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NTUEEShen-IuanLiuAnalysisandDesignofPhase-LockedLoopsProf.Shen-IuanLiuDepart.ofElectricalEngineeringNationalTaiwanUniversityTaipei,Taiwan10617,R.O.C.Tel.:(02)23635251ext.239Fax:(02)23671909Email:lsi@cc.ee.ntu.edu.twNTUEEShen-IuanLiuBlockdiagramofaphase-lockedloopR1φLPFN1CrystalreferenceReferencedividerPhasedetectorfrfpLoopfilterVCOfoutMaindividerNTUEEShen-IuanLiuLinearmodelofaphase-lockedloopI2πθiθio+-F(s)Kos1NKd=NTUEEShen-IuanLiuLoopFilter(2ndOrder)C1C2R2IVVI=F(s)=(R2+1sC2)!1sC1=sC2R2+1s(sC1C2R2+C1+C2)F(s)=1C1+C2sT2+1s(sT1+1)whereT1=R2C1C2C1+C2,T2=R2C2!Z=T2−1,!p=T1−1=!Z(1+C2C1)NTUEEShen-IuanLiuOpened-LoopResponseG(s)F(s)!P!ZOpened−loopgainG(s)=KdKoF(s)sN(!)P!CNTUEEShen-IuanLiuOpened-LoopResponseGain:−G(s)|s=j!=−KdKo(1+j!T2)!2C1N(1+j!T1)T1T2Phase:(!)=tantantan−1(!T2)−tantantan−1(!T1)+180oLetd(!)d!=oat!=!C!C=1T1T2P=tantantan−1(!CT2)−tantantan−1(!CT1)MaximumPhaseMarginNTUEEShen-IuanLiuOpened-LoopResponse!=!C!|G(j!c)|=1!C1=KdKoT1!C2NT21+j!CT21+j!CT1T1=secsecsecP−tantantanp!CandT2=1!C2T1Hence,ifωcandφparespecified,C1=T1T2KdKo!C2N1+(!CT2)21+(!CT1)2C2=C1(T2T1−1)R2=T2C2NTUEEShen-IuanLiuClosed-LoopResponse Opened−loopgainG(s)=KdKoF(s)sNClosed−loopgainH(s)=NG(s)1+G(s)=++=ωω=+=++=⇒ωωNTUEE Shen-IuanLiuClosed-LoopResponse==ωω=⇒ωωωω=≡ωωω=!ωωω++++=+= NTUEEShen-IuanLiuωωωωωω+−++−−−−−+=Closed-LoopResponse−==ξωωωωξωξωξξω+++−+−=ωωωωωωωωωω+−+++=++++=⇒NTUEEShen-IuanLiuDesignStrategy•Openloopconsiderations•SetC220•C1for65°phasemargin•Setωcωref/5•Setphasemargintoatleast65°oratmaximumP=2tantantan−1(C2C1+1)−#2NTUEEShen-IuanLiuDesignStrategy•Closeloopconsiderations•SetC220•C1for65°phasemargin•Setωnωref/10•DetermineoptimalvaluesforPMandωcP=2tantantan−1(C2C1+1)−#2•Setζ=1andωp/ωn10!C=1R2C2C2C1+1•DetermineoptimalvalueforICHgivenR2ICH2#=NKoC1(R2C2)2(C2C1+1)3/2NTUEEShen-IuanLiuReferenceSpurAttenuation•Currentswitchingnoiseinthedividersandthechargepumpcircuitatthereferencerate,Fref,maycauseunwantedFMsidebandsatRFoutput.•Thespurioussidebandscancausenoiseinadjacentchannels.Additionalattenuationfromtheaddedpassiveloopfilterisrequired.R3C3R2C2C1ChargepumpVCO•3rd-orderfilterNTUEEShen-IuanLiuDesignofthe3rd-orderfilterAtten=20logloglog[(2#FrefR3C3)2+1]whereT3#R3C3•TheaddedattenuationfromthelowpassfilterisT3=10(Atten/20)−1(2#Fref)2•Intermsoftheattenuationofthereferencespursaddedbythelowpasspole,onehave5!c1T3and1T3fref•RecommendedvalueofT3isNTUEEShen-IuanLiu•Thenewopenloopunitygainfrequency(loopbandwidth)canbeapproximatedtobe!C=tantantan(T1+T3)[(T1+T3)2+T1T3]$[1+(T1+T3)2+T1T3[tantantan(T1+T3)]2−1]C1=T1T2KdKo!C2N$[1+!C2T22(1+!C2T12)(1+!C2T32)]1/2C2=C1(T2T1−1)andR2=T2C2T2=1!C2(T1+T3)Designofthe3rd-orderfilter•Theapproximationforωccanbeusedupto1/5fref.NTUEEShen-IuanLiuDesignExample•Asaruleofthumb:C3%C110andR32R2•ThevalueofC3mustincludetheinputcapacitanceofVCO.Ko=20MHz/vI=5mAFRF=900MHzFref=200kHzN=FRFFref=4500!p=2#20kHz=1.256e5P=450Atten=20dBNTUEEShen-IuanLiuDesignExampleT1=secsecsecP−tantantanp!C=3.29e−6T3=10(20/20)−1(2#200e3)2=2.387e−6!C=(3.29e−6)[(3.29e−6+2.387e−6)2+3.29e−62.387e−6]$[1+(3.29e−6+2.387e−6)2+3.29e−62.387e−6(3.29e−6+2.387e−6)]2−1]!C=7.045e4T2=1(7.045e4)2(3.29e−6+2.387e−6)=3.549e−5C1=3.29e−63.549e−5(5e−3)(20e6)(7.045e4)24500$[1+(7.045e4)2(3.549e−5)2(1+(7.045e4)2(3.29e−6)2)(1+(7.045e4)2(2.387e−6)2)]1/2C1=1.085nFC2=10.6nFandR2=3.35k$IfR3=22k$thenC3=106pFNTUEEShen-IuanLiuPLLBehaviorSimulationbySimulinkNTUEE Shen-IuanLiuPhaseNoiseAtypicalsinusoidalsignalVout(t)=A(t)coscoscos(2#fot+(t))Neglectingamplitudenoise,Vout(t)=2Pcoscoscos(2#fot+(t))theinstantaneousfrquencyforVout(t),f(t)=fo+d(t)dt#fo+%f,For%ffothepowerspectrumS%f=f2SNTUEEShen-IuanLiuPhaseNoiseIf(t)1radian,basedonthenarrowbandFMapproximation,Vout(t)=2pcoscoscos(2#fot+(t))&2Pcoscoscos(2#fot)−2P(t)sinsinsin(2#fot)TheapproximatedRFspectrumisSv(f)'2P4{&(f−fo)+S(f−fo)+&(f+fo)+S(f+fo)}TheSingle-SidebandPhaseNoiseReferencedtoCarrier,L(f)L(f)#fo+f−12fo+f+12SV(f#)df#CarrierPowerL(f)'12S(f)NTUEEShen-IuanLiuNoiseResponseI2πθθioF(s)KosKd=+++θθlprefθ1Nvcoθd++-Lowpass'o'ref='o'd=NG(s)1+G(s)Bandpass'o'lp=NKo/s1+G(s)Highpass'o'vco=N1+G(s)NTUEEShen-IuanLiuNoiseResponseS(f)=Sref(f)N2G(s)1+G(s)2+Slp(f)N2Ko/s1+G(s)2+Svco(f)N211+G(s)2+Sd(f)N2G(s)1+G(s)2,s=j2#f•Thepowerspectrumsaremultipliedbydivider’sratio,N.•ThecrystalreferenceandcounteraretheonlysignificantcontributorsinthebandwidthofthePLL.•AtoffsetfrequencygreaterthanthePLLBW,theVCO’sphasenoiseisdominant.NTUEEShen-IuanLiu NTUEEShen-IuanLiu ωfPLL