Delay and Re ection Noi se Macromodel i ng for Si gnal

Integri ty Management of PCBs and MCMs

Slobodan Simovi ch, Student Member, IEEE, Sharad Mehrotra,

Student Member, IEEE, Paul Franzon Member, IEEE,

and Mi chael Steer Senior Member, IEEE.

NCSU Technical Report NCSU-VLSI-93-09

Al so to appear i n Trans. CHMT, Feb 94.

Abstract

The current approaches to generating wiring rules for high speed PCBs andMCMs are

unsatisfactory because they require intensive manual e�orts or use over-simpl i�cations. In

this paper, an automated approach based on a-priori simulation-based characterization of

the interconnect circuit con�gurations is presented. The improved exibi l i ty and accuracy

providedby this approach, when comparedwith traditional approaches, are demonstrated

via anMCMinterconnect example.

I. Introduction

Inhi gh speed desi gn i t i s necessary to constrai n the l engths and geometry of the nets on a Pri nted

Ci rcui t Board (PCB) or Mul ti Chi p Modul e (MCM) to ensure that ti mi ng and si gnal i ntegri ty

requi rements are met. These constrai nts are typi cal l y ref erred to as `wi ri ng rul es' or ` desi gn

rul es' . It i s al so of ten necessary to constrai n dri ver and recei ver ci rcui t choi ces, termi nati on

choi ce, and the number of vi as.

Awel l devel oped, but hi ghl y manual approach, to generati ng and managi ng wi ri ng rul es

i s presented by Davi dson and Katopi s [1], [ 2] and has been extended and used successf ul l y

el sewhere [ 3] . In thei r approach, the si gnal i ntegri ty expert conducts i ntensi ve si mul ati on studi es

of di �erent net con�gurati ons. Fromthese studi es, ` wi ri ng rul es' whi ch guarantee �rst i nci dent

swi tchi ng are establ i shed. (Note that thi s i s a sl i ghtl y di �erent use of the term`wi ri ng rul e'

than the de�ni ti on gi ven i n the �rst paragraph. ) Del ay and noi se equati ons are then establ i shed

wi thi n the bounds of the rul es. Avari ati on of thei r approach, wi th some l i mi ted tool support,

has al so been devel oped by Matsui et. al . [ 4] , [ 5] . However, most compani es do not have the

si gnal i ntegri ty manpower f or conducti ng such i ntensi ve si mul ati on studi es and use a somewhat

di �erent approach.

The usual i ndustry computer-ai ded approach to managi ng ti mi ng and si gnal i ntegri ty requi re-

ments i s i l l ustrated i n Fi gure 1. In thi s approach, a si gnal i ntegri ty expert speci �es an i ni ti al rul e

1

set based on a combi nati on of si mpl e anal yti c expressi ons (e. g. ti me-of - i ght), rul es of thumb

(e. g. keepstub l ength l ess than trv=10, where t r i s the ri se ti me, and v i s the propagati on speed),

and previ ous experi ence, i ncl udi ng si mul ati on studi es. The physi cal desi gn tool s then produce a

pl acement and routi ng whi ch i s veri �ed through si mul ati on. If si gni �cant vi ol ati ons are detected

through si mul ati on, the desi gner' s judgement i s used to adjust the rul es. The l ayout- si mul ate-

adj ust l oop i s i terated unti l there are no vi ol ati ons. There are a number of probl ems wi th thi s

approach:

� Eventhe most compl ete theory-based equati ons f or predi cti ng del ayandnoi se assume l i near

dri vers and recei vers and capaci ti ve l oads onl y. The del ay and noi se predi cti ons made by

these equati ons are i naccurate when comparedwi th si mul ati on resul ts. Thus, i n hi gh speed

systems, i f the desi gn i s conducted accordi ng to these equati ons, the post- l ayout si mul ator

wi l l report many del ay and si gnal i ntegri ty vi ol ati ons. The l ayout- si mul ate-adj ust l oop

must then be i terated many ti mes, i ncreasi ng total desi gn ti me.

� Many of the rul es of thumb are al so very conservati ve. In addi ti on, i n order to save ti me

duri ng rul e devel opment, the si gnal i ntegri ty experts pref er to speci f y very conservati ve

i ni ti al rul es, e. g. the stub l ength rul e above. Such rul es over-constrai n the router, mak-

i ng i ts j ob more di �cul t. The e�ecti ve resul t i s i ncreased average wi re l ength, i ncreased

routi ng over ows (requi ri ng hand routi ng) and, possi bl y, addi ti onal l ayers, and thus hi gher

packagi ng cost.

� Speci f yi ng and adjusti ng the rul es requi res the cl ose attenti on of a si gnal i ntegri ty expert

as wel l as desi gn and l ayout engi neers. Thi s i s i ne�ci ent and many compani es do not have

requi si te manpower. Furthermore, the si gnal i ntegri ty expert i s of ten not cal l ed i n unti l i t

i s f ound that the prototype does not work.

One approach to sol vi ng the l ast probl emabove i s to repl ace the expert wi th an expert system

that j udges the si mul ati on resul ts. Such an expert systemhas been bui l t by Simoudi s [ 6] .

However, an expert systemgi ves onl y general si mpl e advi ce, e. g. ` i f del ay i s too l arge then

shorten etch l ength' . Detai l ed, quanti tati ve advi ce i s needed to do desi gn.

To sol ve these probl ems, we have devel oped a wi ri ng- rul e management approach based on au-

tomati c a priori si mul ati on-based characteri zati on of the el ectri cal properti es over the physi cal

desi gn space. The a priori characteri zati on repl aces the theory-based equati ons of ten used cur-

rentl y. It al so repl aces the del ay and noi se equati ons used i n the approach devel opedbyDavi dson

and Katopi s [ 1] , [ 2] . The purpose of thi s paper i s to descri be thi s characteri zati on procedure,

f roma si gnal i ntegri ty vi ewpoi nt, and to present the methodol ogy and tool set f or automati cal l y

generati ng wi ri ng rul es.

The advantages of the approach presented here are as f ol l ows:

� Simul ati on-based characteri zati ons are more accurate and more compl ete than the theory

based equati ons. Usi ng thi s approach decreases desi gn ti me and decreases the need f or a

si gnal i ntegri ty expert to cl osel y moni tor each desi gn.

� The generated rul es are not as conservati ve as those based on exi sti ng approaches and thus

do not over-constrai n the router. They produce a l arger permi tted physi cal desi gn space

(i . e. wi ri ng rul e extent) consi stent wi th ti mi ng and noi se requi rements.

2

� Al though generati ng the characteri zati on requi res several hundred si mul ati on runs, one

characteri zati on i s appl i ed to al l of the nets that have the same types and number of

dri vers and recei vers. Addi ti onal l y, the resul ts are re-used across mul ti pl e desi gns and

f or mul ti pl e desi gn purposes, i ncl udi ng oorpl anni ng, pl acement and routi ng, wi thi n a

desi gn. Addi ti onal l y, the characteri zati ons can be conducted wel l bef ore physi cal desi gn i s

commenced. Thus the total desi gn ti me i s si gni �cantl y reduced.

Anumber of probl ems had to be sol ved to make thi s approach vi abl e. Fi rst, the generati on of

si mul ati on studi es and the anal ysi s of si mul ati on resul ts was automated. Second, the number of

studi es requi red to generate a su�ci entl y accurate characteri zati on was control l ed so that thi s

process i s compl eted i n reasonabl e ti me. Thi rd, the characteri zati ons were used wi th the ti mi ng

and noi se constrai nts so as to generate wi ri ng rul es f or a router. The sol uti ons i mpl emented are

di scussed i n the next secti on. Two hi gh speed MCMnet desi gn exampl es are used to i l l ustrate

and veri f y the uti l i ty of the methodol ogy i n Secti ons III and IV. In those secti ons we al so de�ne

and use two measures concerned wi th measuri ng the qual i ty of the wi ri ng rul es produced, the

exi bi l i ty coe�ci ent and the saf ety coe�ci ent.

The descri bed methodol ogy and tool set consi derabl y eases the burden on the Si gnal Integri ty

expert (the person responsi bl e f or generati ng wi ri ng rul es) by automati ng the process of charac-

teri zati on and rul e generati on. The expert sti l l must choose appropri ate si mul ati on model s f or

the di �erent ci rcui ts and i nterconnect structures wi thi n the desi gn. The rest of the rul e gener-

ati ng process i s automated, though the expert can moni tor and change i ts progress, i f desi red.

The methodol ogy descri bed here encapsul ates some of the qual i tati ve knowl edge of the si gnal

i ntegri ty expert whi l e provi di ng numeri cal el ectri cal response `macromodel s' that o�er a new,

hi gher l evel of abstracti on. The end resul t i s a methodol ogy that l eads to accurate but exi bl e

wi ri ng rul es and subsequentl y to l ess conservati ve desi gns, wi th f ewer si gnal i ntegri ty vi ol ati ons,

l ower cost and reduced ti me- to-market.

II. Steps in iring ule roduction

Our approach hi nges on establ i shi ng si mpl i �ed model s of vari ous i nterconnect responses, e. g.

del ay and noi se, accuratel y and e�ci entl y. The steps i n the approach are i l l ustrated i n Fi gure 2.

There are three phases, a characteri zati on phase, a macromodel i ng phase and a wi ri ng rul e

generati on phase. The �rst two phases are conducted bef ore detai l ed desi gn of the l ayout takes

pl ace. They can be perf ormed as soon as the ci rcui t and i nterconnect technol ogi es have been

determi ned. Rul e generati on i s perf ormed at the ti me of actual physi cal desi gn, when the ti mi ng

and noi se requi rements f or each net are preci sel y known.

The obj ecti ve of the characteri zati on phase i s to obtai n a response surface that captures the

ci rcui t responses of i nterest (e. g. del ay and re ecti on noi se) of a general i zed i nterconnect ci rcui t

topol ogy, over a range of certai n design variables, such as l ength. Characteri zati on i s perf ormed

f or each uni que ci rcui t topol ogy, e. g. the two- recei ver CMOS dri ver/recei ver ci rcui t topol ogy as

shown i n Fi gure 3. In thi s exampl e, the desi gn vari abl es are the branch l engths l1 and l2, and

the stub l ength l3. Other desi gn vari abl es, suchas vi a count, can al so be speci �ed, i f the desi gner

desi res.

3

Fi gure 4 shows an exampl e of part of a response surf ace f or the ci rcui t topol ogy shown i n

Fi gure 3. (Pl otti ng the response surf ace i s not a step i n our methodol ogy. Part of the [ 4-

di mensi onal ] response surf ace i s shownhere sol el y f or i l l ustrati ve reasons. ) The el ectri cal response

characteri zed i s settl i ng del ay, whi ch i s de�ned as the del ay f romwhen the si gnal at the output of

the dri ver passes through the 50% poi nt unti l the si gnal at the i nput of the recei ver i s su�ci entl y

settl ed f or correct l atchi ng, as shown i n Fi gure 5. It i s a usef ul del ay measure f or l atched data

si gnal nets [ 7] . The del ay i s characteri zed over a design space, speci �ed by the ranges al l owed

on the desi gn vari abl es, i n thi s case 0 < l1 <10 cm, 0 <l2 <10 cm, and 0 <l3 <10 cm. The

desi gner, or another tool , must speci f y reasonabl e mi ni mumandmaximumranges f or the desi gn

vari abl es. Ranges consi stent wi th the board/modul e si ze are usual l y adequate.

Characteri zati on consi sts of repeatedl y assi gni ng val ues to the desi gn vari abl es f romthei r gi ven

ranges, and si mul ati ng the i nterconnect structure wi th these val ues to obtai n the responses. The

choi ce of val ues to be assi gned i s determi ned by computer experi mental desi gn techni ques [ 8] , [ 9] .

Basi cal l y, these techni ques i nvol ve choosi ng a sui tabl e data i nterpol ati ng f uncti on, and several

combi nati ons of val ues assi gned to vari abl es (cal l ed \sampl es"), so that the i nterpol ati ng f uncti on

accuratel y predi cts the response at untri ed poi nts i n the desi gn space.

Sequenti al sampl i ng i s used to achi eve thi s obj ecti ve as i l l ustrated i n Fi gure 6. Ini ti al l y, a

randomsampl e i s drawn over the enti re desi gn space usi ng Lati n Hypercube Sampl i ng [ 10] . To

determi ne the accuracy of the response surf ace, the response val ue at each \sampl ed" poi nt i s

computed usi ng the i nterpol ant, assumi ng that the response at that poi nt i s not known. The

data i nterpol ati on i s perf ormed by Movi ng Least Square Interpol ati on [ 11] . Thi s i nterpol ated

val ue i s then compared agai nst the si mul ati on resul t. If the di �erence i s unacceptabl y l arge, then

newsampl es are taken f romthe vi ci ni ty of the sampl e poi nt i n order to i mprove the accuracy

of the i nterpol ant. The "newsampl i ng space" speci �es thi s vi ci ni ty. Physi cal l y speaki ng, the

second sampl i ng step takes more sampl es i n the vi ci ni ty of the l ess smooth regi ons i n the response

surf ace, f or exampl e, i n the vi ci ni ty of the ` cl i �' vi si bl e i n Fi gure 4. Further detai l s can be f ound

i n [ 12] .

The sampl es are automati cal l y si mul ated and anal yzed wi th a tool cal l ed MetaSim[ 13] , [ 14] .

MetaSimal l ows general i zed ci rcui t structures to be speci �ed as a col l ecti on of parameteri zed

physi cal obj ects so that si mul ati on studi es can be easi l y conducted.

Once a sui tabl e sampl e i s determi ned, i t i s necessary to capture the response surf ace as a set

of �tted equati on(s) so that wi ri ng rul es can be generated. Li near equati on(s) are pref erred so

that the wi ri ng rul e can be obtai ned anal yti cal l y. For exampl e, i f del ay i s expressed as a f uncti on

of the l engths,

t(l) = a0 + a1l1 +a 2l2 +a 3l3; (1)

then the l ength ranges that meet a del ay requi rement of say t(l) � 1:2 ns can easi l y be f ound

al gebrai cal l y. However, i t i s easy to see that a si ngl e l i near equati on does not accuratel y capture

the response showni nFi gure 4. Fromvi sual i nspecti on at l east twoequati ons woul dbe pref erabl e,

one f or the response to the ` l ef t' of the ` cl i �' , and one f or the ` ri ght' . We have devel oped an

approach whereby a pi ecewi se l i near set of equati ons are automati cal l y produced to represent

the response surf ace. Thi s set of equati ons i s ref erred to as a macromodel .

There are two requi rements on thi s macromodel . Fi rst, i t must be su�ci entl y conservati ve so

that a saf e desi gn i s produced. Second, i t must be su�ci entl y accurate so that the �nal desi gn

4

i s not over-constrai ned. One approach that woul d sati sf y the saf ety requi rement woul d be to

generate a l i near macromodel over the enti re desi gn space that l i es ` above' al l of the sampl e poi nts

(assumi ng a ` smal l er i s better" del ayrequi rement i n the desi gn). Vi sual l y, thi s macromodel woul d

be a pl ane that woul d l i e above the response surf ace shown i n Fi gure 4.

The techni ques used to generate a pi ecewi se l i near macromodel i s expl ai ned ful l y i n Ref erences

[ 14] , [ 15] . An i l l ustrati on of the output produced by the macromodel i ng tool i s shown i nFi gure 7.

(Physi cal l y, sucha response shape mi ght be f ound i n a l ossl ess exampl e, suchas a Pri ntedCi rcui t

Board i nterconnecti on. The ` di p' between sub- regi ons 2 and 3 mi ght resul t f roma resonance

that decreases re ecti on noi se f or these l engths. Asi mi l ar, but smal l er, ` di p' can be seen i n

the response surf ace shown i n Fi gure 4 f or l2 =l3. The magni tude of the resonance i s smal l

due to resi sti ve dampi ng. ) In thi s si mpl i �ed exampl e, the macromodel produces two surf aces i n

each regi on, one above al l of the sampl ed poi nts and one bel ow. The macromodel thus produces

conservati ve rul es f or bothmi ni mumandmaximumdel ay desi gn requi rements. The macromodel

i s al so accurate because the di �erent sub- regi ons were sel ected so as to produce smal l maximum

errors i n the �t. Thi s enti re process i s i l l ustrated usi ng two exampl es, one sui tabl e f or a data

net, another f or a cl ock net. In both cases the ci rcui t structure gi ven i n Fi gure 3 i s used.

III. xa ple 1 { ata et

Inthi s secti on, we obtai n a wi ri ng rul e sati sf yi ng a settl i ng del ay requi rement f or the net topol ogy

shown i n Fi gure 3. The noi se budget f or re ecti on noi se was 0. 1 Vand the l ossy l i nes were

untermi nated. The cross- secti on of the copper l i nes was 8 �mwi de by 4 �mthi ck. Aburi ed

mi crostri pcon�gurati on was usedwi th8 �mof pol yi mi de di el ectri c. Ful l ci rcui t model s f or 24 mA

CMOSdri vers and recei vers were used to generate the resul ts. As the parasi ti c capaci tances were

very l ow, the ri se ti me was f ast, about 700 ps. Thus, wi thout termi nati ons, there i s consi derabl e

ri ngi ng noi se i n the 5 cm+l ong i nterconnecti on whose settl i ng del ay response i s i l l ustrated i n

Fi gure 4. However, at a certai n poi nt when the nets get l onger, the l i ne l osses damp the ri ngi ng

si gnal . Thus settl i ng del ay i s l arger f or the shorter l engths shown i n Fi gure 4 than f or the l onger

l engths.

The ` above' hal f of the macromodel was generated f or settl i ng del ay. (The response surf ace was

obtai ned wi th 240 si mul ati ons, perf ormed over two sampl i ng stages. ) El even di sj oi nt sub- regi ons

were f ormed as a resul t of the macromodel i ng process, the equati ons f or two of whi ch are gi ven

i n Tabl e 1. Al so gi ven i n Tabl e 1 i s the equati on f or the one-pi ece macromodel obtai ned i f no

subdi vi si on i s done.

Awi ri ng rul e was generatedby sol vi ng the macromodel equati ons f or the el ectri cal requi rement

that del ay must be l ess than 3. 5 ns. The resul ti ng wi ri ng rul e i s a regi on encl osed by a set of

pl anar surf aces i n the three-di mensi onal desi gn space.

The rul e was tested by compari ng i t wi th si mul ati on resul ts of 2, 000 randoml y generated

desi gns, al l wi th l engths wi thi n the desi gn space speci �ed (0 <l1; l2; l3 <10 cm). AMonte-

Carl o approach was used to ensure that the desi gns were evenl y di stri buted throughout thi s

desi gn space.

The resul ts are l i sted i n Tabl e 2. The exibi l i ty coe cient measures the abi l i ty of the wi ri ng

rul e to capture al l f easi bl e desi gns. A f easi bl e desi gn i s one that meets al l of the el ectri cal

5

requi rements upon si mul ati on. The coe�ci ent i s de�ned as

exi bi l i ty coe�ci ent =Nrule

Nsim

; (2)

where N sim i s the number of randoml y generated desi gns that are f easi bl e, by si mul ati on, and

Nrul e i s the number of desi gns that were al so predi cted to be f easi bl e by the wi ri ng rul e. A

hi gher exi bi l i ty coe�ci ent i s better, 100%bei ng i deal . Al ow exi bi l i ty coe�ci ent means that

the wi ri ng rul e i s muchmore conservati ve than i t needs to be. The l ower the exi bi l i ty coe�ci ent,

the harder i s the task f aced by the autorouter. The net resul t i s ei ther more ti me i s spent hand-

routi ng unroutabl e nets (or modi f yi ng the rul es by hand) or addi ti onal routi ng l ayers have to be

added. Conventi onal wi ri ng rul e generati on approaches have of ten been cri ti ci zed by desi gners

as maki ng thei r j ob too di�cul t by arti �ci al l y over-constrai ni ng the nets.

The safeness coe cient measures the saf ety of the wi ri ng rul e. It i s de�ned as

saf eness coe�ci ent =N 0

rul e�sim

N 0

sim

; (3)

where N 0

sim i s the number of randoml y generated desi gns predi cted to be i nf easi bl e onl y by

si mul ati on. N0

rul e�sim i s the subset of the N0

sim desi gns that are al so predi cted to be i nf easi bl e

by the wi ri ng rul e. At desi gn ti me, a saf eness vi ol ati on i s detected by post- l ayout si mul ati on.

Asaf eness vi ol ati on resul ts i n some post- l ayout manual re- routi ng to �x the si gnal i ntegri ty

vi ol ati on. The rel ati ve i mportance of exi bi l i ty and saf eness depends on the rel ati ve desi gner

ti me needed to re- route a net to overcome a congesti on probl emversus the ti me requi red to

re- route a net to �x a si gnal i ntegri ty vi ol ati on.

I . xa ple { loc et

Inthi s exampl e, we showhowthe tool s devel opa rul e sati sf yi ng a �rst i nci dent swi tchi ng cri teri on,

i . e. undershoot and overshoot are l ess than the noi se budget speci �cati ons (0. 8 Vand 1. 0 V,

respecti vel y) and that there are no i n ecti ons or porches (` pl ateaus' or at peri ods) i n the ri si ng

and f al l i ng edges of the si gnal . Such a hi gh si gnal qual i ty i s essenti al f or cl ock di stri buti on.

The same ci rcui t el ements and topol ogy i s used as the one descri bed i n Secti on II. The resul ts

are compared wi th the set of 2, 000 randomdesi gns and wi th the si mpl i �ed (` standard' ) rul e

generati onapproach. Arul e i s generated f or a net that must meet the above general requi rements

as wel l as the speci �c requi rement that the 50%del ay f romdri ver output to recei ver i nput be

l ess than 1 ns. Arul e i s generated usi ng a 1-pi ece macromodel , as obtai ned bef ore subdi vi si on,

as wel l as a 10-pi ece macromodel .

Awi ri ng rul e was al so generated usi ng the standard approach i n whi ch 50%del ay i s esti mated

vi a the equati on [ 16] ,

t50%�del ay =l

vprop1 + L= 0; (4)

where l i s the mai n l i ne l ength, vprop i s the si gnal propagati on speed, L i s the l oad capaci tance

per uni t l ength and 0 i s the unl oaded l i ne capaci tance per uni t l ength. (Admi ttedl y, Equati on 4

6

assumes l ossl ess l i nes. However, as no comparabl y si mpl e equati on exi sts f or esti mati ng del ay of

l ossy l i nes, we are f orced to use thi s equati on as the ` standard approach' ref erence. ) Overshoot

and undershoot were control l ed by usi ng the rul e of thumb f or stub l ength, l stub , [ 17]

lstub <v proptr=10; (5)

where t r i s the ri se ti me.

The rul es generatedbyeachof these approaches were testedbyagai n compari ng themwi th the

si mul ati on resul ts of 2, 000 randoml y generated desi gns. The resul ts are reported i n Tabl e 3. The

resul ts showthat the approach descri bed i n thi s paper i s much saf er than the standard approach

to generati ng rul es and produces a si gni �cantl y hi gher exi bi l i ty coe�ci ent, parti cul arl y i f the

10-pi ece macromodel i s used. The saf eness coe�ci ent i s i mprovedover that f or the settl i ng del ay

exampl e i n the previ ous secti on because the response surf ace f or 50%del ay i s smoother than

that f or settl i ng del ay and thus easi er to capture through sampl i ng. The exi bi l i ty coe�ci ent i s

worse because of the mul ti pl e el ectri cal constrai nts on the desi gn speci �ed by the �rst i nci dent

swi tchi ng requi rement.

. i scussion

Inthi s secti onwe di scuss the ti me costs associ ated wi th thi s approach, di scuss some desi gn i ssues,

and descri be howstati sti cal vari ati ons are accounted f or.

Most of the ti me costs i nvol ved wi th thi s approach rel ate to perf ormi ng the si mul ati ons and

the �tti ng of the macromodel s, the overhead associ ated wi th speci f yi ng and testi ng the sampl i ng

steps bei ng negl i gi bl e.

In the case studi es we have conducted, the number of si mul ati on sampl es needed to obtai n a

su�ci entl y accurate characteri zati on i s rel ated mai nl y to the nature of the response and l ess to

the compl exi ty of the ci rcui t (e. g. the number of recei vers). If the response surf ace has many

di sconti nui ti es, or i s otherwi se hi ghl y non- regul ar, then a l arge number of sampl es are needed.

For the MCMl ayout exampl e used here, the number of studi es grew approxi matel y l i nearl y

wi th the number of parameters bei ng vari ed. For exampl e, a f our termi nal net was adequatel y

characteri zedwi th l ess than 600 sampl es. For a l ossl ess PCBl i ne characteri zati on, a l i ttl e i nsi ght

can be used to i mprove the regul ari ty of the surf ace. It was f ound that l i mi ti ng the stub l ength

to l ess than hal f the maximumbranch l ength, resul ted i n a much smoother surf ace than i f the

stub was al l owed to be as l ong as the branch. Such si mpl e rul es can be easi l y automated i nto

the approach. (Davi dson and Katopi s [ 1] , [ 2] were the �rst to real i ze that stub l engths must be

l i mi ted to generate good rul es. Our approach di �ers f romthei rs i n that they requi re the stub

l ength be short enough to guarantee �rst i nci dent swi tchi ng. We just requi re the stub l engths

be short enough to keep the response surf aces f rombei ng too ` rough' . )

The ti me cost of the macromodel i ng step i ncreases mai nl y wi th the dimensi onal i ty. Wi th the

current macromodel i ng approach, when there i s l i kel y to be more than 8-10 dimensi ons, steps

need to be taken to reduce the di mensi onal i ty i n order to control run- ti me. For exampl e i n a 10

recei ver net that i s actual l y a bus, the regul ari ty present i n the l ayout coul d be used to reduce

a 20-di mensi onal probl emto a two-di mensi onal probl em. Thi s i s achi eved by treati ng al l of the

stub l engths as the same, and si mi l arl y f or the branch l engths. The macromodel i ng step can take

7

5 mi nutes to many hours f or each net topol ogy on a typi cal workstati on. Faster macromodel i ng

al gori thms are bei ng i nvesti gated. These ti me costs are smal l , however, especi al l y consi deri ng

that the characteri zati on and macromodel i ng steps can be done earl y i n the desi gn and that

these tasks can be easi l y paral l el i zed across a network.

Our resul ts i ndi cate the val ue of usi ng a settl i ng del aymeasure f or l atched (i e. non-cl ock) data

nets and the val ue of the mul ti -pi ece macromodel . Manydesi gners use a �rst i nci dence swi tchi ng

cri teri a f or non-cl ock nets. In compari ng the resul ts i n Tabl es 2 and 3, i t i s cl ear that though �rst

i nci dent swi tchi ng i s a sl i ghtl y saf er measure than settl i ng del ay, i t i s si gni �cantl y l ess exi bl e (i . e.

more conservati ve). In thi s exampl e, i f the desi gner used a �rst i nci dent swi tchi ng cri teri on f or

si gnal nets, the resul t coul d wel l be a hi gher degree of routi ng congesti on, requi ri ng more hand-

routi ng, dependi ng on the number of wi res to be routed. Fi rst i nci dent swi tchi ng i s sl i ghtl y saf er

because the correspondi ng response surf aces are smoother f or �rst- i nci dent del ay, overshoot,

and undershoot, than they are f or settl i ng del ay. The sampl i ng strategy i s more e�ecti ve at

capturi ng smooth response surf aces. In Tabl e 3, the val ue of the mul ti -pi ece macromodel over a

si ngl e equati onmodel i s wel l val i dated. The exi bi l i ty i mproves consi derabl y wi th onl y negl i gi bl e

degradati on of saf ety.

Process vari ati ons canbe easi l y accounted f or by speci f yi ng 3-� or 6-�stati sti cal corner model s

usi ng techni ques establ i shed byChang [ 18] . Characteri zati ons are perf ormed separatel y f or each

model and then the macromodel i s �tted around al l responses together.

I. onclusions

We have establ i shed an automated process i nwhi ch si gnal del ay and re ecti on noi se are managed

wi thout resorti ng to overl y conservati ve and ul ti matel y costl y desi gn practi ces. Central to thi s

process i s the producti on of macromodel s that accuratel y capture the el ectri cal responses of i n-

terconnect ci rcui ts over any requi red range of physi cal desi gn vari abl es (i ncl udi ng wi ri ng l engths,

number of vi as, l ayer assi gnment, number of l oads, dri ver/recei ver ci rcui t types etc). The macro-

model s are obtai ned by �tti ng pi ecewi se- l i near equati ons to a set of si mul ati on resul ts. The

macromodel must be obtai ned f romsimul ati on resul ts because the avai l abl e anal yti cal expres-

si ons f or ci rcui t el ectri cal responses are i naccurate, especi al l y f or dri ver ci rcui ts wi th non- l i near

output i mpedances, f or mul ti - recei ver nets contai ni ng stubs, and f or hi ghl y resi sti ve thi n �l m

i nterconnecti ons. We have al so shown some measurement resul ts that demonstrate the i mproved

saf ety (f ewer si gnal i ntegri ty vi ol ati ons) and exi bi l i ty (greater ease of routi ng) provi ded by our

approach.

Our sol uti on greatl y reduces the burden on the si gnal i ntegri ty and l ayout engi neers. The

automati c producti on of macromodel s rel eases the si gnal i ntegri ty engi neer f romthe need to

manual l y conduct a l arge number of si mul ati on runs. Our sol uti on al so prevents the si gnal

i ntegri ty engi neer f rombei ng f orced to speci f y overl y conservati ve rul es j ust to reduce the e�ort

requi red.

The automati c appl i cati on of the macromodel s to the generati on of a package l ayout f rom

the ti mi ng desi gn rel eases the si gnal i ntegri ty engi neer f romthe need to become i nvol ved i n the

detai l ed l ayout of a l arge number of desi gns. Thi s automati on al so hel ps guarantee �rst pass

success f or hi gh speed di gi tal desi gns.

8

c o le e e s

The authors woul d l i ke to thankZaki Raki b, arrett Si mpson, andC. Kumar of Cadence, eorge

Katopi s and Jay Di epenbrock of IBM, John rebenkemper of Tandem, Steve Li pa and J.C. Lu

of North Carol i na State Uni versi ty and Wayne Dai of the Uni versi ty of Cal i f orni a (Santa Cruz)

f or di scussi ons duri ng our work. The CMOS dri ver model s were provi ded by Wayne Detl o� of

MCNC. The authors woul d al so l i ke to thank the revi ewers f or thei r caref ul readi ng and val uabl e

comments.

e erences

[ 1] E. E. Davi dson. El ectri cal desi gn of a hi gh speed computer package. I . es. ev. ,

26(3): pp. 349{361, May 1982.

[ 2] E. E. Davi dson and .A. Katopi s. Package el ectri cal desi gn. In R.R. Tummal a and E. J.

Rymaszewski , edi tors, i croel ectronics ackaging andbook, chapter 3. VanNostrandRei n-

hol d, 1989.

[ 3] L. Hei d, M. Degerstrom, C. Nel son, E. Pri est, and . Katopi s. Desi gni ng f or si gnal i ntegri ty

i n hi gh speed systems. In roc. 3rd l ectronic omponents and ec nol ogy onference,

pp. 536{537, 1993.

[ 4] T. Mi kazuki and N. Matsui . Stati sti cal desi gn technqi ues f or hi gh- speed ci rcui t boards. In

I ' I ymposium, pp. 185{191, 1990.

[ 5] N. Matsui and T. Mi kazuki . El ectri cal desi gn technqi ues f or hi gh- speed ci rcui t boards. In

I ' I ymposium, pp. 234{243, 1990.

[ 6] E. Si moudi s. Aknowl edge-based systemfor the eval uati on and redesi gn of di gi tal ci rcui t

networks. I rans on , 8(3): pp. 302{315, March 1989.

[ 7] P.D. Franzon. El ectri cal Desi gn. In D. Doane and P. Franzon, edi tors, ul t i c ip odul e

ec nol ogies and l ternati ves: e asics, chapter 11. VanNostrandRei nhol d (New ork),

1993.

[ 8] J. Sacks, S. B. Schi l l er, andW. J. Wel ch. Desi gns f or computer experi ments. ec nometrics,

31: pp. 41{47, 1989.

[ 9] J. Sacks, W. J. Wel ch, T. J. Mi tchel l , and H. P. Wynn. Desi gn and anal ysi s of computer

experi ments. tat i st i cal ci ence, 4(4): pp. 409{435, 1989.

[ 10] M. D. McKay, R. J. Beckman, andW. J. Conover. Acompari son of three methods f or sel ect-

i ng val ues of i nput vari abl es i n the anal ysi s of output f roma computer code. ec nometrics,

21(2): pp. 239{245, May 1979.

[ 11] Peter Lancaster and Kestuti s Sal kauskas. urve and surface tt ing : n introduction.

Academi c Press, 1986.

9

[ 12] S. Mehrotra, S. Si movi ch, P.D. Franzon, andM.B. Steer. Automati c ci rcui t characteri zati on

through computer experi ments. ec nical eport , 1993.

[ 13] P.D. Franzon, S. Si movi ch, M. Steer, M. Basel , S. Mehrotra, and T. Mi l l s. Tool s to ai d i n

wi ri ng rul e generati on f or hi gh speed i nterconnects. In roc. esi gn utomation onference,

pp. 466{471, 1992.

[ 14] S. Si movi ch. et odol ogy for utomated l ectri cal esi gn of i g peed ystems. PhD

thesi s, North Carol i na State Uni versi ty, 1993.

[ 15] P.D. Franzon, S. Si movi ch, S. Mehrotra, andM.B. Steer. Macromodel s f or generati ng si gnal

i ntegri ty and ti mi ng management advi ce f or package desi gn. In roc. I 1 3

onference, pp. 523{529, 1993.

[ 16] W.R. Bl ood Jr. ystem esign andbook. Motorol a Inc. , 1983.

[ 17] J.A. West. pice simul ation design guide. Si gneti cs, Phi l i ps, 1989.

[ 18] F. . Chang. enerati on of 3- si gma ci rcui t model s and thei r appl i cati on to stati sti cal worst-

case anal ysi s of i ntegrated ci rcui t desi gns. In 11t si l omar onference, pp. 29{34, October

1978.

10

oo o es

Manuscri pt recei ved , revi sed . Thi s work was supported by the Nati onal Sci ence

Foundati on under grants MIP-901704 and DDM-9215755 and by Cadence Desi gn Systems.

S. Mehrotra, P. Franzon and M. Steer are wi th the Pi coLab, Di gi tal Pi cosecond Laboratory,

Department of El ectri cal and Computer Engi neeri ng, North Carol i na State Uni versi ty, Ral ei gh,

NC27695-7911.

S. Si movi ch was wi th North Carol i na State Uni versi ty. He i s nowwi th Sun Mi crosystems,

Mountai n Vi ew, CA94043.

IEEELog Number .

11

io r i es

lo o a o c recei vedthe Di pl . Ing. degree i nEl ectri cal Engi neeri ng f romthe Uni versi ty

of Bel grade, Bel grade, Serbi a, ugosl avi a, i n 1987. In May of 1987, he j oi ned the Computer

Systems roup at Mi haj l o Pupi n Insti tute of Bel grade, where he workedas a computer hardware

desi gner i nt he �el d of hi gh-perf ormance computer graphi cs and real - ti me systems. In 1989,

he j oi ned the Department of El ectri cal and Computer Engi neeri ng at North Carol i na State

Uni versi ty. There we worked on l ow-power systems desi gn and CADtool s f or si gnal i ntegri ty,

earni ng the PhDdegree i n 1993. Hi s i nterests i ncl ude VLSI desi gn, CADtool s f or VLSI desi gn,

si gnal i ntegri ty i n hi gh- speed di gi tal systems, and computer archi tecture. Dr. Si movi ch i s now

wi th Sun Mi crosystems.

a a o a (S' 92) recei ved the Bachel or of Technol ogy degree i n El ectri cal Engi neeri ng

f romIndi an Insti tute of Technol ogy, Kanpur, Indi a, i n 1989, and the M. S. Degree i n El ectri cal

Engi neeri ng f romVanderbi l t Uni versi ty, Nashvi l l e, TN, i n 1991. He i s currentl y worki ng towards

the Ph.D. degree i n the Department of El ectri cal and Computer Engi neeri ng at North Carol i na

State Uni versi ty.

Hi s research i nterests i ncl ude CADfor perf ormance dri ven l ayout synthesi s, ti mi ng veri �cati on

and desi gn of hi gh speed CMOS ci rcui ts by wave-pi pel i ni ng.

a l a o recei ved hi s PhDi n El ectri cal Engi neeri ng f romthe Uni versi ty of Adel ai de, Ade-

l ai de, Austral i a i n 1989. Bef ore compl eti ng hi s PhDhe had worked at AT TBel l Laboratori es

i n Holmdel , NJ i n 1986 and 1987 and wi th the Austral i an Def ence Sci ence andTechnol ogyOrga-

ni zati on. In these posi ti ons he worked on probl ems i n waf er scal e i ntegrati on, ICyi el d model i ng,

and VLSI desi gn. In 1989, Paul Franzon j oi ned North Carol i na State Uni versi ty as an Assi stant

Prof essor.

Hi s current research i nterests i ncl ude the desi gn sci ences f or hi gh speed packagi ng and i nter-

connect, parti cul arl y si gnal i ntegri ty management and opti mi zed MCMsystemdesi gn. Other

i nterests i ncl ude l ow-power el ectroni cs and appl i cati ons of MEMS. Hi s teachi ng i nterests f ocus

on mi croel etroni c systembui l di ng i ncl udi ng desi gn f or si gnal i ntegri ty, packagi ng systemopti -

mi zati on, ci rcui t desi gn, and processor desi gn. He has wri tten and edi ted a book on Mul ti chi p

Modul es.

Dr. Franzon i s a member of the IEEEand ISHM. He i s on the steeri ng commi ttees f or the IEEE

MCMConf erence and IEEETopi cal Meeti ng on El ectri cal Perf ormance of El ectroni c Packagi ng.

In 1993, he recei ved a Nati onal Sci ence Foundati on oung Investi gators Award.

c a l recei ved hi s B.E. and Ph.D. i n El ectri cal Engi neeri ng f romthe Uni versi ty of

ueensl and, Bri sbane, Austral i a, i n 1978 and 1983 respecti vel y. Currentl y he i s Associ ate Pro-

f essor of El ectri cal andComputer Engi neeri ng at NorthCarol i na State Uni versi ty, Ral ei gh, North

Carol i na, U. S.A.

Hi s research i nvol ves the si mul ati on, and computer ai ded desi gn of hi gh speed di gi tal sys-

12

tems i ncl udi ng i nterconnect si mul ati on, the behavi oral model devel opment of di gi tal dri vers and

recei vers i ncorporati ng si mul taneous swi tchi ng noi se, the experi mental characteri zati on of mul -

ti chi p modul es and pri nted ci rcui t boards, the computer ai ded anal ysi s and desi gn of nonl i near

mi crowave ci rcui ts and systems, parameter extracti on usi ng si mul ated anneal i ng techni ques, mi -

crowavemeasurements, andthe desi gnof mi l l i meter-wave quasi -opti cal power combi ni ng systems.

He has authored or co-authored more than 80 papers on these topi cs.

Dr. Steer i s a seni or member of the Insti tute of El ectri cal and El ectroni c Engi neers and i s

acti ve i n the Mi crowave Theory and Techni ques (MTT) Soci ety and the Components Hybri ds

andManuf acturi ng Technol ogy (CHMT) Soci ety. In the MTTsoci ety he serves on the techni cal

commi ttees on Fi el d Theory and on Computer Ai dedDesi gn. In the CHMTsoci ety he serves on

the techni cal programcommi ttee on si mul ati on and model i ng of packagi ng f or the El ectroni cs

Components and Technol ogy Conf erence. In 1987 he was named a Presi denti al oung Investi -

gator.

13

Logic Design

Simulate: Timing Verification Signal Integrity

PCB/MCM Physical Design

Specify initial rules using -Rules of Thumb -Theory-based Equations -Experience

Adjust Rules

Fi gure 1: Current Approach to Managi ng Wi ri ng Rul es.

14

Characterization

Macromodeling

Rule Generation

Circuit Models

Net topology

Timing slack for eachnet of this topology

Beforedetaileddesign

}During physicaldesign

Placement andRouting Tools

Fi gure 2: CADProcess Fl ow.

15

0.8uCMOSdriver

CMOS receiver

CMOSreceiver

TAB lead

1l

2l

3l

Fi gure 3: Exampl e of a ci rcui t topol ogy, i n thi s case a two recei ver net. Thi s case study i s the

one used throughout thi s paper.

16

Fi gure 4: Settl i ng del ay versus l engths f or the net cl ass gi ven i n Fi gure 3. Thi s response surf ace

was obtai ned f roma 1331-poi nt f ul l parametri c study. l 1 i s �xed at 5 cm.

17

Noise budget allowedfor reflection noise

td-settle

Driver:

Receiver:

td-50%

Fi gure 5: De�ni ti ons of settl i ng del ay td�settl e and 50%del ay t d�50% .

18

Latin Hypercube Sampling

Sampling Space

Error Evaluation

NewSampling Space

Fi gure 6: Steps i n sequenti al sampl i ng.

19

ResponseSurface ConservativeFit Macromodel

Set

tling

Del

ay (

ns)

1

2

3

length (cm)

Sub-region 1 Sub- region 2

Sub-region 3

Fi gure 7: Si mpl e exampl e of a generated macromodel .

20

Tabl e 1: Equati ons f or ` above' macromodel f or the enti re i ni ti al regi on and two of the sub- regi ons.

Regi on Equati on: t settl e (ns) = Domai n (cm)

One pi ece 0:693 +0:412l 1 +0:242l 2 +0:188l 3 0 �l 1; l2; l3 �10

subreg 1 0:824 +0:407l 1 +0:332l 2 +0:093l 3 0 �l 1; l2; l3 �10

3:19� 0:141l 1 +0:545l 2 �l 3 �0

2:00+1:13l 1 �0:511l 2 �l 3 �0

3:49�0:158l 1 +0:791l 2 �l 3 �0

�0:903�0:668l 1 +1:99l 2 �l 3 �0

subreg 2 2:67 +0:586l 1 �0:188l 2 +0:195l 3 0 �l 1; l2; l3 �10

3:19�0:141l 1 +0:545l 2 �l 3 �0

2:00+1:13l 1 �0:511l 2 �l 3 �0

3:49�0:158l 1 +0:791l 2 �l 3 �0

�0:903�0:668l 1 +1:99l 2 �l 3 0

21

Tabl e 2: Fl exi bi l i ty and saf eness coe�ci ents f or the rul e produced by the 11-pi ece macromodel

f or settl i ng del ay.

Approach Fl exi bi l i ty Coe�ci ent Saf eness Coe�ci ent

11-pi ece Macromodel 53% 91. 2%

22

Tabl e 3: Compari son of the Standard approachwi th a 1-pi ece macromodel and a 10-pi ece macro-

model .

Approach Fl exi bi l i ty Coe�ci ent Saf eness Coe�ci ent

Standard 12. 9% 90%

1-pi ece Macromodel 14. 6% 99. 7%

10-pi ece Macromodel 39% 99. 1%

23