ApplicationReport - PDF document

ApplicationReport SLAA445–August2010 UsingWindowingWithSNRBoost3GTechnology SourabhGuptaandVinodPaliakara....................................................................High-SpeedConverters ABSTRACT Coherencyisawell-knownrequirementwhenusingFFTtechniquestoexaminethespectrumofthe outputofananalog-to-digitalconverter(ADC).SNRBoost3Gtechnology thiscanbeseenasanunstablenoisefloorinthespectrum.WindowingoftheADCoutputisawell-known solutiontorestorecoherencyandstablespectrum. However,windowingalsomodifiestheamplitudeofthefundamentalsignalandtheSNRvalues.This maskstherealimprovementinSNRduetotheSNRBoost3Gtechnology. Thisapplicationreportexplains recovertheactualSNRoftheoriginalsignal(priortowindowing). Contents 1Introduction..................................................................................................................1 2SNRBoost3GTechnologyCausesLossinCoherency..................................................................2 3UsingWindowing............................................................................................................3 3.1Example AppendixATheory...............................................................................................................5 ListofFigures 1SpectrumofSignalWithSNRBoost3GOn................................................................................2 2Full-BandSNRComparisonWithSNRBoost3GDisabledandEnabled..............................................2 3TimeDomainDataWithSNRBoost3GDisabledandEnabled(WithNoInputSignal).............................. 4UnstableSpectrumWithSNRBoost3GEnabled.........................................................................3 5StableSpectrumWithSNRBoost3GEnabledandAfterWindowing..................................................4 6SpectrumofADCOutputSequence.....................................................................................5 7SpectrumofWindowFunction............................................................................................6 8SpectrumofSignalAfterWindowing ListofTables 1EffectofWindowing........................................................................................................4 2WindowFunctions..........................................................................................................7 1Introduction FFTtechniquesarecommonlyusedtoexaminethespectrumoftheoutputofananalog-to-digital converter(ADC).OneoftherequirementswhenusingFFTistoensurecoherencybetweentheanalog input WhenusinganADCwithSNRBoost3Gtechnology,lossincoherencyisobserved.Thiscanbeseenasan unstablenoisefloorinthespectrum.WindowingoftheADCoutputisawell-knownsolutiontorestore coherencyandstablespectrum.However,windowingalsomodifiestheamplitudeofthefundamental signalandtheSNRvalues.Thismasksthereal Thisapplicationnoteexplainsthescalingcausedbydifferentwindowfunctionsthatcanbeusedto recovertheactualSNRoftheoriginalsignal(priortowindowing). 1 SLAA445–August2010 UsingWindowingWithSNRBoost3GTechnology Copyright©2010,TexasInstrumentsIncorporated SNRBoost3GTechnologyCausesLossinCoherencywww.ti.com 2SNRBoost3GTechnologyCausesLossinCoherency SNRBoost3Gtechnologyworksbyimprovingthenoisewithinaselectbandoffrequencies.Atthesame time,thenoisedegradesoutsidetheselectedfrequencyband(Figure1). Figure1.SpectrumofSignalWithSNRBoost3GOn NotethatalthoughthenoiseintheselectedbandimproveswithSNRBoost3Genabled,thenoiseoverthe entirebanddegrades(comparedtoSNRBoost3Gdisabled).Forexample,thefull-bandSNRis66.91dBFS withSNRBoost3Gdisabledand32.73dBFSwithSNRBoost3Genabled(Figure2). Figure2.Full-BandSNRComparisonWithSNRBoost3GDisabledandEnabled Inthetimedomain,thisSNRdegradationshowsupasanincreaseintherangeofcodevariations.For example,theoutputcoderangeis1LSBwithSNRBoost3Gdisabledand113LSBswithSNRBoost3G enabled(Figure3). 2 SLAA445–August2010 UsingWindowingWithSNRBoost3GTechnology Copyright©2010,TexasInstrumentsIncorporated www.ti.comUsingWindowing Figure3.TimeDomainDataWithSNRBoost3GDisabledandEnabled(WithNoInputSignal) Theincreasednoiseresultsinlossofcoherency.TheFFTspectrumofthisdatahasanoisefloorthatis notuniformlyflatandchangesfromonecapturetothenext. Figure4.UnstableSpectrumWithSNRBoost3GEnabled 3UsingWindowing Windowingcanbeusedtoovercomethelossincoherency.Anyofthecommonwindowfunctions (Hanning,Hamming,Blackman-Harris,etc.)canbeappliedtotheADCoutputdata.Theresultingsignalis nowcoherentwithastablenoisefloorintheFFTspectrum. 3 SLAA445–August2010 UsingWindowingWithSNRBoost3GTechnology Copyright©2010,TexasInstrumentsIncorporated UsingWindowingwww.ti.com Figure5.StableSpectrumWithSNRBoost3GEnabledandAfterWindowing Thewindowinghasonesideeffect:theamplitudeofallthefrequencybinsinthespectrumarereported smallerthantheiractualvalues.Foranarrow-bandsignal,thefundamentalsignalandtherestofthe spectrumaremodifiedbydifferentamountsasshowninTable1. Table1.EffectofWindowing WindowFunction DeltaSNR(dB) DeltaSignalAmplitude(dB) Hamming 4.01 5.35 Hanning 4.26 6.02 BlackmanHarris 5.88 8.90 UseTable1todeterminetheSNRandsignalamplitudeoftheoriginalsignalwithoutwindowingas follows: SNR(pre-windowing)=SNR(post-windowing)–DeltaSNR SignalAmplitude(pre-windowing)=SignalAmplitude(post-windowing)+DeltaSignalAmplitudewhere SNRandSignalAmplitudearereportedindBFSvalues. Inthisway,thecorrectSNRofthesignalwithSNRBoost3Genabledcanbedetermined. 3.1Example Withtheprecedingmethod,theimprovementinSNRusingSNRBoost3GtechnologyintheADS58C48can bedetermined. Consideracasewherethesampleclockis184.32MSPSandtheinputsignalbandwidthis60MHz centeredat46MHz.WithSNRBoost3Gdisabled,thein-bandSNRreportedis68.6dBFS.Afterthe SNRBoost3Gtechnologyisturnedon,aHammingwindowisappliedtotheADCoutputdata.Thespectrum ofthewindowedsignalreportsanin-bandSNRof78.1dBFS. UsingTable1,findthein-bandSNR(prewindowing)withSNRBoost3GON: =78.1dBFS–4.01dB =74.09dBFS ThismeansthattheSNRBoost3Gtechnologyresultedinanin-bandSNRimprovement: =SNR(pre-windowing)withSNRBoost3Gon–SNRwithSNRBoost3Goff =74.01dBFS–68.6dBFS =5.49dBwithinthebandof60MHz. 4 SLAA445–August2010 UsingWindowingWithSNRBoost3GTechnology Copyright©2010,TexasInstrumentsIncorporated www.ti.com AppendixATheory Theaimofthissectionistodeterminethechangeinspectralpowerafterwindowing.Tofindthis,asingle toneinputsignalisusedthatiscoherentandhasknownpower.Theinputsignalisthenmultipliedbythe windowfunction.Thedifferenceinthepowerofthetonebetweentheinputsignalandthewindowed signalgivesthedesiredresult. ConsidertwoN-pointsequencesV(n)andW(n),thatrepresenttheADCoutputdataandthewindow functionsequence,respectively. (1) (2) Forsimplicityofanalysis,theADCoutputsequenceisassumedtobeasingletonewithallothertones havingzeropower.BecausethespectrumfromN/2toN–1isamirrorimageofthespectrumfrom0to N/2–1,thespectrumisrepresentedonlyintherange0toN/2–1,afteradjustingthepowerofeachtone. Figure6.SpectrumofADCOutputSequence Similarly,thespectrumofthewindowfunctionisshowninFigure7. 5 SLAA445–August2010 UsingWindowingWithSNRBoost3GTechnology Copyright©2010,TexasInstrumentsIncorporated AppendixAwww.ti.com Figure7.SpectrumofWindowFunction WindowinginvolvesmultiplicationoftheADCoutputsequencebythewindowfunction. So, (3) ThespectrumofthesignalafterwindowingisshowninFigure8. Figure8.SpectrumofSignalAfterWindowing Notethateachtonewithbinnumber'k'intheinputsignalspreadsintothreetones. •Onemaintone(atbink)havingamplitudem1Aand •Twosidetones(atbinsk±w)havingamplitudesm2A/2. Thechangeinsignalamplitudeofthemaintoneisduetowindowing=20log(m1) Notethatitisassumedthattheinputsignalhaszeroamplitudenoisecomponents.Withnon-zeronoise components,theinputsignalcanberepresentedas: 6 SLAA445–August2010 UsingWindowingWithSNRBoost3GTechnology Copyright©2010,TexasInstrumentsIncorporated www.ti.comAppendixA (4) Similartothesignaltone,eachnoisecomponentisalsospreadintothreetoneshaving (5) Thetotalpowerofallnoisecomponentsafterwindowingis (6) BecauserepresentsthenoisepoweroftheADCoutputsequence,Equation6canbere-written as: (7) (8) Table2liststhechangesinsignalamplitudeandSNRafterwindowingforsomecommonwindow functions. Table2.WindowFunctions WindowFunction m1 m2 w DeltaSNR(dB) DeltaSignalAmplitude(dB) Hamming 0.54 –0.46 1 4.01 5.35 Hanning 0.5 –0.5 1 4.26 6.02 Thisisaparatokeepfromcreatingablankpage 7 SLAA445–August2010 UsingWindowingWithSNRBoost3GTechnology Copyright©2010,TexasInstrumentsIncorporated IMPORTANTNOTICETexasInstrumentsIncorporatedanditssubsidiaries(TI)reservetherighttomakecorrections,modifications,enhancements,improvements,andotherchangestoitsproductsandservicesatanytimeandtodiscontinueanyproductorservicewithoutnotice.Customersshouldobtainthelatestrelevantinformationbeforeplacingordersandshouldverifythatsuchinformationiscurrentandcomplete.AllproductsaresoldsubjecttoTI’stermsandconditionsofsalesuppliedatthetimeoforderacknowledgment.TIwarrantsperformanceofitshardwareproductstothespecificationsapplicableatthetimeofsaleinaccordancewithTI’sstandardwarranty.TestingandotherqualitycontroltechniquesareusedtotheextentTIdeemsnecessarytosupportthiswarranty.Exceptwheremandatedbygovernmentrequirements,testingofallparametersofeachproductisnotnecessarilyperformed.TIassumesnoliabilityforapplicationsassistanceorcustomerproductdesign.CustomersareresponsiblefortheirproductsandapplicationsusingTIcomponents.Tominimizetherisksassociatedwithcustomerproductsandapplications,customersshouldprovideadequatedesignandoperatingsafeguards.TIdoesnotwarrantorrepresentthatanylicense,eitherexpressorimplied,isgrantedunderanyTIpatentright,copyright,maskworkright,orotherTIintellectualpropertyrightrelatingtoanycombination,machine,orprocessinwhichTIproductsorservicesareused.InformationpublishedbyTIregardingthird-partyproductsorservicesdoesnotconstitutealicensefromTItousesuchproductsorservicesorawarrantyorendorsementthereof.Useofsuchinformationmayrequirealicensefromathirdpartyunderthepatentsorotherintellectualpropertyofthethirdparty,oralicensefromTIunderthepatentsorotherintellectualpropertyofTI.ReproductionofTIinformationinTIdatabooksordatasheetsispermissibleonlyifreproductioniswithoutalterationandisaccompaniedbyallassociatedwarranties,conditions,limitations,andnotices.Reproductionofthisinformationwithalterationisanunfairanddeceptivebusinesspractice.TIisnotresponsibleorliableforsuchaltereddocumentation.InformationofthirdpartiesmaybesubjecttoadditionalResaleofTIproductsorserviceswithstatementsdifferentfromorbeyondtheparametersstatedbyTIforthatproductorservicevoidsallexpressandanyimpliedwarrantiesfortheassociatedTIproductorserviceandisanunfairanddeceptivebusinesspractice.TIisnotresponsibleorliableforanysuchstatements.TIproductsarenotauthorizedforuseinsafety-criticalapplications(suchaslifesupport)whereafailureoftheTIproductwouldreasonablybeexpectedtocauseseverepersonalinjuryordeath,unlessofficersofthepartieshaveexecutedanagreementspecificallygoverningsuchuse.Buyersrepresentthattheyhaveallnecessaryexpertiseinthesafetyandregulatoryramificationsoftheirapplications,andacknowledgeandagreethattheyaresolelyresponsibleforalllegal,regulatoryandsafety-relatedrequirementsconcerningtheirproductsandanyuseofTIproductsinsuchsafety-criticalapplications,notwithstandinganyapplications-relatedinformationorsupportthatmaybeprovidedbyTI.Further,BuyersmustfullyindemnifyTIanditsrepresentativesagainstanydamagesarisingoutoftheuseofTIproductsinsuchsafety-criticalapplications.TIproductsareneitherdesignednorintendedforuseinmilitary/aerospaceapplicationsorenvironmentsunlesstheTIproductsarespecificallydesignatedbyTIasmilitary-gradeor"enhancedplastic."OnlyproductsdesignatedbyTIasmilitary-grademeetmilitaryspecifications.BuyersacknowledgeandagreethatanysuchuseofTIproductswhichTIhasnotdesignatedasmilitary-gradeissolelyattheBuyer'srisk,andthattheyaresolelyresponsibleforcompliancewithalllegalandregulatoryrequirementsinconnectionwithsuchuse.TIproductsareneitherdesignednorintendedforuseinautomotiveapplicationsorenvironmentsunlessthespecificTIproductsaredesignatedbyTIascompliantwithISO/TS16949requirements.Buyersacknowledgeandagreethat,iftheyuseanynon-designatedproductsinautomotiveapplications,TIwillnotberesponsibleforanyfailuretomeetsuchrequirements.FollowingareURLswhereyoucanobtaininformationonotherTexasInstrumentsproductsandapplicationsolutions: Audiowww.ti.com/audio DataConverters Automotivewww.ti.com/automotive DLP®Products Communicationsand TelecomDSPdsp.ti.com Computersand ClocksandTimers ConsumerElectronics Interfaceinterface.ti.com Energywww.ti.com/energy Logiclogic.ti.com Industrialwww.ti.com/industrial PowerMgmt Medicalwww.ti.com/medical Microcontrollersmicrocontroller.ti.com Securitywww.ti.com/security RFIDwww.ti-rfid.com Space,Avionics& RF/IFandZigBee®Solutions VideoandImaging Wirelesswww.ti.com/wireless-apps MailingAddress:TexasInstruments,PostOfficeBox655303,Dallas,Texas75265Copyright©2010,TexasInstrumentsIncorporated