Download Pdf The PPT/PDF document "ApplicationReport" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
ApplicationReport SBOA133 ±October2011 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SourabhGuptaandVinodPaliakara........................................................................High-SpeedProducts ABSTRACT InTI ¶slineofhigh-speedanalog-to-digitalconverters(ADCs)withSNRBoosttechnology,outputamplitude tendstodeviatefromitsexpectedvaluewhentheappliedinputamplitudeissmall.Thisapplicationnote explainsthisphenomenonandthereasonsitoccurs. Contents 1Introduction..................................................................................................................2 2Single-ToneInputSignal...................................................................................................4 3Multi-ToneInputSignal.....................................................................................................8 4Example:WhenThermalNoiseDominatestheQuantizationError................................................10 5Conclusion..................................................................................................................11 ListofFigures 1TimeDomainGraphforVIN= ±1dBFS..................................................................................2 2SpectrumGraphforVIN= ±1dBFS.......................................................................................2 3TimeDomainGraphforSmallInputAmplitude,VIN= ±61dBFS.....................................................3 4SpectrumGraphforSmallInputAmplitude,VIN= ±61dBFS.........................................................3 5InputAmplitudeSweptfrom0dBFSto ±80dBFS.....................................................................3 6InputAmplitudeSweptfrom50dBFSto ±80dBFS(Enlarged)......................................................3 7ADCModel...................................................................................................................4 8AnalogInputVINandADCOutputVOUTfor ±1-dBFSInputAmplitude...............................................4 9QuantizationErrorfor ±1-dBFSInputAmplitude.......................................................................4 10SpectrumGraph:ADCOutputfor ±1-dBFSInputAmplitude.........................................................5 11SpectrumGraph:QuantizationErrorfor ±1-dBFSInputAmplitude..................................................5 12AnalogInputandQuantizedOutputfor ±61-dBFSInputAmplitude.................................................6 13QuantizationErrorfor ±61-dBFSInputAmplitude......................................................................6 14SpectrumGraph:ADCOutputfor ±61-dBFSInputAmplitude........................................................6 15SpectrumGraph:QuantizationErrorfor ±61-dBFSInputAmplitude.................................................6 16AmplitudePlotofQuantizationError.....................................................................................7 17PhasePlotofQuantizationError..........................................................................................7 18ADCOutputSpectrumfor16-ToneInputSignalwith ±61dBFSTotalPower......................................8 19QuantizationErrorSpectrumfor16-ToneInputSignalwith ±61dBFSTotalPower..............................9 20OutputAmplitudeforSingle-ToneandMulti-ToneInputSignals.....................................................9 21TimeDomainWaveform:AnalogInputandQuantizedOutputfor ±61-dBFSInputAmplitude.................10 22TimeDomainWaveform:QuantizationErrorfor ±61-dBFSInputAmplitude......................................10 23SpectrumGraph:ADCOutputfor ±61-dBFSInputAmplitude......................................................10 24SpectrumGraph:QuantizationErrorfor ±61-dBFSInputAmplitude...............................................10 MATLABisaregisteredtrademarkofTheMathWorks,Inc.. Allothertrademarksarethepropertyoftheirrespectiveowners. 1 SBOA133 ±October2011 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SubmitDocumentationFeedback Copyright 2011,TexasInstrumentsIncorporated Introductionwww.ti.com 1Introduction Traditionally,signal-to-noiseratio(SNR)inanADCislimitedbyitsthermalnoise.TheN-bitquantization errorinanADCiskeptmuchlowercomparedtothethermalnoise,sothatoverallSNRisnotlimitedby quantizationerror. However,inthecaseofADCswithSNRBoosttechnology(suchastheADS62C15,ADS62C17, ADS58C28,ADS58C48,andADS58C20),thethermalnoisecomponentiskeptmuchbetterthantheN-bit quantizationerror.Forexample,intheADS62C17,thethermalnoisecomponentofSNRisapproximately ±76dBFS,whileitsquantizationerrorcomponentisapproximately ±67.8dBFS. Thisnoisepartitioningresultsinonesideeffect:itisobservedthatatlowerinputsignalamplitudes,the actualoutputamplitudeincludesalargedegreeoferror(typically10%).Refertothetwocasesshownby Figure1throughFigure4. InFigure1andFigure2,theinputsignalamplitudeis1.78VPP(or ±1dBFS),andtheoutputamplitude (reportedbytheFFToftheADCoutput)isalsoquiteclose( ±1.03dBFS). Figure1.TimeDomainGraphforVIN= ±1dBFS Figure2.SpectrumGraphforVIN= ±1dBFS Inthiscase,VOUT,outputamplitudeis ±1dBFSandpredictsinputaccurately. 2 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SBOA133 ±October2011 SubmitDocumentationFeedback Copyright 2011,TexasInstrumentsIncorporated www.ti.comIntroduction InFigure3andFigure4,theinputsignalamplitudeisreducedbyafactor1000to1.78mVPP(or ±61dBFS).Now,theoutputamplitudefromtheFFTreports ±59.8dBFS,oranerrorof1.2dB(closeto 10%error). Figure3.TimeDomainGraphforSmallInput Figure4.SpectrumGraphforSmallInputAmplitude, Amplitude,VIN= ±61dBFS VIN= ±61dBFS Here,VOUT,outputamplitudeis ±59.8dBFSandoverestimatestheinputby1.2dB. Tounderstandthiseffectbetter,letussweeptheinputamplitudefromfull-scaledowntoverysmall amplitudesandnotetheoutputamplituderesult(reportedbytheFFT).Figure5andFigure6showthe summaryofthisexperimentforan11-bitADC. Figure5.InputAmplitudeSweptfrom0dBFSto Figure6.InputAmplitudeSweptfrom50dBFSto ±80dBFS ±80dBFS(Enlarged) Wecanclearlyseethatatamplitudeslessthanapproximately ±50dBFS,theerrorbecomessignificant. 3 SBOA133 ±October2011 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SubmitDocumentationFeedback Copyright 2011,TexasInstrumentsIncorporated Single-ToneInputSignalwww.ti.com 1.1ExplanationofThisEffect Tounderstandthecauseofthisbehavior,itishelpfultostartwithamodeloftheADCthatincludesthe thermalnoiseandquantizationerror. Figure7.ADCModel ThemodelshowsthattheADCoutputdataareaquantizedrepresentationoftheanaloginputthat includesthequantizationerror.Usingthismodel,wecanexplainthebehaviorwithlargeandsmallinput signals. First,wewillconsiderananalysiswithasingle-toneinputsignalbeforemovingtoascenariowith multi-toneorwidebandinputsignals. 2Single-ToneInputSignal 2.1Single-ToneLargeInputSignalAmplitude ThetimedomainwaveformsofFigure8andFigure9showtheADCoutputandquantizationerror(or Q-error)signalsforlargeinputamplitude( ±1dBFSmeasuredasanexample).NotethattheQ-error waveformappearsrandomanddoesnotshowanycomponentoftheinputsignal.Thequantizationerror ispresumedtohaveauniformprobabilitydistribution;thisconditionisalsothebasisfortheclassic, quantizationerror-limitedSNRformulagivenbyEquation1. SNR=6n+1.76(n=numberofbits)(1) Figure8.AnalogInputVINandADCOutputVOUTfor Figure9.QuantizationErrorfor ±1-dBFSInput ±1-dBFSInputAmplitude Amplitude 4 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SBOA133 ±October2011 SubmitDocumentationFeedback Copyright 2011,TexasInstrumentsIncorporated www.ti.comSingle-ToneInputSignal Figure10andFigure11showthespectrumoftheADCoutputandtheQ-error,respectively.Asexpected fromthetimedomainwaveforms,thespectrumofthequantizationerrordoesnothaveanytonesrelated totheinputsignalfrequency;inotherwords,theenergyoftheQ-errorisspreadovertheentirespectrum. Figure10.SpectrumGraph:ADCOutputfor ±1-dBFS Figure11.SpectrumGraph:QuantizationErrorfor InputAmplitude ±1-dBFSInputAmplitude Inthespectrumoftheoutputsignal(Figure10),theinputsignalfrequencycomponentcanbeseenwell abovethenoisefloor.Therefore,theamplitudeoftheinputsignal(asreportedbytheheightofthetonein thespectrum)islargelyunaffectedbytheQ-error. Inthefrequencydomain,Equation2isvalid: (2) Where: VOUT(f)representsthepowerofthetoneatfrequencyfinthespectrum VIN(f)representstheideal(orexpected)powerofthetoneatfrequencyfinthespectrum QERROR(f)representsthepowerofthequantizationerroratfrequencyfinthespectrum As|QERROR(f)| VIN(f),then,VOUT(f)becomesnearlyequivalenttoVIN(f). 5 SBOA133 ±October2011 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SubmitDocumentationFeedback Copyright 2011,TexasInstrumentsIncorporated Single-ToneInputSignalwww.ti.com 2.2Single-ToneSmallInputSignalAmplitude Figure12andFigure13showthetimedomainwaveformsoftheADCoutputandQ-errorforsmallinput signalamplitudes.Comparedtothepreviouscase,theerrornolongerappearsrandomandshowsa strongdependenceontheinputsignal. Figure12.AnalogInputandQuantizedOutputfor Figure13.QuantizationErrorfor ±61-dBFSInput ±61-dBFSInputAmplitude Amplitude Inthiscase,thespectrumoftheQ-error(Figure15)clearlyshowsthefundamentalaswellharmonicsof theinputsignal. Figure14.SpectrumGraph:ADCOutputfor ±61-dBFS Figure15.SpectrumGraph:QuantizationErrorfor InputAmplitude ±61-dBFSInputAmplitude WefindthattheQ-errorcomponentatthefundamentalfrequencyissignificant( ±77.7dBFS)andcanalter theADCoutputfromitsexpectedvalueof ±61dBFS. 6 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SBOA133 ±October2011 SubmitDocumentationFeedback Copyright 2011,TexasInstrumentsIncorporated www.ti.comSingle-ToneInputSignal UsingEquation2andnotingthatthepoweroftheoutputsignalisavectorsumoftheinputsignaland Q-error,wecanseethattheoutputsignalpowerdependsonthemagnitudeandphaseofthequantization erroraswell. UsingasimpleMATLAB model,wethenplottheamplitudeandphaseoftheQ-erroratthefundamental frequency.Figure16showstheideal(orexpected)outputsignalpower(dashedblacktrace)andthe actualADCoutputpower(redtrace). Figure16.AmplitudePlotofQuantizationError Wecannowseethat(dependingonthephaseoftheQ-errorasshowninFigure17),theoutputpoweris eitherunder-oroverestimated.Thismiscalculationexplainsthereasonforinaccuracyoftheoutput amplitudeforsmallinputsignals. Figure17.PhasePlotofQuantizationError 7 SBOA133 ±October2011 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SubmitDocumentationFeedback Copyright 2011,TexasInstrumentsIncorporated Multi-ToneInputSignalwww.ti.com 3Multi-ToneInputSignal Mostreal-worldsystemsemploysomeformofmulti-toneorabandofsignalsratherthanasingletone.A single-tonesignalisfrequentlyemployedduringlabtestingofADCsbecauseitiseasytounderstandand analyzeADCnon-idealityeffectswiththistypeofsignal. Itcanbeobservedthatinthecaseofamulti-tonesignalappliedtoanADC,theaccuracyproblematlow inputsignalamplitudeisnotseen.Infact,theoutputamplitude(fromtheFFT)closelymatchestheinput signalamplitude. Inourmodel,weappliedasignalwith16tonesequallyspacedby200kHz(tomimicamulti-carrierGSM signal)withatotalinputpowerof ±61dBFStotheADC(spectrumgraphshowninFigure18). Figure18.ADCOutputSpectrumfor16-ToneInputSignalwith ±61dBFSTotalPower 8 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SBOA133 ±October2011 SubmitDocumentationFeedback Copyright 2011,TexasInstrumentsIncorporated www.ti.comMulti-ToneInputSignal Asaresultofthemulti-tonenatureofthesignal,theenergyofthequantizationerrorisspreadacrossthe entirespectrum,andnospecifictonesareobserved(Figure19). Figure19.QuantizationErrorSpectrumfor16-ToneInputSignalwith ±61dBFSTotalPower Figure20showstheresultofsweepingtheinputsignalamplitudeandtheexpectedversusactualvalues oftheoutputpower.Itclearlyshowsthattheoutputpowertrackstheinputsignalevendowntoverysmall powerlevels. Figure20.OutputAmplitudeforSingle-ToneandMulti-ToneInputSignals Insummary,then,real-worldsystemsthatemploywidebandsignalsdonotfaceanylimitationsbecauseof thiseffect. 9 SBOA133 ±October2011 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SubmitDocumentationFeedback Copyright 2011,TexasInstrumentsIncorporated Example:WhenThermalNoiseDominatestheQuantizationErrorwww.ti.com 4Example:WhenThermalNoiseDominatestheQuantizationError WhathappensinthecaseoftraditionalADCswherethethermalnoiseisthedominantsource comparedtothequantizationerror? Consideran11-bitADCwiththermalnoiseof ±64dBFSasanexample.Figure21throughFigure24 showhowQ-errorappearsinthetimedomaininthiscase. ComparedtoFigure12andFigure13,theQ-errorseemstobemorerandomandshowslessdependence ontheinputsignalfrequency.ThiseffectisalsoshownbythespectrumoftheQ-errorinFigure23;the energyisspreadovertheentirespectrumandnotonesareseen.Therefore,inthiscase,theoutput amplitude(fromtheFFT)isquiteclosetotheinputamplitude. Figure21.TimeDomainWaveform:AnalogInputand Figure22.TimeDomainWaveform:QuantizationError QuantizedOutputfor ±61-dBFSInputAmplitude for ±61-dBFSInputAmplitude Figure23.SpectrumGraph:ADCOutputfor ±61-dBFS Figure24.SpectrumGraph:QuantizationErrorfor InputAmplitude ±61-dBFSInputAmplitude 10 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SBOA133 ±October2011 SubmitDocumentationFeedback Copyright 2011,TexasInstrumentsIncorporated www.ti.comConclusion 5Conclusion Inthisapplicationnote,wehaveexplainedthebehaviorofanADCwhenitsthermalnoiseismuchbetter comparedtoitsquantizationerror;atsmallinputsignallevelsofasingle-toneinput,theoutputamplitude asreportedbyaFFTanalysishasalargeerrorcomponent. Usingasimplemodel,wethenexplainedthecauseofthiserrorinoutputamplitudeforlowinputsignal levels.Wenotedthatthequantizationerrorisverydifferentatlargeandsmallsignallevels.Atlargesignal levels,theerrorsignalisrandom(thatis,notonesareseeninthespectrum),whereasatsmallsignal levels,theerrorspectrumclearlyshowstonesatthefundamentalfrequencyoftheinputsignalandits harmonics. Next,weshowedthatinthecaseofamulti-toneinput(orabandofsignals),theissueisnotseen:the outputamplitudematchestheinputamplitudeevenatverylowinputpower. Weconcludethatalthoughthisbehaviorischaracteristicofsingle-toneinputsignals(andisimportantfor designersandapplicationengineerstounderstand),mostreal-worldsystemsthatuseabandofsignals arenotlimitedbythiseffect. 11 SBOA133 ±October2011 UnderstandingLow-AmplitudeBehaviorof11-bitADCs SubmitDocumentationFeedback Copyright 2011,TexasInstrumentsIncorporated IMPORTANTNOTICE TexasInstrumentsIncorporatedanditssubsidiaries(TI)reservetherighttomakecorrections,modifications,enhancements,improvements, andotherchangestoitsproductsandservicesatanytimeandtodiscontinueanyproductorservicewithoutnotice.Customersshould obtainthelatestrelevantinformationbeforeplacingordersandshouldverifythatsuchinformationiscurrentandcomplete.Allproductsare soldsubjecttoTI ¶stermsandconditionsofsalesuppliedatthetimeoforderacknowledgment. TIwarrantsperformanceofitshardwareproductstothespecificationsapplicableatthetimeofsaleinaccordancewithTI ¶ warranty.TestingandotherqualitycontroltechniquesareusedtotheextentTIdeemsnecessarytosupportthiswarranty.Exceptwhere mandatedbygovernmentrequirements,testingofallparametersofeachproductisnotnecessarilyperformed. TIassumesnoliabilityforapplicationsassistanceorcustomerproductdesign.Customersareresponsiblefortheirproductsand applicationsusingTIcomponents.Tominimizetherisksassociatedwithcustomerproductsandapplications,customersshouldprovide adequatedesignandoperatingsafeguards. TIdoesnotwarrantorrepresentthatanylicense,eitherexpressorimplied,isgrantedunderanyTIpatentright,copyright,maskworkright, orotherTIintellectualpropertyrightrelatingtoanycombination,machine,orprocess publishedbyTIregardingthird-partyproductsorservicesdoesnotconstitutealicensefromTItousesuchproductsorservicesora warrantyorendorsementthereof.Useofsuchinformationmayrequirealicensefromathirdpartyunderthepatentsorotherintellectual propertyofthethirdparty,oralicensefromTIunderthepatentsorotherintellectualpropertyofTI. ReproductionofTIinformationinTIdatabooksordatasheetsispermissibleonlyifreproductioniswithoutalterationandisaccompanied byallassociatedwarranties,conditions,limitations,andnotices.Reproductionofthisinformationwithalterationisanunfairanddeceptive businesspractice.TIisnotresponsibleor restrictions. ResaleofTIproductsorserviceswithstatementsdifferentfromorbeyondtheparametersstatedbyTIforthatproductorservicevoidsall expressandanyimpliedwarrantiesfortheassociatedTIproductorserviceandisanunfairanddeceptivebusinesspractice.TIisnot responsibleorliableforanysuchstatements. TIproductsarenotauthorizedforuseinsafety-criticalapplications(suchaslifesupport)whereafailureoftheTIproductwouldreasonably beexpectedtocauseseverepersonalinjuryordeath,unlessofficersofthepartieshaveexecutedanagreementspecificallygoverning suchuse.Buyersrepresentthatthey acknowledgeandagreethattheyaresolelyresponsibleforalllegal,regulatoryandsafety-relatedrequirementsconcerningtheirproducts andanyuseofTIproductsinsuchsafety-criticalapplications,notwithstandinganyapplications-relatedinformationorsupportthatmaybe providedbyTI.Further,BuyersmustfullyindemnifyTIanditsrepresentativesagainstanydamagesarisingoutoftheuseofTIproductsin suchsafety-criticalapplications. TIproductsareneitherdesignednorintendedforuseinmilitary/aerospaceapplicationsorenvironmentsunlesstheTIproductsare specificallydesignatedbyTIasmilitary-gradeor enhancedplastic. OnlyproductsdesignatedbyTIas specifications.BuyersacknowledgeandagreethatanysuchuseofTIproductswhichTIhasnotdesignatedasmilitary-gradeissolelyat theBuyer \nsrisk,andthattheyaresolelyresponsibleforcompliancewithalllegalandregulatoryrequirementsinconnectionwithsuchuse. TIproductsareneitherdesignednorintendedforuseinautomotiveapplicationsorenvironmentsunlessthespecificTIproductsare designatedbyTIascompliantwithISO/TS16949requirements.Buyersacknowledgeandagreethat,iftheyuseanynon-designated productsinautomotiveapplications,TIwillnotberesponsibleforanyfailuretomeetsuchrequirements. FollowingareURLswhereyoucanobtaininformationonotherTexasInstrumentsproducts Products Applications Audio www.ti.com/audio CommunicationsandTelecom www.ti.com/communications Amplifiers amplifier.ti.com ComputersandPeripherals www.ti.com/computers DataConverters dataconverter.ti.com ConsumerElectronics www.ti.com/consumer-apps DLP Products www.dlp.com EnergyandLighting www.ti.com/energy DSP dsp.ti.com Industrial www.ti.com/industrial ClocksandTimers www.ti.com/clocks Medical www.ti.com/medical Interface interface.ti.com www.ti.com/security Logic logic.ti.com Space,AvionicsandDefense www.ti.com/space-avionics-defense PowerMgmt power.ti.com TransportationandAutomotive www.ti.com/automotive Microcontrollers microcontroller.ti.com VideoandImaging www.ti.com/video RFID www.ti-rfid.com OMAPMobileProcessors www.ti.com/omap WirelessConnectivity www.ti.com/wirelessconnectivity TIE2ECommunityHomePage e2e.ti.com MailingAddress:TexasInstruments,PostOfficeBox655303,Dallas,Texas75265 Copyright 2011,TexasInstrumentsIncorporated