Frequency Synthesizer Design at the Transfer Funct

Fractional-NFrequencySynthesizerDesignattheTransferFunctionLevelUsingaDirectClosedLoopRealizationAlgorithmCharlotteLauMichaelPerrottMassachusettsInstituteofTechnologyOutlineƒBackgroundonΣ−∆fractional-NfrequencysynthesizerƒLimitationsoftheopenloopdesignapproachƒClosedloopdesignapproachƒResultsandverificationƒConclusionsTheImportanceofFrequencySynthesizersƒFrequencysynthesizersarecriticalcomponentinallwirelesssystems-Generateasinewavewithtunablefrequency-EnablemodulationofsignalstodifferentfrequencybandsRequirescarefulandprecisedesignonnoiseanddynamicperformanceFractional-NFrequencySynthesisƒDitherthedividevaluebetweenintegervaluesƒAchievefractionaldividevaluesVeryhighfrequencyresolutionPFDChargePumpNsd[m]ref(t)out(t)e(t)div(t)DitheringModulatorv(t)N[m]LoopFilterDividerVCOFrefFout=M.F*FrefMM+1M.FNoiseSourcesƒChargepumpnoiseƒVCOnoisePFDNsd[m]ref(t)out(t)e(t)div(t)DitheringModulatorv(t)N[m]LoopFilterDividerChargePumpVCOff-20dB/decChargePumpNoiseVCONoiseΣ−∆Modulator:QuantizationNoiseƒDitherusingaΣ−∆modulatorƒShapeΣ−∆quantizationnoisetohighfrequenciesPFDNsd[m]ref(t)out(t)e(t)div(t)Σ−∆Modulatorv(t)N[m]LoopFilterDividerChargePumpVCOff-20dB/decChargePumpNoiseVCONoisefΣ−∆QuantizationNoiseComplicatesthePLLdesignPLLModelforDynamicandNoiseAnalysesPerrottet.al.JSSC,Aug.2002Φdiv[k]Φref[k]KVjfv(t)Φout(t)H(f)1Nnom2πz-1z=ej2πfT1-z-1n[k]T1Φd[k]T2πPFDDividerLoopFilterC.P.VCOαTristate:α=1XOR:α=2Icp(period=T)en(t)VCO-referredNoiseΦvn(t)PFD-referredNoiseDivideValueVariationƒClosedloopbehaviorcanbedescribedbytheclosedloopresponseG(f)ParameterizedPLLModelGoal:Designawell-controlledG(f)Φvn(t)TG(f)G(f)Φd[k]en(t)Φout(t)Φn(t)f0f01-G(f)G(f)fo-20dB/decG(f)G(f)2πNnomSen(f)SΦvn(f)1/TαVCO-referredNoisePFD-referredNoiseDivideValueVariationfofoHowWellCanWeControlG(f)?ƒBasicproperties:-Bandwidth-Shape-Type-RolloffcharacteristicsƒOtherdesiredproperties:-Systemstability-RobustnessinfaceofparasiticsƒRelationshipbetweenA(f)andG(f)leadstotheclassicalopenloopdesignapproachClassicalOpenLoopDesignApproachOrder,TypeTopologyofH(f)Poles/Zerosfz1fp1...|A(f)|\A(f)G(f)BandwidthSpecs:ABCBAABCCABCExample:SecondOrder,TypeIwithParasiticPolesOrder,TypeTopologyofH(f)Poles/Zerosfz1fp1...|A(f)|\A(f)G(f)BandwidthSpecs:H(s)-90o-180o20log|A(f)|ffp3\A(f)Openloopgainincreased0dBDominantpolepairABCBAABCCfpfp2Re(s)Im(s)0Re(s)Im(s)0G(s)PhasemargindecreasedfpA(s)ABCs=2πfExample:SecondOrder,TypeIwithParasiticPolesStabilityOrder,TypeTopologyofH(f)Poles/Zerosfz1fp1...|A(f)|\A(f)G(f)BandwidthSpecs:H(s)-90o-180o20log|A(f)|ffp3\A(f)Openloopgainincreased0dBDominantpolepairABCBAABCCfpfp2Re(s)Im(s)0Re(s)Im(s)0G(s)PhasemargindecreasedfpA(s)ABCs=2πfƒConstrainedforapplicationswhichrequireprecisefilterresponseƒPoorcontroloverfiltershapeƒComplicatedonceparasiticpolesaretakenintoaccountƒInadequateforsystemswiththirdorderrolloff-PhasemargincriterionbasedonsecondordersystemsLimitationsofOpenLoopDesignApproachClosedloopdesignapproach:DirectlydesignG(f)byspecifyingdominantpoleandzerolocationsonthes-plane(pole-zerodiagram)ClosedLoopDesignApproach:Overview(I)ƒG(f)completelydescribestheclosedloopdynamics-DesignofthisfunctionistheultimategoalƒInsteadofindirectlydesigningG(f)usingplotsofA(f)1.SolveforG(f)directlyasafunctionofspecificationparameters2.SolveforA(f)thatwillachievedesiredG(f)PerformanceSpecifications{type,fo,...}|A(f)|\A(f){K,fzA,fpA,...}G(f){fz,fp,...}A(f)1+A(f)=OpenLoopDesignApproachClosedLoopDesignApproachG(f)1-G(f)=A(f)G(f)ClosedLoopDesignApproach:Overview(II)ƒMustresolvetwokeyissues:-HowcanwespecifyanddirectlydesignG(f)?-Howcanweaccountfortheimpactofparasiticpolesandzeros?PerformanceSpecifications{type,fo,...}|A(f)|\A(f){K,fzA,fpA,...}G(f){fz,fp,...}A(f)1+A(f)=OpenLoopDesignApproachClosedLoopDesignApproachG(f)1-G(f)=A(f)G(f)Wewilladoptatwo-stepalgorithmStep1:SpecificationsforDesiredG(f)ƒBandwidth:foƒOrdern:1,2or3ƒShape:Butterworth,Bessel,Chebyshev1or2,Elliptical,etc.ƒTypeofG(f):IorIIfofrolloff=-20ndB/decadeG(f)(dB)0Step1:DesignofG(f)ƒAccordingtothespecifications,wecancompletelyparameterizeG(f).Forexample:Bandwidth:foOrder:3rdShape:ButterworthType:II(fz/fo=1/8)Re(s)Im(s)0-w0-wz-wcp60oƒOnceG(s)isspecified,assumingnopole/zerocancellationandparasitics,A(s)canbesolvedusingƒFromthelastslide,SolvingthealgebragiveswhereK,wp,andQarefunctionsofclosedloopparametersStep1:CalculationofCorrespondingA(f)SpecificationsOpenloopparametersuniquemappingTableLookupProcedureStep2:IncorporationofParasiticPoles/ZerosƒMustresolvetwokeyissues:-HowcanwespecifyanddirectlydesignG(f)?-Howcanweaccountfortheimpactofparasiticpolesandzeros?PerformanceSpecifications{type,fo,...}|A(f)|\A(f){K,fzA,fpA,...}G(f){fz,fp,...}A(f)1+A(f)=OpenLoopDesignApproachClosedLoopDesignApproachG(f)1-G(f)=A(f)G(f)9ImpactofOpenLoopParasiticPoles/ZerosIntroductionofparasiticpolesshiftsthedominantpolesExampleofatypeI,3rdordersystem,OriginalDesignnoparasiticpoledominantpolesaddedparasiticpoledominantpolesshiftawayImpactofParasiticPoleImpactofOpenLoopParasiticPoles/ZerosExampleofatypeI,3rdordersystem,OriginalDesignnoparasiticpoledominantpol