

F(t) = 2 an cos 27rpnt, (21)ncompa ra ble p-m and f-m r epresent at ions ca n be writ ten

[& = 80 cos 27r(fot + ao) + m

z 1an cos 2rp.t ,

nphase modulat ion ; (22)

[ 2 1= 80 cos 2r (fot + 80) + /c.fO ~ sin 2mp.t ,nfrequency modula t ion . (23)

These expressions are similar , bu t t hey differ in one impor tan t r espect .The coefficien ts of the pm terms are independent of p. for phase modula-t ion but a re inversely propor t iona l to p. for fr equ en cy modu la tion .Pha se modulat ion may t her efor e be conver ted t o frequ en cy modula tionby placing in t he m odulat or a filt er whose ga in is inversely pr opor t iona lto frequency. Similar ly, frequency modulat ion may be conver ted tophase modulat ion by placing in its modulator a filt er whose gain is pro-por t iona l to the modulat ing frequency. Thus the essent ia l differencebetween fr equ en cy and ph ase modu la tion lies in t he ch ar act er ist ic of t he fil-t er in t he modulator . The rela t ive advantage of one system over the ot herdepen ds on t he modu la tin g fu nct ion F(t) and on the frequent y spect rumof undesired in ter ference. In actua l pract ice it is customary to useneither pure phase modulat ion nor pure frequency modula t ion . Thelower a udio fr equ en cies a re usua lly fr equ en cy modula ted, a nd t he h igh erfrequencies are phase modula ted. Appropr ia te. filt ers in the receiverst r aigh t en ou t t h e fr equ en t y ch a ra ct er ist ic.


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SEC.2.6] FIN ITE PULSE TRAINS 19where the symbol ~.,0 is equal to unity when n = O; otherwise it equalszero.This equ at ion is illust r ated in F ig. 211 for a situa t ion in which fO >> f,.

It can be seen tha t apar t from the ca r r ier frequency ~0, t her e ar e a hostof sideband frequencies separa ted from jo by mult iples of f,; these a ret he on ly fr equ en cies pr esen t a nd h ave amplit udes det ermin ed by E q. (26).A good dea l of informat ion is conta ined in such a t ra in of pulses. The

PRF, phase of pu lses, etc., cou ld be ascer ta ined if requ ired. If thequan t ity to be determined is merely the existence of the pulse t ra in , how=ever , a complete analogy can be drawn to the c-w case of Sec. 21. Theamplitude pu lse t ra in is a kind of ca r r ier , which in itself conta ins lit t leinformat ion . It may, h owever , be m odula t ed t o in cr ease t he in format iontha t can be t ransmit t ed and, as in previous cases, maybe modula ted inamplit ude, r adio fr equ en cy, or ph ase. In addit ion , it is possible t o modu-la te it by va rying the PRF or by varying the pulse length or width .These methods of modula t ion as well as methods for detect ion will bediscu ssed in la t er sect ion s.2.6. F inite Pulse Tra ins.-In rada r applica t ions a t ransmit t er is made

to send ou t r -f energy in a succession of pulses. The frequency of theradio wave itself may be ext r emely high, and the dura t ion of a singlepulse may be on ly a few microseconds. Occasionally a system is madewhere the pulse dura t ion , or length , is as small as 0.1 ~sec. The pulsesa re r epeat ed at an audio ra te, tha t is, from perhaps 50 to 10,000 pps.Th e pu lses of r -f en er gy a re sen t ou t in to spa ce per ha ps omnidir ect ion allybut more usually concen t ra ted or focused in cer ta in regions by a direc-t ional antenna system. Object s in these r egions will reflect or sca t t ert he radia t ion . Some of th is sca t t ered energy is picked up by a receivingsystem usually loca ted near the t ransmit ter . The receiver must becapable of passing t o the indica tor the video pulses, tha t is, the detectedr -f pu lses t ha t cor respon d t o t he sca tt er ed or r eflect ed pu lses of r -f en er gy.One of the major difficult ies in the radar problem is t o make the receivingsystem sufficient y sensit ive t o det ect the sca t t ered r -f ener gy of object ssevera l miles away. The limita t ion in sensit ivity is genera lly imposedby noise of some sor t genera t ed with in the receiver (see Chap. 5), orgover ned by ext er na l in ter fer en ce (see Chap. 6).The fundamenta l purpose of the radar set is to provide informa t ionI Th is d evelopmen t r equ ir es t h at t h e s u cces s ive p u ls es h a ve a d efin ed r -f p h as e, a s

th ou gh th ey were determ in ed from a m as ter c-w oscilla tor of frequ en cy j,. Th es u bs equ en tch a pt ers of th is b ook d ea l on ly with p u ls e t ra in s in wh ich th e p ha se frompa lm to pu ls e m ay or may not be ran dom ; it m akes no differen ce in th e recep tionproces sfor a mplitu de pu ls es , s in ce th e ou tpu t of a ny detector is in sen sit ive to r-fphsse . Th e ma th ema tica l s pecifica tion for a t ra in of r -f p u ls es h a vin g r an d om ph as esis different from Eq. (24), h owever; th e s in e term will con ta in , in a dd it ion , a ra n domph see an gle d ep en d en t u p on t he in d ex k .


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20 TYPES OF S IGNALS AND THEIR RECEPTION [SEC.2.6that permits the human observer t o loca te objects of par t icula r in terest .With a direct ional antenna system the azimuth and elevat ion of searchare known; and by the system of pulses, t he range of or distance to ar eflect in g object can be foun d. This r an ge is m easur ed by t he t im e differ -ence bet ween the t ransmit ted pulse and t he received echo pulse. Sincet he a ngu la r loca tion of t he r eflect in g object r equ ir es a dir ect ion al r adia tor ,a gen er al sea rch of t he en tir e r egion r equ ir es some sor t of sca nn in g. Th esca nn in g or sea rch in g mot ion of t he a nt en na syst em is u sua lly r epr odu cedin some form within t he in dicat or , so t hat ea sy cor rela tion of t he pr esen ceof a par t icular echo with a par t icular azimuth or eleva t ion can be made byt he obser ver . Becau se of t he scanning a ct ion, t he r et ur n signal r eflect edfrom an object consist s of a fin ite tra in of r -f pulses. This t ra in of pulsesis, of course, repea t ed a t t he next scan.The scanning can be accomplished in many ways, and t he pulse video

in forma tion a t t he ou tpu t of t he r eceiver ca n be pr esen ted on t he in dica torin many ways. Th e m et hod of scanning is dict at ed by bot h t he funct ionof the radar set and mechanical considera t ions for moving the antennaassembly. The method of indicat ion is usually one that makes t he radarin format ion most in telligible t o t h e obs er ver . Some of t he mor e commonin dica tor s u sed a re list ed below for r efer en ce.

The Type A or Linear Time-base Oscilloscope .Th is in dica t or con -sist s of a cathode-ray oscilloscope in which the video signals from ther eceiver a re impr essed u pon t he ver tica l deflect ion pla tes a nd a lin ea r saw-tooth sweep voltage is applied t o t he horizon tal deflect ion plates. Thishor izontal sweep is usually sta r ted by the init ia l impulse from the radart ransmit ter and is made to move across the oscilloscope at a ra te con-venient for r ada r r an ge measu rement s. The next t ransmit ted impulsestar t s the Sweep over again. Thus, near -by objects that scat ter the r -fenergy will cause a visual ver t ical deflect ion, or pip (also ca lledblip ), near the star t ing edge of the sweep; a reflect ing object a t adistance will produce a pip a t a horizon ta l posit ion cor responding to therange of the object . Thus the linear t ime base provides a range measurement of objects scat ter ing the r -f pulses. The amplitude of the videodeflect ion , or pip, is a mea sur e of t he effect ive sca tt er ing cr oss sect ion ofthe object in quest ion . It is a lso a funct ion of the range of the object ,becau se of geomet rica l fa ct ors, and a funct ion of t he over -a ll sensit ivit yof the radar set . The type A oscilloscope thus essent ia lly providesinformat ion about the range of an object and some informat ion as to itsradar size. It does not give azimuth or eleva t ion informat ion , butth is can always be obta ined from separa te dials geared to represen t theantenna coordina tes. Because of the t ime necessary for the observer to S ee R adar S can ners and R ad urnes, Vol. 2 6, Rad ia t ion Labor a tor y S er ies .zS e e Cat h od eRay Tu be Displays, Vol. 22 , Radia t ion Labor a tor y Ser ie s .


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SEC. 2.6] FIN ITE PULSE TRAINS 21coordina te the A-scope range with elevat ion and azimuth? the system isnot well suited to rapid scanning or sea rch . It is most useful in themeasurement of radar range on systems tha t have a broad antenna-

1 radia t ion pat tern and eithe~ do not scan at all or scan rela t ively slowly.

I

This type of indica t ion , however , is sensit ive in the detect ion of weakechoes.In addit ion to other obvious advantages, a radar can give far more

precise range informat ion than anopt ica l range finder . The radar rangeer ror can, unlike t he opt ica l, be in depen dent of t he r ange itself and can bemade assmallasa tenth of the equiva lent range represen ted by the pulselength . For high precision the sweep on the A-scope would have to beext remely linear and well ca libra ted or some other marking device pro-vided. It is customary to provide range marks, or a ser ies of sharpt iming pips, to mark the sweep at convenien t in terva ls. If ext remeprecision is requ ired, a movable delayed-t iming pip is provided whoset ime delay is ca libra ted and accura tely known. It may be genera tedfr om a cryst a l-con t rolled oscilla tor . This t iming pip can be made tocoincide with the desired radar echo, whose accura te range can thus bedetermined. Where the sweep length is very long in comparison with thepulse length as present ed, it is difficult t o see t he r ela tive posit ions of t heecho pip and t iming pip. For th is purpose an especia lly fast hor izonta lsweep may be provided. Such an oscilloscope is known as an R-scope(range). It is merely an A-scope in which the star t of the sweep may beaccura tely delayed and the sweep speed made sufficient ly grea t todelinea te the desired echo and t iming pip. The R-scope is also useful inexamining the character of the returned echo pulse or pulses and isgenera lly mor e sensit ive than the A-scope in the detect ion of ext remelyfeeble echoes.

The Type B Oscilloscope.Th is in dica tor wa s in it ia lly developed t oadd azimuth informat ion to what was presen ted on the A-scope; thiswas done by impressing t he video signals from t he r eceiver on t he con tr olgr id of th e ca t hode-r ay oscilloscope. The video signals t her efor e modu-la te t he beam cu rr en t in t he oscilloscope a nd con sequ en tly t he in ten sit y oflight output . Under these condit ions the ver t ica l pla tes of the oscillo-scope a re left free. It is necessary only to impress on these pla tes avoltage that cor responds to the azimuth of the radar antenna . As theantenna is made to scan in azimuth, the t race of the t ime-base sweep ismade to move up and down in synchronism with the antenna posit ion .This type B oscilloscope therefore produces on its screen a br ight spotwh ose posit ion in r an ge a nd azimu th on t he oscilloscope fa ce cor respon dsto the actua l range and azimuth of a reflect ing object . It is t herefore aradar map, differ ing from the usual map by a distor t ion caused on ly byth e par t icular coor dina tes chosen. Like t he deflect ion-m odu la ted


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22 TYPES OF S IGNALS AND THEIR RECEPTION [SEC. 2.6t ype A oscilloscopes, in ten sit y-modu la ted oscilloscopes su ch a s t ype Bare very sensit ive in the det ect ion of weak echoes; bu t the in tensity-modula ted osu lloscopes are much bet ter adapted for scanning systems.Because it is conven ien t to view the oscilloscope face like a map, ant ]beca use t he r adar -sca nn in g fr equ en cies a re gen er ally I)elow t he flickerfr equency for the human eye, it is customary to use for the screen of theca th ode-r ay t ube a specia l m at er ia l wh ose light ou tpu t deca ys r ela tivelyslowly wit h t im e.

The Plan-posit ion Indicator, or PPI.This is the name given anin ten sit y-modu la ted oscilloscope in wh ich t he t im e-ba se sweep is m ade t osta r t a t the cen ter of the tube and move radia lly outward. The azimuthof this radial sweep on the oscilloscope is made to cor r espond to theazimuth of the radar an tenna . This type of sweep is usua lly provided bya magnet ic deflect ion yoke placed around the neck of the ca thode-r aytube. As the antenna is scanned in azimuth , t he magnet ic yoke issynchronously rot at ed about t he axis of th e tube. This synchronizat ionis easily accomplished by dr iving the yoke by a synchro motor or someot her r emot e mech an ica l syn ch ro-t ra nsm ission device. Thus the PPIprovides a map of all radar echoes, where the map scale factor is merelythe ra t io of twice the velocity of the radio wave to the sweep speed.Because of the ease with which a t rue map can be in terpret ed, the PPIis an idea l indica tor for use with radar set s searching cont inuously inazimuth. In tensity-modula ted r ange marks a re genera lly provided forca libra t ion purposes. They appear as concent r ic br igh tened r ings a tr egu la r ly sp aced r adia l in t er va ls.

The Range-height, or RH, In dica tor . -h eit her t he t ype B oscilloscopenor the PPI can presen t eleva t ion information , and for radar set s whosefunct ion is heigh t-finding some other indica tor is desirable. Withoutrecour se t o a three-dimensiona l in tensity-modula ted indica tor , whichhas not yet been devised, t he presen ta t ion of eleva t ion informat ionrequires the omission of either azimuth or range informat ion . If theazimuth informat ion is suppressed, an indica tor presen t ing range andheigh t , or RH oscilloscope, can be provided. The radar an tenna is madet o nod or oscilla te in eleva t ion angle. The angle of the deflect ion yokein an oscilloscope of th e PPI var iety is made to follow th e antenna eleva-t ion angle in such a way thht the indica tor presen ts a t rue radar map of apa rt icu la r ver tica l sect ion of spa ce. Thus the RH indica tor will presen tt ru e r an ge a nd h eigh t of r ada r t ar get s, n eglect in g, of cou rse, t he cu rva tu reof the ea r th s sur face. The range and heigh t scales can , if necessary,be expa nded or con tr act ed t o pr ovide con ven ien t va lues.

The Type C Indicator.If the r ange informat ion is suppressed, anindica tor presen t ing azimuth and eleva t ion informat ion, or type Cindica tor , ca n be pr ovided. Beca use t he r an ge in forma tion is su ppr essed,the indicator will show a br igh t spot on its scr een a t an eleva t ion and


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24 TYPES OF S IGNALS AND THEIR RECEPTION [SEC.27detector , most of the signal energy is lost , the remainder being forced tocompet e wit h n oise pr odu ced a ft er det ect ion . For this reason th is typeof receiver is not so sensit ive as the superheterodyne for weak signals,perha ps by a factor of 104 in power . However , the r -f bandwidth can bema de severa l h un dr ed m ega cycles per secon d in ext en t.Th e super het er odyn e r eceiver is a lmost u niver sa lly u sed in r ada r a ppli-ca tion s, beca u se it h as bet ter sen sit ivit y t ha n t he sin gle-det ect ion r eceiverand bet t er stability than th e su perregen era tive receiver . At the veryhigh frequencies the r -f amplifica t ion , because of it s limita t ions anddifficult ies, is not customar ily used, but the r -f signal is usually imme-dia tely conver ted in to an i-f signal. The i-f amplifier therefor e has ar ela tively gr ea t volt age ga in , per ha ps a s much a s 10G,wea k sign als bein g,a s a r esu lt , made su it ably la rge for lin ea r d et ect ion or r ect ifica tion . Thisamplifica t ion must be of such a nature tha t it has a sa t isfactory responseto the desir ed pulses. From Fig. 2.11 it can be seen that most of theenergy in the pulses is concent ra ted in a band of frequencies rough lyequal to the reciprocal of the pulse length . Therefore the r-f and i-fbandwidths must each be of the order of magnitude of the reciprocal ofpulse length . Since the pulse lengths in use va ry from 107 to 10s see,the bandwidths must be of the order of 105 to 107 CPS. This is the chiefdifference between receiver s made for radar pulses and those made forr adio t ran sm ission , t h e la t ter being designed t o pa ss on ly audio fr equencies.Some superregenera t ive receivers have been const ructed for pulse

recept ion . The quench frequency must be high compa red with the recip-rocal of the pulse length to make sampling sufficien t ly frequen t . Forpulse lengths of less than 1 psec, th is has been found difficu lt to do.Fur thermore the cr it ica lness of adjustment has grea t ly rest r ict ed theusefulness of such receiver s. Never th eless, cer t a in of their proper t ies,such as high gain over sa t isfactory bandwidths, necessita t e taking theminto considerat ion.In all these methods of recept ion the main object of percept ion is to

become aware of the existence of the incoming r-f signal. The quest ionis n ot on e in volvin g t he deta iled ana lysis of th e signa l ch ara cter ist ics butsimply whether or not the signal exists. As poin ted out in Sec. 2.5, it isoften usefu l t o con sider th e detect ion of a ser ies of pulses tha t a re modu-la ted in some manner a t a slow rate. The informat ion one wishes toa bst ra ct fr om t his t ype of sign al is t he r ela tively slow modu la tion fu nct ionappear ing in the pulse t ra in , in much the same way that one wishes toabst ract the modula t ing funct ion from an a-m or f-m c-w signal.2.7. Amplitude-modula ted Pulse Tra ins.-There a re two reasons

wh y it is usefu l to consider th e percept ion of th e modula t ion funct ion of amodula ted pulse t ra in . First of all, the echoes obta ined in radar recep-t ion are indeed modula ted by changes in the character ist ics of the targetu nder surveillance, The effect ive sca t ter ing cross sect ion of the target


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SEC. 2.7] AMPLITUDE-MOD ULATED PULSE TRAINS 25may vary with t ime because of changes in the ta rget aspect or posit ion;it may also vary in a way character ist ic of the par t icular t arget it self.For example, pr opeller rota t ion on an air craft will give r ise t o aper iodicch an ge in it s effect ive r ada r sca tt er in g cr oss sect ion . In forma tion con -cern ing the modula t ion of received pulsed echo tra ins may therefore behelpful inder iving informat ion concern ing the nature of the ta rget . Asanother example, one can see that the phase of the returned radar echodepends upon the tota l path length taken up by the radio wave and there-fore changes markedly with ta rget movement . By a phase-detect ionscheme a modula t ing funct ion that depends on target speed can thus bederived. The phase changes brought about by ta rget movement can beconven ient ly measured by one of two genera l methods. The coheren t -pu lse syst em mixes t he in comin g ech oes wit h a st ron g loca l c-w gen er at orwhose phase is reset to the phase of the t ransmit ted pulse each t ime it isproduced. The result ing echo amplitude will be constant from pulse topulse unless the ta rget in quest ion moves dur ing this t ime interval by anamount that is appreciable with respect to the wavelength of the r -fsignal. As the ta rget moves, the echo will be seen to beat up and downwith a frequency given by the Doppler shift . By analyzing the phasemodu la tion of t he r et ur n pu lses, t her efor e, in forma tion con cer nin g r adia lt arget speed can be der ived.A second method of phase detect ion is possible. Instead of utilizing

the local source of phased c-w oscilla t ions, the echo from the movingta rget is mixed with other st rong echoes from fixed ta rgets. Again beatsin the echo amplitude are obta ined in the same way as for the coheren t -pulse system. The presence of these beats depends, however , upon thepresence of local fixed echoes at the same range as the target . Since thiscondit ion is not under the observer s cont rol, the system has a limitedarea of usefulness. It is, however , much simpler than t he coh er en t-pu lsesystem.On e of t he main uses for modula ted pulse tra ins, however , lies in their

a pplica tion t o specia lized communica tion syst em s. Such systems havethe advantage of highly direct ional propaga t ion character ist ics and ahigh degree of secur ity. In these systems a cont inuous succession ofpulses modula ted at speech frequencies is sen t out . As poin ted out inSec. 2.5, th e modula t ion it self may be applied t o t he pulses in severa l dif-ferent ways. Amplitude modula t ion will be discussed in this sect ion ,and other types of modula t ion in Sec. 2.8.The amplitudes of the cont inuously recur r ing pulses are assumed to

vary in accordance with the modula t ing funct ion. If t he modula t ingfunct ion is one that can take on both posit ive and nega t ive values withrespect to its normal or quiescen t value, there must be provided, as inprevious examples, a ca r r ier t erm la rge enough to preven t the en t ir eamplitude funct ion from rever sing sign. The funct ion of the receiver

A


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26 TYPES OF SIGNALS AND THEIR RECEPTION [SEC.2.7is to obta in the modula t ion funct ion from the rela t ively complica tedtra in of incoming pulses. The fir st step in the chain of events is thedetect ion of the r-f signal to provide video pulses, just as in the case ofnormal radar echo detect ion . Since distor t ion of the modulat ing func-t ion is undesirable, linear detect ion is grea tly prefer red; and for the sakeof sensit ivity, a superhet erodyne receiver should be used. The ampli-tudes of th e video pulses are st ill S1OW-1Yodula ted by th e modula t ingfunct ion . The possibility of ga t ing the pulses a t this point makes th ist ype of communicat ion system much more secure than the ordinary a-mc-w signal. The proper video pulses can be selected by a gate whosePRF is the same as tha t of the desired signal and whose t iming is madeto coincide with the pulses either by a specia l t iming pulse or by auto-mat ic locking voltages der ived from the incoming pulses themselves.Th e sen sit ivit y of t he r eceiver t o wea k sign als in n oise is a ffect ed by ga tin gand by the ga te length itself. This poin t will be discussed in Chap. 10.Th e spect rum of t he pu lses ca n be der ived in a st ra igh tforwa rd fa sh ion .

Let us represent the modulat ing wave F(t) by the funct ionF(t ) = 1 + Esin 27rp(t + 8), (27)

where e is the fract ional modula t ion and p is t h e modu la tin g fr equ en cy.This funct ion is now t o r epresent the amplitude of the pulse t rain, whichhas a PRF denoted here by ~, and pulse lengths indica ted by,. For thesake of simplicity it is supposed that the pulse amplitude a t the sta r t ofthe pulse will assume the value of F(t ) and tha t the pulse amplitude ism ain ta in ed con st an t t hr ou gh ou t ea ch pu lse. Th at is, t h e sign al fu nct ionwill be given by

F.(t) = z ()F ; A,(t), (28)rkwhere

( O otherwise.The Fou rier development of F,(t) becomes

.+: 2[sin 7dTf,7r 1 c0s2+-@=1~ sin m(ljr + p) s in [2m(lj, + p)t np + 2rp6]+lfr+p

1~ sin m(t j, p) sin [%(lj, p)t + m,p 2Tpti] . (29)+ljrp


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%C. 2 .7 ] AMPLITUDE-MODULATED PULSE TRAINS 27It can be seen tha t , in genera l, many frequencies a re presen t in F.(t),namely, all the harmonics of the PRF f, and cross terms between theseharmonics and the modula t ing frequency p. The amplitude of any termof fr equency j is modified by the familiar (sin m.f) /mj because of thepulse length T. A con ven ient cha rt for rea ding off all fr equ encies pr esentis shown in F ig. 212. Ou tput frequencies ar e given on the abscissa sca lefor any input modula t ing frequency chosen on the ordina te sca le. The

OutputfrequenciesFIG. 2-12 .Outpu t frequencies for a given modu la t ing frequen cy.ou tpu t frequ encies presen t ar e th ose which a ppear a t th e in ter sect ions ofa h or izonta l line, wh ose ordin ate is th e modula t ing frequ en cy p, with th ea r ray of diagonal lines and ver t ica l lines shown in the diagram. Anexample is shown by the dot ted line drawn for p = j,/4; the outpu t fr e-quencies ar e shown to be 2?lf, and z (2.., f f./4).The diagram shown in Fig. 2.12 is not su itable for indicat ing th e in ten-

sit ies of the var ious components. A simple ru le to remember is t ocon sider t ha t a ll in ter sect ion s wit h dia gon al lin es yield amplit udes wh icha re c t imes t hose of th e ver t ica l lines.modified a ccording to t he individua l

Fu rt herm ore, all in~ersect ions arepulse spect rum (sin mj)/mf and


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28 TYPES OF S IGNALS AND THEIR RECEPTION [SEC.2.7t her efor e fall off with in crea sin g fr equ en cy. A typica l spect rum is sh ownin Fig. 2.13, where f,~ = 0.2 and p = f,/4 as shown in Fig. 212. Thefr equ en cies sh own with dot ted lines a re th ose cau sed by th e modulat ionitself.It would be possible to pu t the video pulses direct ly in to a loud-

speaker and der ive sound that conta ins the modulat ing funct ion (seeFig. 2.13). It would also conta in many undesired and ext remely annoy-ing frequencies. These undesired frequencies a re all h igher than themodulat ing frequencies provided p < f,/2 and can thus be filtered ou tbefore going in to the loudspeaker it self. Generally, the desired audiocompon en t must be gr ea tly amplified beca use of its sma ll en er gy con ten t.

FIG. 2 .13 .V1deospectrum of modula tedpu lse t ra in .The filter ing and audio amplifica t ion may be great ly helped by theso-called boxcar genera tor , or demodu la tor . This device consist s ofa n elect rica l cir cu it t ha t clamps t he pot en tia l of a st or age elem en t, su ch asa capa citor , t o th e video pulse amplitude each t ime th e pu lse is r eceived.At all t imes bet ween , th e pulses t he stora ge elem en t main ta ins th e poten -t ia l of the preceding pulse and is a ltered on ly when a new video pulse isproduced whose amplitude differs from tha t of the previous one. Thename boxcar gen er at or is der ived fr om th e fla t st eplike segments of th evolt age wave.The outpu t of the boxcar genera tor is given by Eq. (29) (by put t ing

7 = l/f,) and can also be obta ined from Fig. 2.13. It can be seen tha tnone of the lf, terms remain except the d-c term. The outpu t frequencypr esen t a t t he modu la tin g fr equ en cy p is a lso in ciden ta lly mu ch amplifiedbecause of the increased pulse length . The ou tpu t volt age, however ,st ill does conta in at r educed amplitude the cross-modula t ion terms.Never theless, the main body of in ter fer ing audio frequencies has beenremoved, and therefore the problem of addit ional filter ing is grea t lysimplified. The boxcar genera tor can be used on ly on ga ted systems,


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SEC.27] AMPLI TUDE-MODULA TED PULSE TRAINS 29unfor tuna tely, or a t least on systems from which an accu ra t ely t imedclampin g pulse is a va ila ble.If cross-modu la t ion terms in the ou tpu t must be avoided, the h ighest

modu lat ion frequency must be substan t ia lly less than one-ha lf of thePRF f,. If a filter is u sed to separa te th e ou tpu t frequencies, it will havea cu toff or a t t enuat ion cu rve tha t is not in fin itely sharp; therefor e themaximum value of p must be fu r ther rest r icted. If p is limited to j,/3,then one octave exist s for the filter to ach ieve it s cu toff value. This iscon sider ed t o be a n a ccept able va lu e. It will be n ot iced th at th is r est ric-t ion will a pply t o a ll of t he pu lsed communica tion sch emes, sin ce it followsdirect ly from t he effect of samplin g th e signal volt age at discr ete t im es.Before proceeding to other forms of modu lat ion , th e par t played by

var ious detect ion processes shou ld be considered. The first detect ionpr ocess (a ct ua lly t he so-ca lled secon d det ect ion in a su per het er odyn ereceiver ) r educes the r -f voltage to a video volt age. This provides ameasu re of th e in tensity of the r -f wave withou t regard to it s exact r -fst ructure. This video voltage st ill va r ies at a fa ir ly h igh ra te and maycontain modulation intelligence. An a ddit ion al det ect ion pr ocess, t ha t is,boxca rs with au dio filter in g, will br in g ou t t he modula tion fr equ en cies.St ill another , or fou r th , detect ion can be provided. This one measuresthe average in tensity of these audio voltages; that is, it measures thefract iona l modu la t ion c. Thus the detect ion process is one tha t pr inci-pally provides a measure of the average in tensity of a funct ion . Becauseof t his a ver agin g pr ocess, t he fr equ en cies pr esen t in su ccessive det ect ion sbecome progress ive ly lower .One more poin t r egarding the demodu la ted signal shou ld be noted.

The video ou tpu t is a measu re of the signa l size and can th erefore be useda s a sign al-a ct ua ted con tr ol volt age. It is somet imes conven ien t to usethk voltage to con t rol the ga in of the receiver . Thk con t rol must clea r lybe made of such a sign tha t an increase in video signal will r educe ther eceiver ga in ; otherwise th e system will be regenera t ive. With th isdegenera t ive system, the receiver ga in tends to main ta in the averageou tpu t signal constan t in size regardless of inpu t signal size. The act ionof th is type of au tomat ic gain con t rol, or AGC, will be descr ibed inCh ap. 11.When the AGC does not n eed to be rapid, an idea l a r rangemen t is to

use the ou tpu t of the boxcar genera tor as th e feedback con t rol voltage.This a r rangemen t is shown in block form in Fig. 2.14, wh ere all th e par t sa re self-explana tory with the except ion of the filter between the th irddetector and ga in -con t rol lead. The funct ion of th is filter is essen t ia llyto pass on ly the d-c componen t to the ga in con t rol lead, thus effect ivelyrem ovin g th e desir ed modulat ion fr equ en cies. In th is fash ion thesemodu la tin g fr equ en cies t hem selves a re n ot degen er at ed in t h o r eceiver .


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30 TYPES OF S IGNALS AND THEIR RECEPTION [SEC.2.8If t h e filt er pa sses t h e modu la tin g fr equ en cies, t h ey will be d egen er a ted

and grea t ly r educed in amplitude a t t he receiver ou tput . They a re not ,in gen er al, com plet ely degen er at ed beca use of t he fin it e ch an ge in ou tpu tsignal r equ ired to cause a cha nge in r eceiver ga in . F or some applica t ionsth is fin ite degenera t ion is not ser ious, since audio amplifica t ion willrestor e the amplitude of the modula t ion signal. In addit ion , because ofthe rapid feedback, t he speed of AGC is grea t ly increased. The filter ,however , must considerably a t tenua te the PRF, or oscilla t ion willdevelop because of the cross terms of Fig. 2.12.

Receiverr-f and .%cond SingleEh - + selector Thirdi-f amplifier detector detector EwtgateJIGain-control lead l=] II low-pass Ifilter

FIa. 2.14.Au dio-modu lat ionreceiver with au tomat icgain control.2.8. Ot her Types of Modu la tion . Pulse-length or Pulse-m.dth Modula-

t ion .In th is case th e modula t ion is accomplished by var ia t ion s in pulselength . The PRF and the pulse amplitude a re held constant . Recep-t ion con sists of det ect in g t he r -f pu lses, t hen con ver tin g t he len gt h va ria -t ion s t o amplit ude va ria tion s. As poin ted ou t in Sec. 2.7, t he PRF mustbe a t least th r ee t imes tha t of the highest modula t ing frequency, and alow-pass filt er must be u sed to exclude undesired cross terms.Th e con ver sion fr om pulse len gth t o amplitude is most easily a ccom-

plished by passing the signa l th rough a filt er of limited pass band.Th rou gh su ch a filt er , if it s ba ndwidt h is con sider ably less t ha n t he r ecipr o-ca l of the maximum pulse length , th e outpu t respon se will ha ve an ampli-tude propor t iona l to the product of input pulse length and amplitude.This opera t ion can be accomplished in the r -f and i-f sect ions of ther eceiver befor e det ect ion t akes pla ce. It is most conven ient , however ,to limithe incoming signals (usua lly done most easily a fter detect ion )before conver t ing the pulses to amplitude-modula ted signals. Thelimiter plays the same role as the limiter for f-m radio (see Sec. 2.3);tha t is, it elimina tes amplitude var ia t ions in r eceived signals produ cedby fading and reduces in t er ference of a type in which peak voltages ar ever y h igh . The bandwidth of the r eceiver in fron t of the limiter shouldbe adequate to pass the shor test pulse proper ly. From Fig. 2.11 it canbe seen tha t t he bandwidth should exceed the reciproca l of the shor t estpulse length .In addit ion to peak limit ing, it is usua lly desirable to provide a lowerlimit below wh ich n o ou tpu t signa l occu rs. If t he in pu t sign als fa ll belowsom e defin ed min imum level, n oise or in ter fer en ce in t he r eceiver r en der s


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SEC. 2.8] OTHER TYPES OF MODULATION 31them useless. Therefore a lower limit , wh ich excludes thk noise, isbeneficia l. The presence of both a lower and upper limiter const it u tesa s licer , so named because the ou tpu t volt age is propor t iona l to th einput voltage only with in a nar row voltage range or slice. Th e slicedou tpu t of t he len gt h-modu la ted pu lses will con sist of a ser ies of r ela tivelyclean con st an t-amplit ude len gt h-modu la ted pu lses su it able for imme-dia te con ver sion t o a -m pu lses.As in the case of a-m pulses, gat ing can be employed with in the limits

of pu lse lengths used. A ga te length as long as the longest pu lse mustbe used; th is wou ld appear to favor sligh t ly the use of a-m pulses whereaccu ra t e gat ing of a size equa l to the pulse length at all t imes is possible.

Frequency OTPhase Modulation.In th is type of modula t ion one canth ink first of an ordinary f-m or p-m con t inuous wave as descr ibed inSees 2.3 and 24. The pu lses merely select shor t segmen ts ou t of th isr -f wave; they th erefore bear defined frequen t y and/or phase changesdetermined by the or igina l modula t ion . The process of recept ion con -sists of limit ing the pulses, then passing them th rough a frequency-to-amplitude slope filter . F rom th is poin t they are handled like a-m pu lses.The pu lse frequencies spread ou t over a band about equal in width to ther ecipr oca l of t h e p ulse len gt h . Th er efor e t he fr equ en cy devia tion sh ou ldbe made la rge compared with th is band of frequencies. In the t ruepu lsed case, it is n ot rea lly essen t ia l tha t the phase of the r -f signal wh ichis being frequency modulated be accu rat ely defined a t the sta r t of eachpu lse, sin ce th e frequ en cy-t~am plitu

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MIT Radiaton Lab Series V24 Threshold Signals

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