BSTJ 50: 4. April 1971: Statistical Circuit Design: Linear Circuits and Statistical Design. (Semmelman, C.L.; Walsh, E.D.; Daryanani, G.T.)

9.9 MB·English

Statistical Circuit Desig

Linear Ci

its and Statistical De:

en

By G, L, SEMMETMAN, F. D. WALSIT and ©. T. DARYANANL §
(aoniteecved Noranter 1, M0)

‘The design of tear ciruits requires the designer to coil ele=
mens tolerances, detributions avi cnrmlations and how hey interact
Aeith proposed manufacturing tat Sus and aertce conions such
ts fempernture od aging. Analyeat meth can he used ix a tiwsted
Iramber of eves; silaion mets sing tore modern computers
hermit study of more compler dieign problema. The principal themes
Of this paper ave the desienr's node for compmcsionad wirctace and
he woaye in hich computer jnegrams may be arpenised to meet
those neede. Peo computer programe for this purznse re dered
‘One tea general puspnen anatyna program for forge cctwcrka having
facp topoiony ‘Phe other ss o mone speraiced prograns suitable for
“put” etwovie hick rvay be and ax Buisinp Bike £0 form 0
vaio of flor ad ucla nenorks.

In tho Bel Syste, the origin o* inven i the sttitien) Cusgn of
linear eis Toe in BSstry. er? have boon no Inver han the
farliet ping for repeaters wat flrs for earier systems, 28 n0
fnnch ayetem is poseble withone presen eextre of funnel Ios
Charecteristics, 4s he tral ist eso a casiereysten ie alas
Iinieh greater thas Ube vost @t the design eum, use of the most ad-
“tance design procedures tl technics nowa, including staisttal
tuethods, has always brn justified

"The election of tlevanes fr component parte ie one of the many
lopige which is under the contvel of the doigner. He mure sleet
eles wn specify taanactoring Ws sw ax not to inezease costs
Ciaher by paving wert for uanewemarily wesie clamonts or by
ejecting vovzctly sbeomnbleq networks in presntios Inthe pet, the
tole that. ave ven availabe we the designer to asst a te detersi=
ht of tolerance limits have ranged from prmiive so highs eopie-
1130 nw aa seeimas mmcacicna socamaa, APR 207

Wiest? and matherottion. Ia the presnt rx, which ie dominate!
by electronic compiters, siletion methods may prove tho meet
valuuble af all. The purpose of this paper is eo review some of the
busie mrchods of esiewating and combining deviation characeeritics,
pointing out th power and Tiations a Wiese mathode, end to
Aeacrbe additional eapabiies clsainabe from tna general arp
computer programa. These eval he dexiyaer to determine the vest
in prostuotion wl in verses, uf sperifying given at of tolerances,
Aistributione, comlations, tuning end tasting proce and eervie
feoniitions. All the material x oom to linear networks, shel a
ites, equalizer a retbark supers, which are desig and
built to frequency domain speciestions

1 Analyial Betas

Engincers engaged in designing electrical networks and selesting
tolerances for their components Rave traditionsy used the classes!
fesign technique whieh consists of aking a fet approximation,
amputing er rzssuring i performance snd veSsiog he approcmne=
tion. That thie peosedune workee well aad ccrxerged rapidly when
poled to setvors design ean be aeen from the following. ‘The mage
inerameter design poges for fers and eomparahle metheds for other
Tetworks eve the engincer az understanding af the senitvity of he
‘rious components, i, which emma hee Sa grate effect in
hae patt of the frecueray sporty, Te led intaiively to ah the
Syecfention of the teste that would ie afer to assure ascurate
Franviasture and vo che Xnowlege of which few enmpnnente need
fateful ceruing at any frequenay, i onder to erleet appropriate
tolerances, A few eneultions oe leberatory measurement fllowed by
torn experimental arithmetic wookt then prodiee the nenessary
{olersnee nits, Ae the element tolerances ing wed were ema, the
resting network devistions were prnporeinnal anc auld be eombined
By sinple adiion, Adiing lhe absolute walle af the min p=
snieible deviations would produee wors-este behavier endif system
perforin lnits wete ant che job wes dane:

‘Mathainaticians eam to the seretace of the design engineered
devicad clever Inbor-raving methode of decenmining the deviation
fHlecte and of combining ther incarly. For cxarple, the rata of chenge
ff the diving point impedance of a teeroeal nesnork with eespect to
1 branch impedsnes i ven by

a0)
Lissa emer 11

sin! the vale of change ofa tesaater impede is

#- 00)
eg ie pn ll os nex qn a an aed

{a Tig. 1* One of tno lions fr athe brane cecal Uhen peat
foch inlvival driving point er rameter Fapedanee deviolivy he
Falosited ene saved to repaeeect thy »seimwe clement tolerance,
Ae slate aluve, Hse sere) evitions ray’ be oiled “0 evaluate
the buovior of « nriark wih any one et of element ales.

ore wish, hnsevnr, aw be abeka hy doug & pagan ia
lve eomples plane witin which the iapedunre rit Ti Taia may be
ove in tne lowing, ramen: Solet a plas oF mings 2ga Tor the
Cepavin wach seman frome te tmnt, erie eo mle che
feel eonypnent uf s2ch sealed deviation positive, Alling 2 sealed
fevdations wis Cae» em wl giv she rgxtmaet pach of dhe poke ace
uocemive suimese azo obtained yy evening the slgas of the seulel
evn tion, we at time, su ob ooguoen 6! He inevessing wages,
Whoa el ses hve hoon reversod, the Hebert piah iv abtalnod
tind n nce! revacel in fis cavae seyuente gezeraea the other bull
Iv The oonver aolygos an rele te Res pi.

SHI mere oy Ie Terre bye superimposing 4 “swily of elipace
caea of which sntans 2 apace: pervert ut lve inivrae 0° neuweds
felch woule. de anfacnted ite lewurin basing the see0med
folrrances, ‘Tis wor be viowr if ths dictizccion of ears element
tule ie gavesiar ard ile standard deviation bs keane

‘Fgome 2 illueeuts huth Hs inpedasee Gelygon and line: far

Bl Nye

15g Raden Wear ait cr he deed seeks ot
irae, Lnladiag fe taf mstock sce iaaiting fas expe
Estepona’
1152 tae meas se ncaeeNL vou, SemOL IL

‘imple filer whetethe stendand deviation i taken ae 40 percent of she
folerenco lina samme forthe pyar

1.8 Liniatons to Pose Atehads

‘The Bre imitations acc the foot tht lange valerate: do eu pert
toa wsteepolution ta ape deviation stapes wad ‘hal Use dy nol
farthing nese. Other diets arisy ‘when enphinested desig,
enti sinh ae Ger eye oon aig aciquae®
16 eed. The designer éevelaps na ed” For bis Beige and the net-
spor patorniine bests mrs mesic ba evey elesent Eurthes,
the elle way nal ave gsosian itebtiame, For exainple, 10
parcect componente mey uve a biogdal stitution eeu wt
Eveappliar’® socting the crocuct aoe relling the 5 percent eleeats
Fleewhoee. It riay bo Smipessibe to cletrmine ‘whecber aigh ar low
‘yehus of 2h slemencsehonld be wed to evaluate wurst-viae hiaoio
heceuin a Tange tanger one eer’ vaine may reveree the sigz of
te easing for amor eae, Finally, te woh eae may Br 9
hed that system pecformance requiremenia are nat mot and figstar
tnlevanon, faalory djartnent, avlestive atamly, or veduced veld
Te be rene Ary’ of these inescares tho cost né manutoctie,
fomplisses tha catigne’ tank, and seine: more fererfl methods
‘i tevaining the tenons, eustnvnes ant teste for peodtion,

rows he aso asian, ii appatont tha oy in rave ces wil
the aelceion o° tolerates bo a sttaghcioreard procter where linear
healtion and stele aiion at desietion shapes wi sufi,
Frequrads, the matlrmaticl nl pnginesving complexities yt he
‘fsguer’s lak hegond the limite: analyte method availabe vada,

‘Mente Carla®corcputertohniquee pevntsmslatng che eatntical
behavior of random varisbie and imitating the tuning and teving
fotion perforined in tke faetory. Sueh oomputer programe con tale
the pase of phe prfustin rin, and Farieh comparable ifoema-
tien in #thuca shoots time end a faetion of the ont

Tx thice methode the computer is propramed to senerwe 9 <9-
‘quenoe o2 winehers which appear ta a casual gbservero be rendom,
hough theiedietibution sind periodicities sv known and carole
foxtrolie!. By matzemstieal icursformation, thae rombers aro
Iwoditnd to reprernt poesible veluer ar each nctwork clement and
te digplay tae appnaptiava rominal value, tolerance, distsbution shape
ft somndasion ith other elewente. Further eqylanason af the
aenn crm 1188

A = Fea jeostl
sa ceteriean

ig. 2 Sing ies citing sem mp poo a lib

‘vethode wil be found in Agpentic A. Many retwarcs ewurcnl of
fuck sinalte vervents are eomputed aad the reste sored wit,
Proposed cxes its, A vauy ui tbe compiter ontput il able the
ths gor ‘leis le sukabicy of the aon! velies, terances
sud test,

"The roinies of hit savelo ceeorhes two consater programs,
rwesran and meta, Wish perforna (hie situa io The prema exe
Jered to llfeent neds, hue within e+ oww ston eF epplcution
‘uci i general parpoee poograts

‘wean is peogeam for enulatizg sed swaying vetworks such
x Eller, equaleens, fed-bark arplidizs, ele, huving saan elements
fnd arbiruey topology. counts insertion Tees ane rlaen Tomes
{Et both ene of the newark Wit The cesgner ean obtain informne
sion on tect vel, the sulci between tects im his rsp, lemme
fersitivies, and selnted eater plate and istgragse, This informe
ion laud ep hin alread une nore inemeationehine sone
emen€ values, soleranes, distributions and teete wien ate nol
icons ur the nevurk polos

Teas, am the other Baal to cal ony with networks af Sxed
topology, whose trumeferfuetin i eetrozed ta a biquadtatieSanetion
ff Treaeney deine in qoaton (1)]. By snty'ng he element vives
‘used and eonneating a zumaber of sich sesioun in inden low nae
Iighpaey, bndjcs fitters anal various tynce 0! equulizers en be com
rerutted, nae falitetes speci euaelaion song vlemt as,
‘attory tuning rictsue, service eadcone suck as hish a ow tem
enlace enpcare nd seine perforinanes eet ssh ae gin, pee
find dil. Thelw service manson ate on'ttad, ae test botome fe
tery produnson tess; if elle, enleo- Ile atom performence
cocks

anevate is eepable of yeforming Valence gaalyais rompatations an
feast miority ofthe razsiisioa networis ia poudueon today, The
Ihe ay snl Tob Lnped stent, having speried nami
na? vanes, tolreness azilcieibations, aac) wd eubaesucksy ee
svile? hy adie ‘vis ghivh ave abeaized exter by eae
tion or saeusicment, masa Sule perasbec ixeile by evicing
tack Luuped ener hy av naw ervouns his the apesied enter
fave and having 4 uritonu, proinn or ari'-a-y listshution shape,
TH eorolation of eevicione or tuning 2 rosin, eprciasulmualiaes
may be inerted, Ue persrbed eres Us aren oon led nie
(Gon teas and input and onepit retar Loses ane ecrsputed sb euch
Serif fen ene. Shera ntcnoires ty be peared eames
ther quamftios Tor can peraohed meceore the complet cat af ele-
tents nid all swans of rs portinnance ae Sande ou die
file for lcer row hy x pectpreemnnr ‘The same yeoman
values are compared to the ezeut requinacene, to determine if the
tetrone putes or file, ene to enllate vo production yieuts, The
‘lata on disk ane chen reviewed tn clloet other standane. outs and
Ue Tiki, sealer pha and hetagrame vegnestd Ly oho design
‘ne onfpt ll deere ren fall ow The ast ftp
viteble ss nss.ar sluukl be of gceal soitaner vo e designee ho
bas litle sneigh> nto the ensitisiies of she elezente, the icerveion
‘oF Ge devia onan Ue sealinabip of both tthe Ue. nie
psn ermones 11656,

Speeifeation ofthe Network

‘A earixy ef types o informeticn eu be used lo spay oe retin
lobe analyze Teean eoutein vreidnr, industoe,eapecitore and ea
ined eurrentseurecs, Aen a qualee faecen, oF (tay bo spol’
for the iesortare and expariern, Posallel sad ava resonant cious
iniy be specified by supplying ons or af tbe relive eompenents an
the resovuntfrequeney All ‘he nae itans eye assgoed tolerance
Jute ad. distsbution shapes gx aguas. Uniform and gaussian
shapes ate basin, other speial shapes may be ro iu ol exeeution
fine, I eorrlations or factory (unig operations must be sivulated,
serial subroutines eam be writen fr (hiv purpose

‘imran an allow fied shoetsonks robe nese inthe overall ne
sor, These subnelwarks are sere fy saying thie definite a
Imiane matrices. The warsix deca ane genesaly obtained ‘om an
figs of the salto oy geneesTpmrpoee Tear network sale
seis program bul nny alee eave fro rearseenents

“The auboctyork featats lows nerman te perform ¢tolerasee sal
ysis onthe sities! companents of « hig elven in eunble angunt

htt, Consider, for exazap., the widrbens empier shave in He.
Tie eomalese emalier vine 8D mules soe! IIT comperente. By
blarkng she einait rt toe fot-port snl work as sewn, the we

svork to conn! is vedo to 24 aes and 28 elements, Tae 26
tlestents are Ihe eritiecl vrnperents the fecbae pathe end in

ensivior postions Pre Zerward parh, The soplete citeut eantaine
o Panera TEP

CT
116 rm rms, sme PecaUGAL, JOMAVER, APRIL

onmars, cronparl (runToriers, and high-fraquerey
‘arsstors, Acwrate huspa sertent aaeéels for Uiese desions, per
ealusly the (rsfunse, ale st axa Hemever, hey can be eel
incorporated inco a uuyeae analysis by supply their measured Y=
nur dts (os, on ely, waaauned dats redwood nd traraforsed
ta give Vematn dato

sez mmurar Out

‘A Monte Carlo anulysis enn proce such vest quantiles of data
that the designer, enntronted wieh the complete roults, might have
tafioaltyidenying and exireting signoaat fact. Te isthe Lask of
f postprocesor program to reud the disk Mer and organize thee dua,
ino bret vomperhenaile forme

“The postproeesnr has two general classes of output, defaatt output
which always produced and eptonal output which i pmdueed only
fs specifiod The defval omiput tana general nature al not oF great
feta or length. The requested output eas be se voluminous as the
engineer desire,

22 Default Output

"The default cups rmsists of four sections. Te Pee ertion giver
a summary of the te slate, Ta ierndee the peroest lel, aver-
{ge value, elencard desiavnn, rasi value and minis wale for
fh tat ace gives tae overall vor eld, combining all ws,

"The sevord section of default output nw wenco-rortelation among
peice of lesle, The peeuda-oomrelerion s fenod cx the Heuston ofthe
Delworks Tor which the paseo ross of te (wo teats sgreed. For
fxemple, suprove fen nets were produced, the rs neven passed
fest I, the fet nie ped lest 2, and tho remainder failed in box
vee, The psenlo-avelatinn would then Be O8 ay networks 1 hough
Fand 10 gave identical russeail reals onthe two tests, This output
can be uenfl in oucng the numberof eee performed withontsneri-
fleing reliability of perfor. Temey also be ueefl in determining
‘an aptimal sequence ia whieh lo perform the tats

"The third srsion of eetoult output blues cack poromete’s nome,
rominal vali, average valve sd sbyidard deviation. ‘This informa:
tion is seul ow hee om he natdom dstribalins nnd on the ale
fquecy of the senple sine, For exaryple, the nomial value and the
sSvirage valuo should fe the eume for all the parameters with a ey
‘netsesl density Seton

"The fina section af default oulput gives Une correlation zaman, est
hinssw ercerss ust

values ans parameter An approximation to the senakvity uf exch
‘ust value to ecch parameter ie also print

‘rom chap soptelations ane sensitivity esimates, the ensinece is
iver insight ive aw individual eiremt comspencats eect his eireui's
fvevall perarmanee, ‘Mone isportant, uy give Kin Avetion to
fovlow ia excenirg these shaves thak may requice Cger Iulrsnces
snl those whieh may hevs broader lulecanees

28 Optional Ouiyut

‘The optional outynis as there seein: tabular onfp eater plate
sd hietogrums, Tabular oulput ie merely listing of the random ele
ther’ values ox tnt valor for eae chem, Civile which fed
ets ave fuse for easy ieatfieation, Lest res aa lesen vues
tay be antranied tha the aul of «cost rny be Tiss in a ale
tum glieent to the values of a eemers to whieh the tees 36 very
sensitive

‘There azo thece ee seater ples avaiable: test ys Westy ee
sent va. tet, abl element, clement. Figure 4 shows a sealier plot

ig. eae pla of elon ln va heat ae
1138 rap amu. svetmr mBExBENE SormMAL, ava Ter

of a tee eagle vo, sm een salu, ‘The various ssmbuls pried on
{Calter jot ingiate te muzber uf points thu fll inco a particular
{eetaauln el, the are points the blacker the eybal.

The ecutter pole give en enginer more insight int how quantities
in bie ievait incorat, Thes peeve ir» with a type of petorial ine
ovtsetion that is no avidide from cornealion coficents or sei-
{vi muni, In Hig. 4 for example, tke xorinal value of the ee
rent cern inthe center of the plot and st this pola: the sope othe
feet curve fs near sero, Henos the pal dervetive of the tat eeu,
sth respect tothe elment value and th coerliion eefient wohl
Be-anall Mowever, he vet molt gest infec! by the element
value

Sater can praiuos Viagrans of an’ mamber of coment values and
leat valocs.tistogveme nf elemen: vale can be use usw eherk on the
Fanviom number eietributins ane fhe éerally function routine in
Iaurae. Hiengrems of the eel values give the approximate shape of
the probability denity forthe tt

8 Summary of weweae Chadian

‘buvtar provides 4 user with enysicerable feiblity in severe re-
pect, ‘he unksaredeeeeption ngoage pennits any eonguraton,
‘The momiere of disibacon types, breteies, ule ara scbne:warks
ave eecenaaly walled ae same storage methods are tle a
Feeult te sige unl number of networks corpus will probably be
Festrietd by computer uring, ttn, cost umd nurerioal precision,
Father than by erty dimonsione, Experience hes infeed that when
1 very Inge nebwenk ie eieouneved, the most sensitive elements can
bo scien iy prelsinary eonrpoler roca an pextions of the eabine
stueture, One or more audition, rune ean tex be mde wth only
‘hace elements varying 0 obtsiz nal dat,

‘ain lo insertion loss and return lee ealeatons, whieh are
provided by the program, users way wrice subroutines to cyte
ther maeeures af network porformanee. Subroutines or siulaing
tuning adjustment, sor insoveing eovrlaton effects, and for com
puting other measures of the ntwerk peTormanee may also be waicen,
‘Tho slanlan! and aptiona outputs ate designed vo cavers bros rage
of fypae af ata anc metaace uf presomacion. hia Warley shoud e
Inlpil in iseavering ussospectd Ssvreelationsl:pe avon ees ant
betmeen tests and prance valnes, For fais voasoa, itis probably
Aesirable to investiante ensiderahly tore test taan will ewally be
‘sed in production