xviiPrefaceFinally Chapter7 will make use of the oscillators to realize frequency syn-thesizersfor radiofrequencies. Spectral purityperformance will beaddressed,in addition to the design of low-power frequency dividers and high speed phase-frequency detector/charge-pumpcombinations.Manybooks,papers and internal technical notes fromPhilipsResearch con-tributed in making the presented material state-of-the-art.The authors do notpretend thatthis bookis complete,however;eachchaptercouldprovideenoughdiscussion for a book in itself. The authors would therefore want to apologizeforanyimperfections.AcknowledgementsWe are indebted to many people for their advice, assistance, and contributionsto the development of this text; it is impossible to include all of their names.Wewould especially liketothankPeterdeVreedeandEdwinvanderHeijdenfor their contributionstothedesigns of theLNAs inChapter3.Wewouldalsoliketo thankTirdad Sowlati, SifenLuo and VickramVathulyafor their helpfuldiscussions on thePA chapter.ThebipolarPA design is a result of theirre-search activities.Many thanks are alsogiven to William Redman-Whiteforhissupport on the difficult noise measurements of the mixers.We would also liketo thankHenk JanBergveldfor contributions toChapter 2.The Chapter on os-cillators was reviewed by Peter Baltus, Hans Hegt, Dieter Kasperkovitz, ArthurvanRoermund and Pepijn vandeVen.Theyprovided veryuseful feedback.Zhenhua Wang gave substantial contributions for the section on low-power pro-grammable dividers,andDieterKasperkovitz, Jon Stanley and OnnoKuijkenforthe sectiononhigh speedphase-frequency detector/charge-pump combina-tions.The authors are indebted to all reviewers for theirkind assistance.DOMINE LEENAERTS,JOHANVANDERTANGANDCICEROVAUCHER
xixGLOSSARYUnitSymbolDescriptionrelative magnitude of the phase noise due to loopαif(fm)filterelementsdBcrelative amplitude ofa spurious signal with respectasptothe carrierm?AareaAeamplitudeerrorAppower conversion gainAuvoltage gainVALOamplitude of the carrier signalVAspamplitude ofa spurious signalbratioofthetime constants of theloopfilter t2/t3βsmall-signal common-emitter currentgainβ(jw)transfer function in oscillator feedback modelFccapacitanceFC1,C2capacitancesoftheloopfilterFCabdrain-bulk capacitanceFfixed capacitance in resonator circuitC fixedFCgdgate-drain capacitanceFCggintrinsicgate capacitanceFCgsgate-source capacitanceFCjscollector-substratejunction capacitanceFCjuncdrain junction capacitancedBc/Hzcarrier to noise ratio at offsetfrequency fmCNR(fm)dBc/HzCNRnormnormalized carrier to noise ratioFCμucollector-base capacitanceFCpcapacitancein parallel resonator circuitFCparparasitic capacitanceFC#emitter-base capacitanceFCscapacitance with series resistanceFCshsource-bulk capacitancedBCPidB1-dB compression point (output referred)Sepduty-cycle of the outputpulseof a charge-pumpevEgbandgap energyF/mdielectric constantEF/moxidepermittivity(=3.45-10-15F/m)EoxF/mvacuumpermittivity(=8.8510-16F/m)E0S2characteristic impedance in free space (= 377 2)no
xxCIRCUITDESIGNFORRFTRANSCEIVERSpa(fm)rad//Hzrms phasenoisepowerdensityof main dividerpephaseerrorradpe,(fm)equivalent synthesizer phase noise floor at the inputrad?/Hzof thephase detectori;(fm)open-loop phase noise power density generated byrad?/Hztheloopfilterelementsdmphase margin (radians in equations, degrees in figures)Φ:(fm)phase noise power density of the PLL output signalrad-/Hzpalp(fm)"low-pass"phase noisepowercomponent of(fm)rad?/Hzpahp(fm)"high-pass"phasenoisepowercomponentof2(fm)rad?/HzΦpa(fm)rms phase noise power density of phase frequencyrad//Hzdetectorprer(fm)rad//Hzrms phase noise powerdensity of reference dividerduco(fm)rms phase noisepowerdensityof free-runningVCOrad//Hzpx(fm)rmsphasenoisepowerdensityofcrystal oscillatorrad//HzffrequencyHz8fresidual FMHzAfpeak frequency deviation of a carrierHzfaavailablebandwidthHzfeopen-loop bandwidth, 0 dB cross-over frequencyHzfeenerHzcenterfrequencyfaiufrequency of the signal at the output of a frequencyHzdividerfmHzfourier frequency (offset,modulation or basebandfrequency)fmaxHzmaximumoscillation frequencyfminHzminimumoscillationfrequencyfascHzoscillation frequencyfoutHzoutput limitedfrequencyfrefHzoperationfrequencyof thePFDfuHzinput limited frequencyfrHzcut-off frequencyfxtalfrequency of crystal oscillatorHzFnoise factorFouroutput frequency of a PLLHzFOMnfigure of meritrelatedtoparameternrreflectioncoefficientGgain
xxiG(s)open-looptransferfunction of aPLLGaavailablepowergainA/Vtransconductancegmminimumtransconductanceforoscillator startupgm-startupGmaxmaximum powergainGp(delivered)power gainGTtransducer gainH(s)closed-looptransferfunction of aPLLH,(jo)transferfunction in oscillatorfeedback modelArms carrier currenticarrier=rms1AcurrentAlepamplitude of the output current of a charge pumpAIteakleakage current inthe tuning lineof theVCOAloutinstantaneous output current of a charge pumpAItailtail current of a differential pairAlrunetuning currentdBIPnn-thorderinterceptpointdBIIPnn-th order input referred interceptpointdBIMnn-th order intermodulationIA3/Hzmean square noise current over a bandwidth fTiamarA?/Hzbipolar output noise current in 1 HzTAMOSA3/HzMOSoutput noisecurrent in1HzT'nose-orA2/Hzclosed loopmeansquare noiseoutput currentin1HzkBoltzmann's constant (=1.38 . 10-23 J/K)J/Kkppropagation constantKecoHz/ACCOtuning constantHz/AKrailrmsrms sensitivity of foscfor tail currentvariationsKpdA/radgain of PFD/CP combinationKucoHz/VVCO tuning constantC(fm)SSB phase noise to carrier ratio at offset fre.fmdBc/HzLHinductanceLlength oftransistorm入wavelengthmLfingerfinger length of transistormHLpinductance inparallel resonator circuitHLinductance with series resistancenan integerNnumberof oscillatorstagesNmain divider division ratio, integer
xxiiCIRCUITDESIGNFORRFTRANSCEIVERSNBWnoisebandwidthHzNFnoise figuredBOIPnn-th order output referred intercept pointdBPauavailablepowerWPerrierWcarrier powerPDCWDC input powerPdeldelivered powerwPaissWpower dissipationPinWinput powerProisesource resistance noise powerdBm/HzPoWoutputpowerPRFWRF outputpowerPWtransmitted power0phase shiftrad0(t)stochastic phase variableradpradpeak phase deviation ofphase modulationcharge of the electron (=1.602 . 10-19 C)cqQqualityfactorQercapacitorquality factorQLCqualityfactorof parallel resonatorcircuitQtsinductor quality factorQRCRCoscillatorqualityfactorRreference divider division ratio, integerR2resistanceR1S2resistanceusedinthePLLloopfilterRatiouarvaractorcapacitanceratiorb2base resistanceReff2effective bulkresistanceRg2gate resistance (due to poly)R;2input resistanceRin2gate resistance due to non-quasi static behaviorRL2load resistanceR.2output resistanceRp2loss resistance in parallel resonator circuitR,radiation resistance2R.2source resistanceRseriesS2series resistance2rnbase-emitter resistanceRsheet resistance2/口presistivityof metal2.cm