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英文资料1IntroductionTheuseofthesystemonchipSoCtechniqueallowsforanunprecedenteddegreeofminiaturizationofrubidiumatomicfrequencystandards.AcompactdirectdigitalfrequencysynthesizerDDFSplaysanimportantroleinourminiaturizedrubidiumatomicfrequencystandardsformodulated5.3125MHzsinewavegeneration.DDFSsareabletogeneratesinglephaseorquadraturesinusoidswithexcellentfrequencyresolution,goodspectralpurity,veryfastfrequencyswitching1,andphasecontinuityonswitching.Generally,aDDFSconsistsofaphaseaccumulator,aphasetosineconvertersineROM,andaDAC.Ateachclockpulse,thephaseincrementwordinafrequencyregisterisaddedtothephasevaluepreviouslyheldinthephaseaccumulator.Thephasevalueisgeneratedusingthemodulo2joverflowingpropertyofajbitphaseaccumulator2.Theoutputfrequencyistherateoftheoverflows,whereΔpisthephaseincrementword,jisthenumberofphaseaccumulatorbits,fclkisthesystemclockfrequency,andfoutistheoutputfrequency.Thepreviousconstraintisrequiredbythesamplingtheorem.ThespectralpurityoftheconventionalDDFSispartlydeterminedbytheresolutionofthevaluesstoredintheROM.ItisdesirabletoincreasetheresolutionoftheROM,butsometimeshigherresolutionmeanslargerROMsize.However,theaccessspeedandthemaximumoutputfrequencydecreaseastheROMsizeincreases.LargerROMstoragealsomeanshigherpowerconsumption,lowerreliability,andgreatlyincreasedcosts.SoitissignificanttoreducethesizeoftheROMundertheconditionofmeetingthehighresolutionrequirementoftherubidiumatomicfrequencystandard.Themostelementarytechniqueofcompressionistostoreonlyπ/2radofsineinformation,andtogeneratetheROMsamplesforthefullrangeof2πbyexploitingthequarterwavesymmetryofthesinefunction3.ThequarterwavememorycanbefurthercompressedbyusingmodifiedSunderlandtechnique,sinephasedifferencetechnique,QuadlineapproximationQLAtechnique,andquantizationanderrorROMQEROMtechnique.Thephaseofaquarterofasinewavecanbedecomposedasφαβγ,whereα,β,andγare,respectively,themostsignificantbitsMSBs,themiddlebits,andtheleastsignificantbitsLSBs.ThewholecompressionprocessinthispaperisdepictedinFig.1.A10bitonchipcurrentsteeringDACisalsoimplementedtoconvertthedigitalamplitudewordtoanequivalentanalogamplitude.2PhaseaccumulatorA32bitphaseaccumulatorisusedinthisDDFS.Figure2showstheblockdiagramofthephaseaccumulator.Thephaseaccumulatorisbasedona32bitripplecarryadder,withastringoffulladdersthatoperateonthesameclockphase.Theoutputsofthefulladdershavebuiltinregisters,andthesumbitsfeedbackinternallytoperformaccumulation.AmultiplexerMUXisusedtoselectthephaseincrementwordfromthe32bitphaseincrementwordsstoredinregisters.Inordertoguaranteethephasecontinuity,theselectsignalshouldbesynthesizedwiththesystemclocksignaloftheDDFS.3Phasetosineconverter3.1SinefunctionsymmetrytechniqueThefullperiodsinewavecanbereconstructedwithonlyπ/2radofthesineinformationbyexploitingthequarter2wavesymmetryofthesinefunction.Figure3showsthedetailsofthismethod.Sincethemostsignificanttwobitsofthephaseaccumulatorrepresentthequadrantofthesinefunction,themostsignificantbitMSBisusedasthesignbitoftheresult,andthesecondmostimportantbit2ndMSBisusedtocontrolwhetherthephaseshouldbeincreasingordecreasing4.Thelowj2bitsofthephaseaccumulatoroutputaresenttoacomplementcontrolledbythe2ndMSBtogenerateaddressesforthequartersineROM.Theslopeofthesawtoothisinvertedforthesecondquadrant,asshowninFig.3.ThewaveformattheoutputofthequartersineROMisthequantifiedsinewave.Thefullperiodsinewaveisgeneratedattheoutputofthesecondcomplement,whichconsistsofm1exclusiveorgatesandaninverter.Thus,theROMcapacitydecreasesattheexpenseofadditionallogic.3.2ModifiedSunderlandtechniqueToreducetheROMsize,thisDDFSusesthemodifiedSunderlandtechniquebasedonsimpletrigonometricidentities5.Thephaseaddressofaquarterofasinewavecanbedecomposedasφαβγ,whereαistheMSBs,βisthemiddlebits,andγistheLSBs.Thequarterwavesinefunctionisgivenbywherejisthenumberofthephaseaccumulatoroutputbits.Equation2canbesimplifiedfurthertoTheinformationfromthefirsttermontherightofEq.3isstoredintoacoarseROM.ThesecondtermontherightofEq.3isstoredintoafineROM.Thismethodworksbyintroducingthe1/2LSBsoffsetsintothephaseandamplitudeofthesineROMsamples.However,significantsavingsinROMsizecanberealizedduetothesmallmagnitudesofβandγrelativetoα.The10bitphasedataofaccumulatoroutputsisdividedintothreepartsinthisdesign.Computersimulationsdeterminetheoptimumpartitioningratioα4,β3,andγ36.3.3Sine2phasedifferencetechniqueThesineamplitudeofthefirsttermontherightofEq.3isreducedusingthesinephasedifferencetechnique,andtwobitsofthewordlengthcanbesavedbyonlystoringthedifferenceofthesineamplitudeanditsphase.3.4QLAtechniqueTheQLAwaveformisusedtoapproximatethesinephasedifference,whichiscalculatedusingEq.4.TheQLAapproximationcanbeexpressedwithfollowingfourexpressions.Thedatafor0αβ/2j11/8aregeneratedthroughshiftingdownthephaseαβ/2j2by1bit.Thedatafor1/8αβ/2j11/4aregeneratedthroughshiftingdownthephaseαβ/2j2by2bitandbychangingthefirstandsecondMSBsofthephaseto10.Thedatafor0αβ/2j11/4andthedatafor1/4αβ/2j11/2aresymmetric.Acomplementisneededtoreconstructthesymmetricwaveform.Twobitsofwordlengthcanbesaved.crαβyαβqlaαβ10maxcrαβ≈0126maxyαβ113.5QE2ROMtechniqueBasedonthecontinuityofthedatathatneedcompressing,theROMsizeoftheDDFScanbefurtherreducedusingtheQEROMtechnique.Inthisdesign,thesecondtermontherightofEq.3andcrαβarebothcompressedusingtheQEROMtechnique.TheROMsizecanbereducedto2lm2anbitsusingtheQEROMtechnique,wherel,m,a,andnare,respectively,thelengthoftheaddressofthequantizationROM,thelengthofthedatainthequantizationROM,thelengthoftheaddressoftheoriginaldata,andthelengthofthedataintheerrorROM.TheremaybeseveralgroupsofparametervaluesthatminimizetheROMsize.Tofindthese,thefollowingalgorithmisused.1Findthemaximumamplitudeoftheoriginaldataandfigureouthowmanybitsittakestorepresentthisvalue.Themaximumvalueofmcanberepresentedbymaxm.2Setmmaxm.3Setla,whichistheaddresslengthoftheoriginaldata.4Calculatethequantizedvalues.5CalculatetheerrorsbetweentheoriginaldataandthequantizationROMdata.6Determinehowmanybitsittakestorepresenttheseerrors.7CalculatethetotalROMsize2lm2an.8Decreaselby1.Ifl0,thengoto9orelserepeattheprocessfrom4to7.9Decreasemby1.Ifm0,thengoto10orelserepeattheprocessfrom4to7.10DeterminetheoptimumvaluesoftheaboveparametersthatminimizethetotalROMsize.crαβisstoredintoacoarseROMthatisdividedintoaquantizationROMandanerrorROMusingtheQEROMtechnique.TheabovecalculationsindicatethattheminimumsizeofthecoarseROMfora10bitoutputDDFSis480bit253273480.ThesecondtermontherightofEq.3isstoredintoafineROM,whichisalsodividedintoaquantizationROMandanerrorROMusingtheQEROMtechnique.TheminimumsizeofthefineROMfora10bitoutputDDFSis288bit251272288.SothetotalROMsizefora10bitsineoutputisonly768bit.3.6ArchitectureofthephasetosineconverterFigure4showstheblockdiagramofthephasetosineconverter,whichconsistsofcomplement,multiplexersMUXs,ROMs,andadders.ThecomplementareusedtorecoverthefullwaveoutputfromthequartersineROMbyinvertingthephaseandamplitudeappropriately.FourcolumnMUXsandthreeaddersarealsorequired.Figure5showstheintermediateresultsduringtheapproximationprocess.Figure6showsthesumofthedatainthecoarseROMandthefineROMandthefinalerror.Figure7showstherelativebitpositionsofthedatausedforreconstructingasinewave.Thefirstrowrepresentsthe7bitphase,thesecondrowrepresentsthe7bitquadlineapproximation,thethirdrowrepresentsthe3bitquantizationROMdatainthecoarseROM,thefourthrowrepresentsthe3biterrorROMdatainthecoarseROM,thefifthrowrepresentsthe1bitquantizationROMdatainthefineROM,thesixthrowrepresentsthe2biterrorROMdatainthefineROM,andtheseventhrowrepresentsthe9bitoutputoftheaddersinFig17.TheDDFSrequiresthesmallestROMcomparedwiththeDDFSusingothercompressionmethodsinTable1.Moreover,theROMusingthistechniquecanproduceagoodspurlevel,asshowninTable1.4DigitaltoanalogconverterInthisdesign,anonchip10bitsegmentedcurrentsteeringdigitaltoanalog
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