Modulating Direct Digital Synthesizer数字频率合成器 文献译文Word文档格式.docx
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Modulating Direct Digital Synthesizer数字频率合成器 文献译文Word文档格式.docx
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Inthepursuitofmorecomplexphasecontinuousmodulationtechniques,thecontroloftheoutputwaveformbecomesincreasinglymoredifficultwithanalogcircuitry.Inthesedesigns,usinganon-lineardigitaldesigneliminatestheneedforcircuitboardadjustmentsoveryieldandtemperature.AdigitaldesignthatmeetsthesegoalsisaDirectDigitalSynthesizerDDS.ADDSsystemsimplytakesaconstantreferenceclockinputanddividesitdownatoaspecifiedoutputfrequencydigitallyquantizedorsampledatthereferenceclockfrequency.ThisformoffrequencycontrolmakesDDSsystemsidealforsystemsthatrequireprecisefrequencysweepssuchasradarchirpsorfastfrequencyhoppers.Withcontrolofthefrequencyoutputderivedfromthedigitalinputword,DDSsystemscanbeusedasaPLLallowingprecisefrequencychangesphasecontinuously.Aswillbeshown,DDSsystemscanalsobedesignedtocontrolthephaseoftheoutputcarrierusingadigitalphasewordinput.Withdigitalcontroloverthecarrierphase,ahighspectraldensityphasemodulatedcarriercaneasilybegenerated.
ThisarticleisintendedtogivethereaderabasicunderstandingofaDDSdesign,andanunderstandingofthespuriousoutputresponse.Thisarticlewillalsopresentasampledesignrunningat45MHzinahighspeedfieldprogrammablegatearrayfromQuickLogic.
AbasicDDSsystemconsistsofanumericallycontrolledoscillator(NCO)usedtogeneratetheoutputcarrierwave,andadigitaltoanalogconverter(DAC)usedtotakethedigitalsinusoidalwordfromtheNCOandgenerateasampledanalogcarrier.SincetheDACoutputissampledatthereferenceclockfrequency,awaveformsmoothinglowpassfilteristypicallyusedtoeliminatealiascomponents.Figure1isabasicblockdiagramofatypicalDDSsystemdesign.ThegenerationoftheoutputcarrierfromthereferencesampleclockinputisperformedbytheNCO.ThebasiccomponentsoftheNCOareaphaseaccumulatorandasinusoidalROMlookuptable.AnoptionalphasemodulatorcanalsobeincludeintheNCOdesign.ThisphasemodulatorwilladdphaseoffsettotheoutputofthephaseaccumulatorjustbeforetheROMlookuptable.ThiswillenhancetheDDSsystemdesignbyaddingthecapabilitiestophasemodulatethecarrieroutputoftheNCO.Figure2isadetailedblockdiagramofatypicalNCOdesignshowingtheoptionalphasemodulator.
FIGURE1:
TypicalDDSSystem.
FIGURE2:
TypicalNCODesign.
TobetterunderstandthefunctionsoftheNCOdesign,firstconsiderthebasicNCOdesignwhichincludesonlyaphaseaccumulatorandasinusoidalROMlookuptable.ThefunctionofthesetwoblocksoftheNCOdesignarebestunderstoodwhencomparedtothegraphicalrepresentationofEuler’sformulaejwt=cos(wt)+jsin(wt).ThegraphicalrepresentationofEuler’sformula,asshowninFigure3,isaunitvectorrotatingaroundthecenteraxisoftherealandimaginaryplaneatavelocityofwrad/s.Plottingtheimaginarycomponentversustimeprojectsasinewavewhileplottingtherealcomponentversustimeprojectsacosinewave.ThephaseaccumulatoroftheNCOisanalogous,orcouldbeconsidered,thegeneratoroftheangularvelocitycomponentwrad/s.Thephaseaccumulatorisloaded,synchronoustothereferencesampleclock,withanNbitfrequencyword.
ThisfrequencywordiscontinuouslyaccumulatedwiththelastsampledphasevaluebyanNbitadder.TheoutputoftheadderissampledatthereferencesampleclockbyanNbitregister.WhentheaccumulatorreachestheNbitmaximumvalue,theaccumulatorrollsoverandcontinues.PlottingthesampledaccumulatorvaluesversustimeproducesasawtoothwaveformasshownbelowinFigure3.
FIGURE3Euler’sEquationRepresentedGraphically
ThesampledoutputofthephaseaccumulatoristhenusedtoaddressaROMlookuptableofsinusoidalmagnitudevalues.Thisconversionofthesampledphasetoasinusoidalmagnitudeisanalogoustotheprojectionoftherealorimaginarycomponentintime.Sincethenumberofbitsusedbythephaseaccumulatordeterminesthegranularityofthefrequencyadjustmentsteps,atypicalphaseaccumulatorsizeis24to32bits.SincethesizeofthesinusoidalROMtableisdirectlyproportionaltotheaddressingrange,notall24or32bitsofthephaseaccumulatorareusedtoaddresstheROMsinusoidaltable.OnlytheupperYbitsofthephaseaccumulatorareusedtoaddressthesinusoidalROMtable,whereY<
NbitsandYistypicallybutnotnecessarilyequaltoD,andDisthenumberofoutputmagnitudebitsfromthesinusoidalROMtable.
SinceanNCOoutputsacarrierbasedonadigitalrepresentationofthephaseandmagnitudeofthesinusoidalwaveform,designershavecompletecontroloverfrequency,phase,andevenamplitudeoftheoutputcarrier.ByaddingaphaseportandaphaseaddertothebasicNCOdesign,theoutputcarrieroftheNCOcanbeMarrayphasemodulatedwhereMequalsthenumberofphaseportbitsandwhereMislessthanorequaltotheYnumberofbitsusedtoaddressthesinusoidalROMtable.ForsystemdesignsthatrequireamplitudemodulationsuchasQAM,amagnitudeportcanbeaddedtoadjustthesinusoidalROMtableoutput.NotethatthisportisnotshowninFigure2andthatthisfeatureisnotdemonstratedinthesampleQuickLogicFPGAdesign.Finally,frequencymodulationisagivenwiththebasicNCOdesign.Thefrequencyportcandirectlyadjustthecarrieroutputfrequency.SincefrequencywordsareloadedintotheDDSsynchronoustothesampleclock,frequencychangesarephasecontinuous.
AlthoughDDSsystemsgivethedesignercompletecontrolofcomplexmodulationsynthesis,therepresentationofsinusoidalphaseandmagnitudeinanon-lineardigitalformatintroducesnewdesigncomplexities.Insamplinganycontinuous-timesignal,onemustconsiderthesamplingtheoryandquantizationerror.
TounderstandtheeffectsofthesamplingtheoryonaDDSsystem,itisbesttolookattheDDSsynthesisprocessesinboththetimeandfrequencydomain.Asstatedabove,theNCOgeneratesasinusoidalwaveformbyaccumulatingthephaseataspecifiedrateandthenusesthephasevaluetoaddressaROMtableofsinusoidalamplitudevalues.Thus,theNCOisessentiallytakingasinusoidalwaveformandsamplingitwiththerisingorfallingedgeoftheNCOinputreferencesamplingclock.Figure4showsthetimeandfrequencydomainoftheNCOprocessing.Notethatthisrepresentationdoesnotassumequantization.
Basedontheloadedfrequencyword,theNCOproducesasetofamplitudeoutputvaluesatasetperiod.Thefrequencydomainrepresentationofthissinusoidisanimpulsefunctionatthespecifiedfrequency.TheNCO,however,outputsdiscretedigitalsamplesofthissinusoidattheNCOreferenceclockrate.Inthetimedomain,theNCOoutputisafunctionofthesamplingclockedgestrobesmultipliedbythesinusoidwaveformproducingatrainofimpulsesatthesinusoidamplitude.Inthefrequencydomain,thesamplingstrobesofthereferenceclockproduceatrainofimpulsesatfrequenciesofKtimestheNCOclockfrequencywhereK=...-1,0,1,2....Sincethesamplingclockwasmultipliedbythesinusoidinthetimedomain,thefrequencydomaincomponentsofthesinusoidandthesamplingclockneedtobeconvolvedtoproducethefrequencydomainrepresentationoftheNCOoutput.
ThefrequencydomainresultsaretheimpulsefunctionatthefundamentalfrequencyofthesinusoidandthealiasimpulsefunctionsoccurringatKtimestheNCOclockfrequencyplusorminusthefundamentalfrequency.Thefundamentalandaliascomponentoccurat:
K*Fclk-Fout
K*Fclk+Fout
WhereK=...-1,0,1,2.....andK=0istheNCOsinusoidfundamentalfrequency
FoutisthespecifiedNCOsinusoidoutputfrequency
FclkistheNCOreferenceclockfrequency
FIGURE4NCOOutputRepresentationTimeandFrequencyDomain
TheDACoftheDDSsystemtakestheNCOoutputvaluesandtranslatesthesevaluesintoanalogvoltages.Figure4showsthetimeandfrequencydomainrepresentationsoftheDACprocessingstartingwiththeNCOoutput.TheDACoutputisasampleandholdcircuitthattakestheNCOdigitalamplitudewordsandconvertsthevalueintoananalogvoltageandholdsthevalueforonesampleclockperiod.ThetimedomainplotoftheDACprocessingistheconvolutionoftheNCOsampledoutputvalueswithapulseofonesampleclockperiod.Thefrequencydomainplotofthesamplingpulseisasin(x)/xfunctionwiththefirstnullatthesampleclockfrequency.Sincethetimedomainwasconvolved,thefrequencydomainismultiplied.ThismultiplicationdampenstheNCOoutputwiththesin(x)/xenvelope.ThisattenuationattheDACoutputcanbecalculatedasfollowsandasampleoutputspectrumisshowninFigure5:
Atten(F)=20log[(sin(pF/Fclk)/pF/Fclk)]WhereFistheoutputfrequencyFclkisthesampleclockfrequency
FIGURE5:
DACOutputRepresentationinTimeandFrequencyDomain
Asidefromthesamplingtheory,thequantizationoftherealvaluesintodigitalformmustalsobeconsideredintheperformanceanalysisofaDDSsystem.ThespuriousresponseofaDDSsystemisprimarilydictatedbytwoquantizationparameters.TheseparametersarethephasequantizationbythephaseaccumulatorandthemagnitudequantizationbytheROMsinusoidaltableandtheDAC.
Asmentionedabove,onlytheupperYbitsofthephaseaccumulatorareusedtoaddresstheROMlookuptable.Itshouldbenoted,however,thatusingonlytheupperYbitsofthephaseaccumulatorintroducesaphasetruncation.Whenafrequencywordcontaininganon-zerovalueinthelower(N-Y-1:
0)bitsisloadedintotheDDSsystem,thelowe
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