High-Speed Analog Computers

266 Pages·1970·18.86 MB·English

by  Rajko Tomovic

High-SpeAenda loCgo mputers
HIGH­
SPEED
ANALOG
COMPUTERS
RAJKO TOMOVIC
InstitMuitkea loPvu pi,n BelgraYdueg,o slavia
WALTERJ .K ARPLUS
AssociPartoef essor DepoafrE tnmgeinnte ering
UniversoifCt ayl iforLnoisaA ,n geles
DOVER PUBLICATIONISN,C .N,E W YORK
PREFACE
ImmedifaotlelloyWw oirnlWgda rI Iw hetnh nee wdleyv eltoepcehdn ique
ofe lectarnoanlicocog m putawtaisfio rnsi tn trodtuotc hepedu bltiwco,
typoefsa naldoegv iacpepse atrooe ffde arp proxiemqautpaerllo ym ise.
Thewseer tehr ee petoirht iigvhe- scopmepeudat netdrh soe n e-sohrso lto w­
speceodm puteIrnts h.foe l lowdiencga hdoew,e vtehroe,n e-schoomt­
puterre ceisvuecodhv erwhealcmcienpgt aanndpc ree feraemnocneg
enginteheatrthst e e r"ma nacloomgp utbeerc"av mier tusaylnloyn ymous
witohn e-sahnoatl og comBpytu htleea rt1se9. 5 0t'hsti rse bnedg atno
reverPsoes.s iabsal r ye souflc to mpetbiytt ihdoein g ictoamlp uatnedr
possibbelcya uosfte h ed evelopomfne enwte lecttreocnhinci aq ues,
resurgoefrn ecpee tciotmipvuet abteigoann .
Thep rimapruyr poosfte h ibso oiks t oi ntrotdhurece ea dteotr h e
electdreovniiaccne dcs i rcwuhiitccsho mbitnoce o nstirteupteet iat ive
compuftaecri alsiw teyla,lst os urvaepyp licoaftr ieopnesta intailvoeg
computteoer nsg ineperroibnlgIe nmv si.eo wft hper edomipnlaaoncfte
one-sahnoatlc oogm puttehribsso, o mku sbte r egaradsae nda dvanced
textbtoroeka otniefn agc oefat b roafide ldA.c cordiitin sga lssyu med
thatthr ee adaelrr ehaadasyc ertain oafem xopuenrtia enpndec res pective
regaradnianlcgoo gm putatTihoemn a.t egreinaelr caolvleyir nea od n e­
semesctoelrl ceoguer isnae n alcoogm putawtoiuolbnde o new ayo f
acquitrhibinasgc kgroMuanndoy.t hreera dweirhlsal v gea ineeqdu iva­
leenxtp erbiyec nocnet awcittishn dusctormipaulfat ceirl ities.
Becauosfte h er elataidvvealnync aetdu orfet hete xitt, appeared
approptroii antcel auldseao c onsidearmaobuloneftm atertihaailts
pertitnoet nheten t iraen alcoogm putfiienlbgdu tw hicihsg enerally
omitfrtoemdi ntrodtuecxttoSsru.yct ho paiscc so mpuptreorg ramming,
erraonra lyasnidss c,a lairntegr eaitnte edr omfst herierl attoif ounn­ da
mentmaalt hemadtiisccailp lThiinpser se.s entiasit nitoenn tdoe d
supplermaetnhtteh rat no r epltahcmeeo r"ep racttirceaalt"mo efn ts
thessueb jienci tnst rodutcexttoTsro.ya pprefcuilatlthyeet soep itchse,
somfaem iliawriittthhy te e chnioqfau devsa nced
studesnhto ulhda ve
v
Prfaece
vi
calcualnudms atrmiext hodPsa.r ticeumlpahra siisps l actehdr oughout
onc ontribuotfii vnoensst igwahtoosrweso riks normalalvya ilntaoobt l e
alrle aderFso.re xamplteh,ew orko fB ihovsankdiT ihanionfe rror
analyissci osn seirdeidn s omdee tla.i
Theb ooki ncluadne istn roductainodtn h remea in padretvso ted
respecttiotv heeloyre yq,u ipmeanntda, p pltiicoanIsn.t hei ntroductory
chapttehreg eneraaplp roatcoht hes ujbecotf a nalocgo mputatiiso n
outlianenddt, h en otations yamnbdo luissemtd h roughtohuett e xatr e
defined.
ParIt t reatthset heoreftuincdaalm enrteallastt ioav nea lcoogm puta­
tion. aTphpelesyqe u atlolr ye petiatnidov nee -schoomtp uteCrhsa.p ter
2c onsidtehrebs a sipcr inciupnldeesr lypirnogg rammoifnd gie ffrential
equatiwoinsts,hp ecieamlp hasoins t her elatbieotnw ecelno sed-loop
methoadnsd P icarmde'tsh oodfs uccesaspipvreo xtiimoans.
Chapt3es ru rvevyasr iomuest hoodfse rroanra liyss.T hec onceopft
sensitfuinvcittiyod nuse Mtiol ler Muarnrda ays,w elals t o Bihovski,
isc onsidiensr oemded etaainld, tmweot hofdosr e mplyoign anagl o
computeforrst hee xperimednettaelr minoaftt ihoensc eo efficieanrtes
presentTehde.a pproacohfeM sa cneRea,y monda,n dM arsocacnid,
Miurfao rt hee rroarn alyosfil si nesairum latiaornesc ompraeda nd
summraized.
Chapt4e irs d evotteodt hes electoifso uni tasbclaefl aec toarnsda
consideroaftt hieeoff ne cotfd rtia fndz erooff seitno peratiaomnpialfli ers
used in rceopmeptiuttievres .
InP arItIt hem ajocro mponeonftr se petidtieiffrveen tainaall yzaerres
surveyed. 5Ci hsda epvtoetrte odl ineealre meinntcsl udai cnogm pari­
sono ft het hreme ajoaprp roachetso operational amdpelsiifigentr,h e
adaptaotfpi ootne ntitoomh eihtgfr eerqsu eonpceyr aatnitdoh nde,e sign
ofa ddearnsd i ntegratTohrens e.w liyn trodutceecdh nioqfud ey namic
stora(gmee moriysd) e scriabnedad n,u mbeorfc ompleetlee ctrcoonmi­c
putecri rcuairteps r eseed.n t
Chapt6et rr eantosn linceoamrp uteelre menptasr,t icumlualrtliyp liers
andf unctgieonne ratAo rmse.t hoodf" unviersfauln ction generation"
usinvgo ltage compwahriachthao srb se,es nu ccessufsuelidln Ey u rope,
isd escribdeedt aiiTnlh .eu se tohfeH alelff ecfotr m ultipliicsaa ltsioo n
briecfloyn sidered.
Chapt7er d escriobuetsp uetq uipmefonrt thdei sploafry e petitive
solutibyoo nssc illostcwoocp oeosr,nd aitpel ottaenrdsf ,o rth em easure­
menotf s pecipfoiicn( tisn stantvaanleuoeousfst) h es olution.
Chapt8e cro nsidauexrilsir aye qupiment includignegn eratoforrs t he
controoftl h er epetirtaitoeenq, u ipmefonrt thiem positoifio nni tial
conditainodn s,p oswueprp lies.
Preface vii
ParItI Ii sd evotetdoa surveoyf a pplicatoifor nesp etidtiiffveer ential
analyzerCsh.a pte9r b rieflcyo nsidtehress o lutioofo nr dinadriyff erential
equatiwointssh p ecieamlp hasoinsa comparisooftn h er esulotbst ainable
witrhe petiatnidvo en e-shcootm puters.
Chapte1r0c onsidtehrets reatomfpe anrtt idailff erenetqiuaalt iownist h
particuelmaprh asoinst hostee chniqfuoerws h icrhe petiotpievrea tiiosn
particulsauriltya blTeh.e seI nclutdhee D YSTA C techniqiunew hich
timei sd iscretwihzieldte h es pacdee rivatairveem sa intainiendc on­
tinuoufso rm,t heD SDT techniqiunev olvitnhger eplacemoefn atl l
derivatibvye fisn itdei fferenacpep roximatiaonndst ,h eM onte-Carlo
methouds inrga ndome xcitations.
Chapte1r1t reaitnsa similfaars hitohnes olutioofin n tegerqaula tions.
Chapte1r2 i ncludae dsi scussoifot nh eu seo fs tatisttieccahln iqiune s
analocgo mputaticoonn,fo rmatlr ansformatiaonndst ,h ea pplicatoifo n
ultra-rdaipffiedr enatniaally zers.
A portiont hoemf a terprieasle ntetdh itisen x tboaopkp earoerdi ginally
int heb ookC alculaAtneaulrosgR ieqpueetsib yt Rif.sT ,om ovicw,h ich
wasp ublishienFd r encbhy Massone tC iei.n P ariisn 1 958.A lthough
theg enercahla pter stroufct thuarmteo nographha sb eenr etaintehde,
entire htaesbx ete nc ompletreelvyi saendd r ewritteAn c.o nsiderable
amounotf n ewa ndo rigimnaalt erhaisba ele na ddeads w ell.
We takpel easuirnae c knowledgwiintgth h anktsh ea ssistaanncdhe e lp
ofD r.F .H .R aymondH,. M eissingGe.r K,o rna,n dG . R.K aelinA.
portioofnt hes ecretawroirakil n volvienpd r eparitnhgem anuscriwpats
supportbeyd a granotf t heF ordF oundatitoont heU niversity of
CalifornaitaL osA ngelfeosr e ducatiodneavle lopment.
RAJKTOO MOVIC
WALTER J. KARPLUS
Apr1i9l6 2
CONTENTS
I I
Introduction
1.G1e nerRaelm ar1ks ,
12. HistoDreivceall opomfRe enpte tei tAinvaCloomgp ut2e rs,
1.T3h eA nalog Computer3 Approach,
14. Selecotfi otCnho em putVearr ia5b le,
15. Elemeonfta Ds iffereAnntailaylz5 e r,
PART I THEORY
-
2 AnalytiFcoauln dations 13
2.G1e neral R1em3a rks,
FUNDAMENTPARLI NCIPLES
2.L2i neDaireff renEtqiuaalt io1ns4,
2.N3o nlineDaireff renEtqiuaialot n1s9,
PROGRAMMITNEGC HNIQUES
2.T4h eC omputer P2r4og ram,
2.T5h eT ransformat2i8o n
eAt,
2.T6r eatmoefPn rto blienmW sh ich 1,2 9
an i=
3 ErroArn alysoifsA naloCgo mputers 36
3.G1e nerRaelm ar3ks6,
3.R2e latbieotnw eSetna bialnidAt cyc ura3c8y ,
3.S3e nsitiCvoietffiyc ienatnsdt hSee nsitiEvqiutya t4i1o n,
3.E4r rAonra lybsyMi esa nosft hCeo mput4e3r ,
3.E5r roArn alysoifLs i neaSry stem5s3,
viii
Contents ix
4 ScaFlaec tors 59
4.G1e neRreamla r5k9s ,
4.D2e termionfat thTieio mnBe a s6e0,
4.D3i reMcett ho6d3,
4.M4e thoofdA uxiliary 6E5q uations,
4.I5n terreolfSa ctaFilaoecn t o6r8 s,
4.E6ff eocftD riufpto Snc aFlaec tor6i9 ng,
PARTI I- EQUIPMENT
5 LineEalre ments 77
5.1G eneRreamla r7k7s ,
5.2A ddit7i8o n,
Baspirci nci78p les,
Errocrasu sbeynd o ninfaimnpiltigefa ii8en0r,
Errocrasu sbeyldi miteda nbdwi8d1t h,
Errocrasu sbeydd r i8f3t ,
Errors bcyaa mupsleidgfi reicrdu rre8n4t s,
Errors bcyap uarsaesdci atpiacc i8t5a nce,
5.I3n tegr8a5t ion,
Geneprrailn c8i5p les,
Errcoaru sbeynd o ninfignaii8tn9e,
Errors bcyla iumsiebtdae ndd wi8d9t h,
Errocrasu sbeyad m plidfriiaefnrtdg ricdu rre9n0t s,
5.D4y namMiecm or9y2,
5.O5p eratAimopnlailfi 9e5r s,
Generdael sitgenc hni9q5u es,
Practaimcpallir fieearl iz9a9t ions,
5.E6r roirnPs a ssEilveem e1n0t6s ,
6 NonliOnpeearra tions 110
6.G1e neRreamla r1k1s0,
6.C2o ntinuouMsu-lTtyipp1el1 i1e rs,
6.3D iscrete-Type1 1M5u ltipliers,
6.I4n diMruelctti p1l1i9e rs,
6.p5i vis1i2o1n ,
6.D6i reFcutn ctGieonne ra1t2i2o n,
6.F7 unctGieonne rabtyAi popnr oxima1t24i ons,
6.U8n iveNrosnalli Onpeearra t1o37r s,
6.G9e neraotfFo urnsc toifoT nwsoV aria1b4l3e s,
Contents
x
7 OutpuEtq uipment 154
7.G1e neRreamla r1k45s ,
7.O2s cillDoisscpolp1ai5yc5s ,
7.M3e asureomfIe nnstt antVaanleu1oe6u5s s,
7.T4i me-CBaalsieb r1a06t ion,
7.U5s eof L ow-SpOeuetdpD uetv ic10e6 s,
8 AuxiliaDreyv ices 163
81.G eneRreamla r1k36s ,
8.C2h oiocfte h Ree petRiatti1eo36,n
8.I3n iCtoinadli t1i56o ns,
8.R4e ctangVuollatra Igmep ulGseen erat1o96r ,
8.P5o weSru pp1l07y ,
PART III- APPLICATIONS
9 OrdinarDyi fferentEiqaula tions 177
9l. F irst-EOqrutdaieor1n 7,7
9. 2S econd-EOqrutdaieor1n 87,
9.F3o urth-EOqrudaetr1i 97o n,
9.N4o nnleiaErq uati1o8n1s ,
9.S5t abiSltiutdyi 1e48s ,
9.F6o urSieerri1 e68s ,
9.S7p aGrekn erSaitmourl a1t8i7o n,
9.N8o nliMneecahra nSiycsatl1e 98m ,
9.T9w o-PoiBnoutn darVya lue Prob1l9e1ms ,
IO PartiDailff erentEiqaula tions 195
10.Ge1n eRreamla r1k9s5,
10.D2is cret-eC-oSnptaicneuo1u79s -Time,
1.03C ontinucoeu-sD-riSesptcmae-eT1,i 98
1.04D iscrete-Space1-99D iscrete-Time,
1.05T heM otne-CMaertlho o2d05,
11 IntegrEaqlu ations 212
1.11Ge neRreamla r2k1s2,
1.12U soe fT woC omputSipnege2 d1s3,
1.13M ethoodf S uccesAspipvreo ximat2i1o5ns ,
1.14E pleofS olut2i1o6n s,
xam s