Fault Sensitivity Analysis and Reliability Enhancement of Analog-to-Digital Converters(4)

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

Fig.8.(a)α-particlehitonthedrainofaPMOStransistor(b)Theα-particlehitmodeledasacurrentsource

0.020.0180.0160.014

1pC2pC3pC4pC5pC

Fig.10.Thesensitiveandinsensitivepartsofanode

0.0120.010.0080.0060.0040.002

00

1

2

3

4

5

6

Time (ns)

Fig.9.Currentpulsegeneratedasaresultofanα-particlestrike

8(a)showsthedrainofaPMOStransistorandtheeffectoftheinjectedcharge.Anα-particlehitgenerateselectron-holepairsalongitstrajectory.Thesechargecarriersdriftunderthein u-enceoftheelectric eldacrossthejunctiongivingrisetoaninjectioncurrent(Iinj)thatcanbemodeledbyequation(1).Vistheinitialvoltageonthenode(drainofthePMOS),dVisthevoltagechangeduetotheα-particlehitandisdependentonIinjandtheloadconnectedtothenode.Figure8(b)showsthecurrentsourceequivalentmodelofthetransientfaultcausedbyanα-particlehit.Figure9showsthecurrentpulsesthataregen-eratedasaresultofanα-particlehitfordifferentvaluesoftheinjectioncharge.Thus,anα-particlehitonacircuitnodecanbesimulatedbyconnectingacurrentsourceinjectingacurrentpulseofIinjatthesaidnode.B.TheoreticalBasis

Traditionally,faultconditionsinsimulationstrategieshavebeenvariedalongthreedimensions:space,timeandinjectionlevel.Itisimportanttoconsidervaryingtheinputstothecircuitaswell,sincethiscanhaveabearingonselectingcriticalblocksforredesign.Thisisduetothefactthatablockidenti edasacriticalblockforoneinputmaynotbeassensitiveforanotherinput.Hence,criticalblocksshouldbeidenti edbasedonthedistributionoftheinputvalues.Thecircuitshouldbeoptimizedforinputvalueswhicharethemostprobable.

Thedesign owofADCscanbebroadlyclassi edintothreesteps:1)Choosingthearchitecturebasedontherequirementsandspeci cations

oftheapplication.2)Schematicentryoftheselectedarchitectureandfunctionalveri cation.3)Finallayoutdesignofthecircuitandare-veri cationwithparasitics.Sincefaultconditionshavetobevariedspatially,thephysicaldesignstep(3)isthemostsuitablepointtocarryoutthefaultsensi-tivityanalysis.However,thecomplexityofthedesigneffort

fori=1,2,···,nwherenisthenumberofcircuitnodesinablock.ThePOFisnowde nedas

n1

Ei(4)POF=

ni=1

neededtocreatethelayoutemphasizestheneedtomovetheanalysistoanearlierstage.Whenmovingthefaultsensitivityanalysisupinthedesigncycleweexpecttoreducethenumberoftimeconsumingdesigniterations,butshouldalsoexpecttopayapenaltyintermsofaccuracyoftheresults.

Faultsensitivityanalysisatthetransistorlevelschematiccanbedonebyselectingnodesinthecircuitandinjectingα-particletransientsatthesenodes.Wede nethefaultsensitivityofablockastheprobabilitythatanα-particlehittingtheblockwillresultinacircuitfailureandwedenoteitbyPOF(ProbabilityofFailure).Foragiveninputvoltage,POFiscalculatedasfollows.Anα-particletransientisinjectedintoeachnodeoftheblockandwedenotetheoutcomeoftheexperimentbyEi:

1iftheinjectionintonodeiresultsin

afailureEi=(3)

0otherwise

Current (A)

Thiscalculationassignsequalweightstoallnodes,whichmaycauseinaccuraciessincetheareasofdifferentnodesmayvaryconsiderably.Ahigheraccuracycanbeachievedbyas-signingtoeachnodeaweightwhichisproportionaltotheareathatitconsumes[16].However,acircuitnodemaymapontotwotypesofareainthelayout:fault-insensitivearea(inter-connect)andfault-sensitivearea(terminalsoftransistorscon-nectedtothenode)(seeFigure10).Itisknownthatanα-particlehithasapotentialofresultinginanerroronlyifithitstheactivearea(fault-sensitivearea)ofatransistor[4].Ahitattheinterconnect(fault-insensitivearea)willnotcauseatran-sientfaultbecauseofthelackofasigni cantelectric eldinthatarea.Wetherefore,assigntonodeiaweight,denotedbywi,givenby

As,i

(5)wi=i=1As,iwhereAs,iistheareaofthefault-sensitiveportionofnodei.ThesizesofthetransistorsintheschematicscanserveasagoodestimateforAs,i.WenowcalculatethePOFas

POF=

n i=1

wiEi(6)

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