Low-Power Crystal and MEMS Oscillators-Vittoz 2010.pdf
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Low-Power Crystal and MEMS Oscillators-Vittoz 2010.pdf
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SeriesEditorAnanthaChandrakasan,MassachusettsInstituteofTechnologyCambridge,MassachusettsForothertitlespublishedinthisseries,gotoIntegratedCircuitsandSCrystalandMEMSOscillatorsEricVittozTheExperienceofWatchDevelopmentsEricVittoz1015LausanneSwitzerlandISSN1558-9412ISBN978-90-481-9394-3e-ISBN978-90-481-9395-0DOI10.1007/978-90-481-9395-0SpringerDordrechtHeidelbergLondonNewYorkCoverdesign:
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2010930852EcolePolytechniqueFdraledeLausanne(EPFL)evittozieee.orgTomywifeMoniqueContentsPreface.xiSymbols.xiii1Introduction.11.1ApplicationsofQuartzCrystalOscillators.11.2HistoricalNotes.21.3TheBookStructure.21.4BasicsonOscillators.42QuartzandMEMResonators.72.1TheQuartzResonator.72.2EquivalentCircuit.82.3FigureofMerit.102.4MechanicalEnergyandPowerDissipation.152.5VariousTypesofQuartzResonators.152.6MEMResonators.182.6.1BasicGenericStructure.182.6.2SymmetricalTransducers.213GeneralTheoryofHigh-QOscillators.233.1GeneralFormoftheOscillator.233.2StableOscillation.253.3CriticalConditionforOscillationandLinearApproximation.273.4AmplitudeLimitation.273.5Start-upofOscillation.293.6Duality.303.7BasicConsiderationsonPhaseNoise.313.7.1LinearCircuit.31viiviiiContents3.7.2NonlinearTimeVariantCircuit.333.8ModeloftheMOSTransistor.364TheoryofthePierceOscillator.414.1BasicCircuit.414.2LinearAnalysis.424.2.1LinearizedCircuit.424.2.2LosslessCircuit.464.2.3PhaseStability.504.2.4RelativeOscillatorVoltages.514.2.5EffectofLosses.524.2.6FrequencyAdjustment.544.3NonlinearAnalysis.554.3.1NumericalExample.554.3.2DistortionoftheGateVoltage.574.3.3AmplitudeLimitationbytheTransistorTransferFunction.584.3.4EnergyandPowerofMechanicalOscillation.684.3.5FrequencyStability.694.3.6EliminationofUnwantedModes.714.4PhaseNoise.774.4.1LinearEffectsonPhaseNoise.774.4.2PhaseNoiseintheNonlinearTimeVariantCircuit.784.5DesignProcess.844.5.1DesignSteps.844.5.2DesignExamples.895ImplementationsofthePierceOscillator.935.1Grounded-SourceOscillator.935.1.1BasicCircuit.935.1.2DynamicBehaviorofBias.955.1.3DynamicBehaviorofOscillationAmplitude.975.1.4DesignExamples.1005.1.5ImplementationoftheDrain-to-GateResistor.1025.1.6IncreasingtheMaximumAmplitude.1065.2AmplitudeRegulation.1075.2.1Introduction.1075.2.2BasicRegulator.1085.2.3AmplitudeRegulatingLoop.1155.2.4SimplifiedRegulatorUsingLinearResistors.118Low-PowerCrystalandMEMSOscillatorsix5.2.5EliminationofResistors.1205.3ExtractionoftheOscillatorySignal.1235.4CMOS-InverterOscillator.1245.4.1DirectImplementation.1245.4.2Current-controlledCMOS-inverteroscillator.1295.5Grounded-DrainOscillator.1325.5.1BasicImplementation.1325.5.2Single-SubstrateImplementation.1336AlternativeArchitectures.1376.1Introduction.1376.2SymmetricalOscillatorforParallelResonance.1376.2.1BasicStructure.1376.2.2LinearAnalysiswiththeParallelResonator.1396.2.3LinearAnalysiswiththeSeriesMotionalResonator.1406.2.4EffectofLosses.1436.2.5NonlinearAnalysis.1446.2.6PhaseNoise.1496.2.7PracticalImplementations.1576.3SymmetricalOscillatorforSeriesResonance.1646.3.1BasicStructure.1646.3.2LinearAnalysis.1656.3.3NonlinearAnalysis.1726.3.4PhaseNoise.1776.3.5PracticalImplementation.1836.4VandenHombergOscillator.1906.4.1PrincipleandLinearAnalysis.1906.4.2PracticalImplementationandNonlinearBehavior.1936.5ComparisonofOscillators.1946.5.1PierceOscillator
(1).1956.5.2VandenHombergOscillator
(2).1966.5.3ParallelResonanceOscillator(3).1966.5.4SeriesResonanceOscillator(4).197Bibliography.201Index.203PrefaceIntheearly60s,thewatchmakingindustryrealizedthatthenewlyinventedintegratedcircuittechnologycouldpossiblybeappliedtodevelopelectronicwristwatches.Butitwasimmediatelyobviousthattheprecisionandstabilityrequiredforthetimebasecouldnotbeobtainedbypurelyelectronicmeans.Amechanicalresonatorhadtobeused,combinedwithatransducer.Thefre-quencyoftheresonatorhadtobelowenoughtolimitthepowerconsumptionatthemicrowattlevel,butitssizehadtobecompatiblewiththatofthewatch.Afterunsuccessfulresultswithmetallicresonatorsatsonicfrequencies,ef-fortswereconcentratedonreducingthesizeofaquartzcrystalresonator.Severalsolutionsweredevelopeduntilastandardemergedwithathintun-ingforkoscillatingat32kHzandfabricatedbychemicaletching.Afterfirstdevelopmentsinbipolartechnology,CMOSwassoonidentifiedasthebestchoicetolimitthepowerconsumptionoftheoscillatorandfrequencydividerchainbelowonemicrowatt.Low-poweroscillatorcircuitsweredevelopedandprogressivelyoptimizedforbestfrequencystability,whichisthemainrequirementfortimekeepingapplications.Morerecentapplicationstoport-ablecommunicationdevicesrequirehigherfrequenciesandalimitedlevelofphasenoise.Micro-electro-mechanical(MEM)resonatorshavebeende-velopedrecently.Theyusepiezoelectricorelectrostatictransductionandarethereforeelectricallysimilartoaquartzresonator.Theprecisionandstabilityofaquartzisseveralordersofmagnitudebet-terthanthatofintegratedelectroniccomponents.Hence,anidealoscillatorcircuitshouldjustcompensatethelossesoftheresonatortomaintainitsos-cillationonadesiredmodeatthedesiredlevel,withoutaffectingthefre-quencyorthephaseoftheoscillation.Optimumdesignsaimatapproachingthisidealcasewhileminimizingthepowerconsumption.xixiiPrefaceThisbookincludestheexperienceaccumulatedalongmorethan30yearsbytheauthorandhiscoworkers.ThemainpartisdedicatedtovariantsofthePierceoscillatormostfrequentlyusedintimekeepingapplications.OtherformsofoscillatorsthatbecameimportantforRFapplicationshavebeenadded,aswellasananalysisofphasenoise.Theknowledgeisformalizedinananalyticalmanner,inordertohighlighttheeffectandtheimportanceofthevariousdesignparameters.Computersimulationsarelimitedtoparticularexamplesbuthavebeenusedtocrosscheckmostoftheanalyticalresults.ManycollaboratorsofCEH(CentreElectroniqueHologer,WatchmakersElectronicCenter),andlaterofCSEM,havecontributedtotheknow-howdescribedinthisbook.Amongthem,byalphabeticorder,DanielAebischer,LucAstier,SergeBitz,MarcDegrauwe,ChristianEnz,JeanFellrath,ArminFrei,WalterHammer,JeanHermann,VincentvonKaenel,HenriOguey,andDavidRuffieux.SpecialthanksgotoChristianEnzforthenumerousdiscus-sionsaboutoscillatorsandphasenoiseduringtheelaborationofthisbook.EricA.VittozCernier,SwitzerlandFebruary2010SymbolsTable0.1Symbolsandtheirdefinitions.SymbolDescriptionReferenceaPowerfactoroftheflickernoisecurrent(6.71)ANormalizedtransconductanceinseriesresonanceoscillator(6.108)BNormalizedbandwidthinseriesresonanceoscillator(6.108)Ca,CbFunctionalcapacitorsFig.6.37CDCapacitancebetweendrainsFig.6.1CLLoadcapacitanceinseriesresonanceoscillatorFig.6.16Cm(Cm,i)Motionalcapacitance(ofmodei)Fig.2.2CPTotalparallelcapacitanceoftheresonator(2.22)CsSeriesconnectionofC1andC2(4.9)CSCapacitancebetweensourcesFig.6.1C0Parallelcapacitanceofthedipoleresonator(2.1)C1Totalgate-to-sourcecapacitanceFig.4.1C2Totaldrain-to-sourcecapacitanceFig.4.1C3TotalcapacitanceacrossthemotionalimpedanceFig.2.2EmEnergyofmechanicaloscillation(2.23)fFrequencyfmMotionalresonantfrequency(4.140)fsFrequencyofstableoscillation(3.24)fs(mv)Fundamentalfunctioninstronginversion(6.37)fw(vin)Fundamentalfunctioninweakinversion(6.30)FaFlickernoisecurrentconstant(6.71)GaReferenceconductancefortheflickernoisecurrent(6.71)GdsResidualoutputconductanceinsaturation(3.57)GmGatetransconductanceofatransistor(3.53)continuedonnextpagexiiixivSymbolscontinuedfrompreviouspageSymbolDescriptionReferenceGmsSourcetransconductanceofatransistor(3.49)GmdDraintransconductanceofatransistor(3.49)GmcritCriticaltransconductanceforoscillationFig.4.4Gmcrit0CriticaltransconductanceforlosslesscircuitFig.4.6GmlimLimittransconductanceinseriesresonanceoscillator(6.109)GmmaxMaximumpossibletransconductanceforoscillationFig.4.4GmoptOptimumvalueoftransconductanceFig.4.4Gm
(1)Transconductanceforthefundamentalfrequency(4.54)GviTransconductanceoftheregulator(5.52)hs(mi)Transconductancefunctioninstronginversion(6.142)IB0(x)ModifiedBesselfunctionoforder0(4.59)IB1(x)ModifiedBesselfunctionoforder1(4.61)IcCircuitcurrentFig.3.1IcsValueofIcatstableoscillation(3.6)IDDraincurrentFig.3.10ID0DCcomponentofdraincurrent(5.1.2)ID
(1)FundamentalcomponentofIDFig.4.13IFForwardcomponentofdraincurrent(3.40)ImMotionalcurrentFig.2.2ImsValueofImatstableoscillation(3.6)IRReversecomponentofdraincurrent(3.40)IspecSpecificcurrentofatransistor(3.41)I0BiascurrentoftheoscillatorFig.4.13I0startStart-upvalueofbiascurrent(5.45)I0critCriticalvalueofbiascurrentI0Fig.4.14I0critminCriticalcurrentinweakinversion(4.64)I1Complexvalueofthesinusoidaldraincurrent6.3.2.3ICInversioncoefficientofatransistor(3.45)IC0InversioncoefficientatI0=I0crit(4.72)kcCapacitiveattenuationfactor(4.69)KfFlickernoisevoltageconstantofatransistor(3.62)KfiFlickernoisecurrentfunction(3.36)KfvFlickernoise
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