dac-adc习题讲解

Analogbuildingblocksforsignalprocessing1Sampling,DAC,[e-mail]@esat.kuleuven.beKULeuvenESAT–MICASAnalogbuildingblocksforsignalprocessing2Exercise1Determine,forthissample&holdcircuit,therelationbetweenthepedestalerrorandthe-3dBfrequencyduringsamplingmode.Neglectclock-feedthrough.Whathappensifthechannellengthoftheswitchingtransistorisdoubled?Analogbuildingblocksforsignalprocessing3Pedestalerror=errorbecauseofchargeinjectionwhenswitchingoftheSamplingsignal(Φ).Maximumsignalfrequency:-3dBfrequency:2()2injholdoxGSTHholdQVCCWLVVC∆=⋅⋅⋅−=⋅3311and2()()22()dBononholdoxGSTHoxGSTHholdholddBGSTHoxfRWRCCVVLWCVVLCCfVVWCLπµµππµ−−==⋅⋅⋅⋅⋅−⋅⋅−=⋅⋅⋅⋅⋅⇒−=⋅⋅SolutionIAnalogbuildingblocksforsignalprocessingWhendoublingthechannellength@samespeed:ΔVx4Whendoublingthechannellength@sameΔV:f-3dB/44dBdBoxholdholdoxfLfLWCCCWLCV32322−−⋅⋅=⋅⋅⋅⋅⋅=∆µπµπSolutionIIAnalogbuildingblocksforsignalprocessingExercise2WhatistheSNRforanideal12-bitunipolarA/DconverterwithVref=3V,whenasinusoidalinputof1Vppisapplied?WhatinputsignalwouldresultinanSNRof0dB?AnalogbuildingblocksforsignalprocessingSolutionIIdealA/Dconverter,12bitunipolarwithVref=3V1.Sinusoidalinput1Vpp→SNR?:mVLSBmVVLSBq21.012732.023112====σdBASNRVAAVAqrmspprmspp47.641021.0354.0log20log10354.0221322=⋅====⇒=−σAnalogbuildingblocksforsignalprocessingSolutionI2.0dBSNR→App?mVAdBApppp6.001021.022log203=⇒=⋅−Analogbuildingblocksforsignalprocessing8Exercise3A3bunipolarD/AconvertorwithVref=8Vhasthefollowingmeasuredoutputvalues:(-0.01;1.03;2.02;2.96;3.95;5.02;6.00;7.08)VDeterminethegainerror,offseterror,INL,DNL,absoluteaccuracyandrelativeaccuracy.Analogbuildingblocksforsignalprocessing9•Method:1.ConvertmeasuredvaluestoLSBvalues2.Determine&compensateoffseterror3.Determine&compensategainerror4.DetermineINL5.DetermineDNL6.Determineabsoluteaccuracy7.DeterminerelativeaccuracySolutionIAnalogbuildingblocksforsignalprocessing10Ideal[LSB]01234567Measured[LSB]-0.011.032.022.963.955.026.007.08Step1[LSB]01.042.032.973.965.036.017.09Step2[LSB]01.0272.0042.9313.9084.9665.9337Step3[LSB]00.0270.004-0.069-0.092-0.034-0.0670Step4[LSB]0.027-0.023-0.073-0.0230.058-0.330.067SolutionIIAnalogbuildingblocksforsignalprocessing11•Offseterror=-0.01LSB(fistlevelcorrect!)•Gainerror=0.09LSBCompensationofgainerror:totalgainerrormustbedistributedevenlyoverallmeasuredvalues:1stoutputvalue=1.04*7/7.09=1.027LSB2ndoutputvalue=2.03*7/7.09=2.004LSBLastoutputvalue=7.09*7/7.09=7LSB(lastlevelcorrect!)•INL=differencebetweengain&offsetcompensatedvalueandidealvalue:INL1=1.027–1=0.027LSBINL2=2.004–2=0.004LSB=maxINL=-0.091LSBSolutionIIIAnalogbuildingblocksforsignalprocessing12•DNL=differenceinstepsizebetweenidealoutputvaluesandgain&offsetcompensatedvaluesDNL01=(1.027–0)–1=0.027LSB=INL1–INL0=0.027–0=0.027LSB=maxDNL=-0.073LSB•Absoluteaccuracy:(withoutgain&offseterrorcompensation)MaximaldeviationbetweenmeasuredvalueandidealvalueΔabs,max=0.08LSB=0.08V=0.08V=Vref/2^(Neff,abs)=Neff,abs=6.6bSolutionIVAnalogbuildingblocksforsignalprocessing13•Relativeaccuracy:(gain&offseterrorscompensated!)=MaximalINLdeviation:INLmax=-0.092LSB=Neff,rel=6.5bSolutionVAnalogbuildingblocksforsignalprocessing14Exercise4Determinetheoutputerror(expressedinLSBs)ofthis4bR-2RD/AconvertorifRA=2.01RB.WhatwilltheoutputerrorbeifRC=2.01R?Analogbuildingblocksforsignalprocessing15Normaloperation:Supposeb1=1,b2..b4=0Onintermediatenodes:impedances:voltages:RRRRRRRRRRRRRRReqeqeqeqeq====+===124342//2)//(22//21221234248refeqrefeqrefrefVVRVVVRRVVVV=−−==+−=−=Req4Req3Req2Req1SolutionIAnalogbuildingblocksforsignalprocessing16Outputvoltagesisdeterminedbycurrenttooutput:b1=1,rest=0=onlycurrentfrombranch1:Ingeneral:10met22outFFrefVVRiiRRVR−=⋅==1011met222NrefjoutFjjNjFrefjjVbVRiiRbRVR−===⋅==∑∑iiSolutionIIAnalogbuildingblocksforsignalprocessing17RA=2.01RBEquivalentresistanceonintermediatenodesdoesnotchange.Voltageonintermediatenodesdoesnotchange!OnlycurrentthroughRAchanges!=Onlyoutputerrorincaseb1=1.Supposeb1=1,b2…b4=0,,,,0.0025()0.0416outoutidealoutrealFFrefrefAidealArealFrefoutoutFrefVVVRRVVRRRVRVVLSBLSBRVR∆=−=−=∆∆==SolutionIIIAnalogbuildingblocksforsignalprocessing18RC=2.01REquivalentresistanceonintermediatenodeschanges!Voltagesonintermediatenodesdonotremainconstant!434214.022//2.014.0116.062//()16.0564.2264.21256.46256.65eqeqeqeqeqRRRRRRRRRRRRR===+===12212332234364.22128.4316.0632.114.028.03refeqrefeqeqeqVVRVVVRRRVVVRRVV=−==−+==+=SolutionIVAnalogbuildingblocksforsignalprocessing19Outputvoltagedeterminedbycurrentthrougheachbranch.-Erroronoutputbecauseofanerrorincurrentb1=0:V1=-Vref-Erroronoutputbecauseofcurrenterrorincurrentb2.met2ioutFiVVRiiR=⋅=−2,2,,2,,2,422()16163.1110FFidealrealoutbidealoutbrealoutFFrefrefRRVVVVRRVLSBRRVVRRLSB−−+−∆===⋅SolutionVAnalogbuildingblocksforsignalprocessing20-Erroronoutputbecauseoferrorincurrentb3=0.001558LSB-Erroronoutputbecauseoferrorincurrentb4=0.00296LSBMaximumoutputerror(combinederrors):0.000311+0.001558+0.00296=0.00482LSB3,3,,3,,3,322()16161.55810FFidealrealoutbidealoutbrealoutFFrefrefRRVVVVRRVLSBRRVVRRLSB