外文翻译数字频率合成器.docx

外文翻译数字频率合成器.docx

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外文翻译数字频率合成器

中文6217字

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英文原文

ModulatingDirectDigitalSynthesizer

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

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,thelowernon-zerobitswillaccumula