pll-oscillatoren振荡器习题讲解

Analo[e-mail]@esat.kuleuven.beKULeuvenESAT-MICASAnalogbuildingblocksforsignalprocessing2PhaseLockedLoopsAnalogbuildingblocksforsignalprocessing3TheoryThetransferfunctionofaPLLisoneorderhigherthantheorderofthelow-passfilterHlpAnalogbuildingblocksforsignalprocessing4Theory2ndordertransferfunction:InfoRealcoincidingpolesMaximumflatresponsefunction(Butterworth)Maximumflatgroupdelay(Bessel)ComplexpolesAnalogbuildingblocksforsignalprocessing5TheoryDifferentLPFs=f(typephasedetector)=secondorderPLLAnalogbuildingblocksforsignalprocessing6TheoryLoopinlockifvcntldeterminesthefrequencyoftheVCO=fVCO=fin(limitedareaaroundfreerunningfrequencyoftheVCO)Analogbuildingblocksforsignalprocessing7APLLhasanamplifierwithgainA,locatedbehindthelow-passfilter(seebelow).Theconversionfactorofthephasedetectoris3V/radandtheconversionfactoroftheVCOis50kHz/V.Thephasedetectorisanmultiplier.ThePLLisusedforthedemodulationofa5kHzsignalfrequencymodulatedonacarrierof50MHzwith±50kHzdeviation.Designapassivelead-lagfilteranddeterminethegainAinsuchawaythat:1.Themagnitudeofthetransferfunctionofthesmall-signalmodeloftheloopismaximallyflat.2.The-3dBfrequencyofthefiltermustbeequaltothebandwidthofthemodulatedsignal.3.ThelockrangemustbechosensuchthatthefrequencyoftheVCOneverexceedshalfthemaximumrange.ExplainwhathappenstothelockrangeifgainAisincreased.Exercise1:assignmentAnalogbuildingblocksforsignalprocessing8Exercise1:solutionILow-passfilter:Secondordercharacteristics(TakeKLP=A):andAnalogbuildingblocksforsignalprocessing9Exercise1:solutionIILockrange=2xmaximumdeviation:-3dBfrequencyfilter:Analogbuildingblocksforsignalprocessing10Exercise1:solutionIIIMaximumflatresponsefunction:Filtercomponents(TakeC1=10nF):Analogbuildingblocksforsignalprocessing11Exercise2:assignment•InthePLLbelowKpd=1V/Hz,KVCO=1kHz/V,R1=1kΩandC1=85nF.Thephasedetectorintroducesanextradelay∆intheloop.Whatisthemaximumvalueforthisdelayinordertohaveaminimumphasemarginof45?Analogbuildingblocksforsignalprocessing12Exercise2•PM=thephasedistanceawayfroma180phaseshiftataloopgainof11.Calculatetheloopgain(withoutextradelay)2.Calculatethefrequencyatwhichtheloopgainis13.Calculatethephaseshiftoftheloopatthatfrequency(=PMwithoutdelay!)4.Determinetheextraphasethedelayelementcanintroduce5.CalculatethedelayNote:adelayintimedomainISanextraphaseinthefrequencydomainAnalogbuildingblocksforsignalprocessing13Exercise2•Loopgain•UnitygainssRCKKsKsRCKsTVCOPDVCOPD)1(11)(+=+=()2()11996[/]PDVCOunityunityKKTsRCradsωωω==+⇔=Analogbuildingblocksforsignalprocessing14Exercise2•Onωunitythephaseis=-94.8•40.2leftforaPM=45–Tunity(period!)=6.3ms–40.2=11%ofaperiod=∆=0.11Tunity=0.7ms8.94)(−=∠unityTωAdelayinthetimedomainisaphaseshiftinthefrequencydomain!Analogbuildingblocksforsignalprocessing15OscillatorsAnalogbuildingblocksforsignalprocessing16Theory()1oscTjω≥)(sH)(sG+)(sY)(sX+)(sε()()()()1()()1()YsHsHsXsGsHsTs==++Generalnegativefeedbacksystem-Barkhausencriteria(oscillationcondition)()180oscTjω∠=−Analogbuildingblocksforsignalprocessing17Exercise1:assignmentThefigurebelowrepresentstheschemeforaWienbridgeoscillator.Theopampinthecircuitcanbeconsideredideal.AssumeR1=R2enC1=C2.1.Findanexpressionfortheoscillationfrequency.2.DetermineaminimalvalueforR4inordertohaveoscillation.3.Extra:Whathappenstothewaveformattheoutput,ifR4islargerthanitsminimalvalue.Analogbuildingblocksforsignalprocessing18Exercise1:solutionI•TransferfunctionoftheRC-network:22231111CRssRCsRCsCRsRCRsRCRVVinout++=++++=Analogbuildingblocksforsignalprocessing19Exercise1:solutionIIPhaseandamplitudeofthesecondorderRCnetworkfresAnalogbuildingblocksforsignalprocessing20Exercise1:solutionIII•Oscillationat0phaseshiftoftheRC-network(noninvertinggainstage!!).•GainoftheRC-network.22211031oscRCGbgtgRCRCωωω−∠===2222224441713RCGRCRCωωω=++=Analogbuildingblocksforsignalprocessing21Exercise1:solutionIV•Oscillationfrequency:•Gainofthegainstageshouldbeequalto3:12oscfRCπ=4343132amplifierRARRR=+==Analogbuildingblocksforsignalprocessing22Exercise2:assignmentThisLC-oscillatorhasanoperatingfrequencyof1GHz.Theinductorshaveaninductanceof5nHwithaQ-factorof4.ThebiascurrentisIis1mA.1.DeterminethevalueCofthevaractorstoachievetherequiredoscillationfrequency.ConsiderM1andM2ideal.2.DeterminetheminimumtransconductanceforM1andM2.Analogbuildingblocksforsignalprocessing23Exercise2:solutionIAmplitudecharacteristicofannon-idealparallelLC-networkfresLRRLQrespsresωω==RpAnalogbuildingblocksforsignalprocessing24Exercise2:solutionII•LCamplifier•180phaseshift(invertinggainstage)•Maximumgainatfrequency:LCfresπ21=Analogbuildingblocksforsignalprocessing25Exercise2:solutionIII•Oscillator?1.Loopgainlargerthan12.Phaseshift0Here360=OK!Analogbuildingblocksforsignalprocessing26Exercise2:solutionIV•VCO:Varactorinsteadofcapacitor.Backtobackdiodewithacommonmodepoint.•CurrentsourceforabetterdifferentialbehaviorAnalogbuildingblocksforsignalprocessing27Exercise2:solutionV152oscfCpFLCπ=⇒=OscillationfrequencyisdeterminedbytheLC-tank:Osc