Testability Measure

1,,VLSITestingandDFT,,CourseTestabilityMeasureTestabilityMeasureWhatdowemeanwhenwesayacircuitistestable?Definition:Afaultistestableifthereexistsawell-specifiedproceduretoexposeitwithinareasonablecost.Acircuitistestableifeachandeveryfaultinitsspecifiedfaultsetistestable.2,,VLSITestingandDFT,,CourseTestabilityMeasureKeysToTestability1.Controllability2.Observability3.PredictabilityTestability=Controllability+Observability+Predictability3,,VLSITestingandDFT,,CourseTestabilityMeasureDesignforTestabilityToconstrainthedesigntomaketestgenerationanddiagnosiseasier.CircuitSizeDFTUnconstrainedTestCost4,,VLSITestingandDFT,,CourseTestabilityMeasureTestability(Controllability/Observability)Measures1.TMEAS[Stephenson&Grason,FTCS,1976;DAC,1979]2.SCOAP[Goldstein,IEEETCAS-26(9),1979]3.TESTSCREEN[Kovijanic1979]4.CAMELOT[Bennettsetal.,1980]5.VICTOR[Ratiuetal.,ITC,1982]5,,VLSITestingandDFT,,CourseTestabilityMeasureStephenson&Grason,sApproachDevelopedforregister-transfer-level(RTL)circuits,butcanalsobeappliedatthegatelevel.Themeasuresarenormalizedbetween0and1toreflecttheeaseofcontrollingandobservingtheinternalnodes.6,,VLSITestingandDFT,,CourseTestabilityMeasureStephenson&Grason,sApproach1.Foreachsignallines,wedenotethecontrollabilityofsasCY(s)andtheobservabilityofsasOY(s).2.ThevaluesfortheCYsandtheOYsofallthesignallinesarederivedbysolvingasystemofsimultaneousequationswiththeCYsandtheOYsasunknowns.TheexpressionusedtocalculateCYforeachoutputzjiswhereCTFisthecontrollabilitytransferfactorofthecomponent.CYCTFnCYjiinzx11,......DUTZZZx1x2xn12m7,,VLSITestingandDFT,,CourseTestabilityMeasureStephenson&Grason,sApproachLetNj(0)andNj(1)bethenumbersofinputcombinationsforwhichzjhasvalue0and1,respectively.Then0CTF1.Eachoutputcontrollabilityisassignedthesamevalue.CTFmjjnjmNN110121.8,,VLSITestingandDFT,,CourseTestabilityMeasureStephenson&Grason,sApproachTheexpressionusedtocalculateOYforeachinputxiiswhereOTFistheobservabilitytransferfactorofthecomponent.OYOTFmOYijjmxz11,9,,VLSITestingandDFT,,CourseTestabilityMeasureStephenson&Grason,sApproachLetNSibethenumbersofinputcombinationsforwhichthechangeofxiresultsinachangeofoutput.ThenNSialsomeansthenumberofinputcombinationsthatcansensitizeapathfromxitotheoutput.TheOTFmeasurestheprobabilitythatafaultyvalueatanyinputwillpropagatetotheoutputs.0OTF1Eachinputobservabilityisassignedthesamevalue.OTFniniNNS121.10,,VLSITestingandDFT,,CourseTestabilityMeasureStephenson&Grason,sApproach3.Fanouts:Letsbeafanoutstemandkbethenumberofitsbranches.ThentheCYsofeachfanoutbranchisTheobservabilityofthefanoutstemsiswherebiarefanoutbranchesofs.4.Sequentialcomponents:Sequentialcomponentsaremodeledbyaddingfeedbacklinksaroundthecomponentsthatrepresentinternalstates.CYCYsk1log.OYsOYiikb111,11,,VLSITestingandDFT,,CourseTestabilityMeasureGoldstein,sApproach---SCOAPSandiaControllabilityObservabilityAnalysisProgram.Themeasuresreflectthedifficultyofcontrollingandobservingtheinternalnodes;highernumbersindicatemoredifficulttocontrolorobserve.Themeasuresare,inasense,minimumcostvaluesforcontrollingandobserving.12,,VLSITestingandDFT,,CourseTestabilityMeasureGoldstein,sApproach---SCOAPCombinational1-and0-controllabilitiesofY=AND(A,B,C):CC1(Y)=CC1(A)+CC1(B)+CC1(C)+1;CC0(Y)=min{CC0(A),CC0(B),CC0(C)}+1.Theresultisincrementedby1sothatthenumberreflects(inpart)thedistancetothePIs.Workingbreadth-firstfromPIstowardPOs,wecalculatetheCCoftheoutputlineofeachlogiccellasafunctionoftheCCsofitsinputlines.13,,VLSITestingandDFT,,CourseTestabilityMeasureGoldstein,sApproach---SCOAPThesequentialcontrollabilityprovidesanestimateofthenumberoftimeframesneededtoprovidea0or1ataparticularnode.ForY=XOR(A,B):CC0(Y)=min{CC0(A)+CC0(B),CC1(A)+CC1(B)}+1CC1(Y)=min{CC0(A)+CC1(B),CC1(A)+CC0(B)}+1SC0(Y)=min{SC0(A)+SC0(B),SC1(A)+SC1(B)}SC1(Y)=min{SC0(A)+SC1(B),SC1(A)+SC0(B)}Whencomputingthesequentialcontrollabilitiesthroughcombinationalcircuits,thevaluesarenotincremented---noadditionaltimeframesneeded.14,,VLSITestingandDFT,,CourseTestabilityMeasureGoldstein,sApproach---SCOAPWhenderivingequationsforsequentialcircuits,SCsareincrementedby1,butCCsarenotincremented.Positiveedge-triggeredDFFwithactivelowreset:CC0(Q)=min{CC0(R),CC1(R)+CC0(D)+CC0(C)+CC1(C)}CC1(Q)=CC1(R)+CC1(D)+CC0(C)+CC1(C)SC0(Q)=min{SC0(R),SC1(R)+SC0(D)+SC0(C)+SC1(C)}+1SC1(Q)=SC1(R)+SC1(D)+SC0(C)+SC1(C)+115,,VLSITestingandDFT,,CourseTestabilityMeasureGoldstein,sApproach---SCOAPObservabilities:CO(P)=CO(N)+CC1(Q)+CC1(R)+1SO(P)=SO(N)+SC1(Q)+SC1(R)Positiveedge-triggeredDFFwithactivelowreset:CO(R)=CO(Q)+CC1(Q)+CC0(R)SO(R)=SO(Q)+SC1(Q)+SC0(R)+1TowatchR,thenhavetowatchQanddriveFFto,1,andthenresetitto,0,.NPRQ16,,VLSITestingandDFT,,CourseTestabilityMeasureGoldstein,sApproach---SCOAPMaydefinetestabilityasfollows:T(l/o)=CC1(l)+CO(l)T(l/1)=CC0(l)+CO(l)InitialConditionNodePIPOINCC0CC1SC0SC1COSO111111----0088888817,,VLSITestingandDFT,,CourseTestabilityMeasureCAMELOTControllability:CY(output)=CTF(output)xf(CYs(inputs));controllabilitytransferfactorwhereN(0)andN(1)arethenumberso