Fault Sensitivity Analysis and Reliability Enhancement of An(5)

Abstract — Reliability of systems used in space, avionic and biomedical applications is highly critical. Such systems consist of an analog front-end to collect data, an Analog-to-Digital Converter (ADC) to convert the collected data to digital form and a

TABLEI

POF

OVERALLARECOMPARISONFORREPRESENTATIVE(1.25V,1.85V,2.35V)VSCOMPLETE(1.05VTO2.55VINSTEPSOF0.1V)INPUTSFOR

THE4-BITFLASHADC

Fig.11.WeightedvsNon-weighted(logscale)approachfortheFIADC(averagedoverallinputs)

Fig.12.WeightedvsNon-weightedapproachfortheSAADC(averagedover

allinputs)

Figures11and12showtheblocksensitivitiesfortheFIandSAADCs,respectively,withthenon-weightedandtheweightedapproach.These guresshowthatthelessaccuratenon-weightedanalysismayleadtoincorrectconclusions.Forexam-ple,SHAinFigure11hasthehighestblocksensitivityaccord-ingtothenon-weightedanalysisbuthasaconsiderablylowersensitivitythanFA1andFA2accordingtotheweightedanal-ysis.Eventhemoreaccuratesensitivitymetricpresentedin(6)treatsallfaultsuniformly.However,somefaultsmayre-sultinlargererrorsattheADCoutputthanotherfaults.Hence,anothermetric,namely,therelativeerrordenotedbyErel,isproposed.Erelisgivenby

Erel= V/Vexp,

V=|Verr Vexp|

(7)

wherepisthenumberofinputvaluesforwhichthesimulationwasperformed,qisthenumberofinjectionlevelsconsideredandristhenumberoftimeinstancesatwhichfaultswerein-jected.Erel,iiscalculatedusing(7)andwiiscalculatedusing(5).TheMaximumRelativeError(MRE)canbeusedasanad-ditionalmetricwhichprovidestheworstcasemagnitudeoftheerror.ThechoiceofametricforsensitivityanalysisisbasedonthedesignobjectivesandnotontheADCarchitecture.Ourearlierworkin[17]hasshownthattheuseoftheAREmetricmaysometimesmasksensitivityimprovements.Therefore,thechoiceofametric(POF,ARE)togaugethesensitivityshouldbebasedonwhetherthecandidateapplicationrequiresareduc-tioninthefrequencyoferrorsorthemagnitudeoferror.Basedontherequirementsofthesystem,anappropriatemetriccanbechosenforthefaultsensitivityanalysis.FollowingarethestepsinvolvedinthefaultsensitivityanalysisofanADC:(i)Calculateweightsofthenodes(wi).

(ii)Performtransientfaultsimulationsonallnodes.

(iii)Basedonthedesignobjectives,useequation(6)or(8)to

calculatethesensitivityoftheconstituentblocks.

Inthiswork,thereductionoffrequencyoferrorsfortheFIandSAADCs,andreductionofrelativesizeoferrorsforthe ashand -ΣADCsweretheassumeddesignobjectives.Therefore,POFhasbeenusedasthesensitivitymeasurefortheFIandSAADCs,andAREhasbeenusedforthe ashand -ΣADCs.C.ADCSensitivityAnalysis

Transientfaultinjectionexperimentswereperformedon4-bittransistorlevelimplementationsofsuccessiveapproxima-tion,foldingandinterpolating, ashand -ΣADCs.There-sultsobtainedfromthesimulationshavebeenusedtogradethefaultsensitivitiesoftheblocksintheADC.Itisessentialtovarytheinputsinthesensitivityanalysisasitcanhaveabearingonselectingcriticalblocksforredesign.However,per-forminganexhaustivesimulationforallpossibleinputsispro-hibitivelyexpensive.Therefore,aschemeofselectingthreerepresentativeinputs,oneeachinthelower,middleandup-perinputrangesandperformingexhaustivesimulationonlyforthoseinputs,wasstudied.Thisstudywasperformedontheanaloganddigitalblocksofa4-bit ashADC.Thesimula-tionswereperformedforeightinjectionlevelsandfourtimeinstancesforeachnode.TheAREandPOFobtainedwiththerepresentativeinputsandwiththecompleterangeofinputs(ataquantizationstepof0.1v)werecompared.TablesIandIIshowthattheAREandPOFforbothcasesarereasonablyclose.Therefore,thesimulationsintheremainingpartsofthisworkwhereVexpistheexpectedcorrectoutputandVerristheerro-neousoutput.

Basedonthede nitionofrelativeerror,auni edmetriccalledtheAverageRelativeError(ARE)whichincludesthemagnitudeoferror,isproposed.IncontrasttothePOFwherealltheerrorsaretreateduniformly,AREgivesmoreweighttoα-particlehitswhichcauselargerrelativeerrorsattheADCoutput.Thesensitivity,characterizedbytheARE,isgivenby

ARE=

n i=1

¯rel,iwiE

(8)

¯rel,iistheaveragerelativeerrorduetoaninjectionatwhereE

nodeiandiscalculatedusing

¯rel,iE

k

1

Erel,i,=

ki=1

k=p·q·r(9)