FM- Frequency Modulation PM - Phase Modulation

1 11FM- Frequency ModulationPM - Phase ModulationEELE445-14 Lecture 30 DSB-SC, AM, FM and PM()[] == =+==tfpdmjDctmjDcccceAtgeAtgtmjtmAtgtmAt gtmAtg )()()()()( )()()(1)()()( :EnvelopeComplex FM :EnvelopeComplex PM :EnvelopeComplex SC-SSB :EnvelopeComplex AM :EnvelopeComplex SC-DSB2FM and PM[][])(cos)(Re)()()()()()()(ttAetgtsAtg tReAetRtgcctjctjctjc +== ====:signal modulated-angle dTransmitteconstantis power constant ais envelope real the EnvelopeComplex FM and PM[][]voltHzDvoltradDdmDtvoltradDtmDtttA etgtsfftfppcctjc 2sec)()()()()(cos)(Re)(= = =+== constant Modulation or deviation Frequency :FM for constant Modulation or ysensitivit Phase :PM for:signal modulated-angle dTransmitte3FM and PMRelationship between mf(t) and mp(t): dmDDtmdttdmDDtmtfpfppfpf = =)()()()(Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc.

2 All rights reserved. 0-13-142492-0 Figure 5 8 Angle modulator circuits. RFC = radio- Frequency , Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0 Figure 5 8 Angle modulator circuits. RFC = radio- Frequency Frequency 2)()(21)(21)())(cos()(cos)(cos)()(tfdttd ttfttAPMorFMtAttRtsciiccc += ==+===:is Hz in frequencyous instantane The5FM and PM differencesradianstmDtp)()(= PM: instantaneous phasedeviation of the carrier Phase is proportional to the amplitude of m(t)voltradiansinDp Modulation Constant Modulation sensitivity Phase sensitivity 2)(2)(2)()()()()(tmDftfdttdtftmDttttpcci pcc +=+==+=+=: Hz in frequencyous Instantane:radians in phaseous InstantaneFM and PM differencesFM: instantaneous Frequency deviationfrom the carrier Frequency is proportional to m(t)radiansdmDttf = )()( 2)(2)(2)()()()()(tmDftfdttdtfdmDttttfcci tfcc+=+==+=+= : Hz in frequencyous instantane The:radians in phaseous instantane Thesec voltradiansinDf6FM and PM differencesFM.

3 Instantaneous Frequency deviationfrom the carrier Frequency is proportional to m(t))(21)(21)()(tmDtftftffcid == voltHzvoltradKDvoltradiansKDffpp 2sec= = = Modulation ConstantsFM[]m(t) of bandwidth the is indexmodulationfrequencydeviationfrequen cypeakdeviationfrequencyBBFtmVVDdttdFdtt dftftffppfcid = == = = = )(max21)(21max)(21)()(7PM and digital Modulation [][]spT duration, symbol one in change Phase pk-pk the is 2 where :index Modulation the signals Digital For then deviation, Frequency peak same the have signals FM and PM the that such set signal sinusoidal a is m(t) when:noteindex Modulation phasedeviationphasepeak deviation Phase = = === 2)(max)(max)(htmVVDttfppppCouch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0 Figure 5 9 FM with a sinusoidal baseband modulating , Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc.

4 All rights reserved. 0-13-142492-0 Figure 5 9 FM with a sinusoidal baseband modulating from PM and PM from FM9FM/PM s(t) waveformsFM and PM with m(t)=cos(2 fmLet For PMFor FMDefine the Modulation indices:10FM and PM SignalsDefine the modulationindices:FM and PM SignalsThen 11 Spectrum Characteristics of FM FM/PM is exponential modulationLet()))2sin(2(Re))2sin(2cos()( tftfjcmccmceAtftfAtu +=+=)2sin()(tftm =u(t) is periodic in fmwe may therefore use the Fourier seriesSpectrum Characteristics of FM FM/PM is exponential Modulation ()))2sin(2(Re))2sin(2cos()(tft fjcmccmceAtftfAtu +=+=u(t) is periodic in fmwe may therefore use the Fourier series12 Spectrum with Sinusoidal Modulationu(t) is periodic in fmwe may therefore use the Fourier series)2sin()(tfjmetg =JnBessel Function13 JnBessel FunctionTABLE 5 2 FOUR-PLACE VALUES OF THE BESSEL FUNCTIONS Jn( )14 TABLE 5 3 ZEROS OF BESSEL FUNCTIONS: VALUES FOR WHEN Jn( ) = 0 Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc.)

5 All rights reserved. 0-13-142492-0 Figure 5 11 Magnitude spectra for FM or PM with sinusoidal Modulation for various Modulation indexes.))1(2cos()1()2cos()1())1(2cos()1 (11011tffJAtfJAtffJAcccccc ==+= 15 Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0 Figure 5 11 Magnitude spectra for FM or PM with sinusoidal Modulation forvarious Modulation Narrowband Frequency ModulationWBFM - Wideband FrequencyModulation Carson s Bandwidth RuleEELE445-14 Lecture 3116 Narrowband FM Only the Joand J1terms are significant Same Bandwidth as AM Using Eulers identity, and (t)<<1:Notice the sidebands are sin , not cos as in AM Narrowband FM as a PhaserAMNBFM17 Frequency Multiplication:Wideband FM from Narrowband FM(s(t))nsi(t) c FMso(t)n x cn x FM The Output Carrier Frequency = n x fc The output Modulation index = n x fm The output bandwidth increases according to Carson s Rulemin2)(2)()()()Re()Re()(ffmouttftnfjtjnntfjtjondmnDtneeeetscc ==== Effective Bandwidth- Carson s Rule for Sine Wave ModulationWhere is the Modulation index fmis the sinusoidalmodulation Frequency Notice for FM, if kfa>> fm, increasing fm does not increase Bcmuch Bcis linear with fmfor PM18 Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc.

6 All rights reserved. 0-13-142492-0 Figure 5 11 Magnitude spectra for FM or PM with sinusoidal Modulation forvarious Modulation , Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0 Figure 5 11 Magnitude spectra for FM or PM with sinusoidal Modulation forvarious Modulation , Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0 Figure 5 11 Magnitude spectra for FM or PM with sinusoidal Modulation for Various Modulation m(t) is a sum of sine waves20 When m(t) is a sum of sine wavesSideband PowerSignal Amplitude:Ac1V:=Modulating Frequency :fm1 KHz:=Carrier peak deveation: KHz:= Modulation index: ffm:= equation:xt() nAcJn n ,() cos cn m +()t =Power in the signal:PcAc221 := W=Carsons rule bandwidth:BW2 1+() fm := 1s=Order of significant sidbands predicted by Carsons rule:nround 1+():=n3=Power as a function of number of sidebands:Psumk()k knAcJn n ,() ()221 =:=Percent of power predicted by Carsons rule: Psumn()Pc100 vs OF TOTAL POWERP sumk()Pc100 kSideband Power = :=JkJn k ,():= ()2:=n3=P021njPj = + 10= 10=22 Sideband Power = := :=n1:=VjJn j ,():=UjVj()2:=U021njUj = +1= = 0 =Sideband Power = :=n1:=WjJn j ,():=XjWj()2.

7 =X021njXj = + = =23 Modulation_index 18=ffcn1+()Fm fcnFm (),fcn1+()Fm + ..:=Bf() ffcn0+()Fm +, ffcnFm ,()+:=Si f()AcJ0 M()() ffc,() 1nkJn k M,() ffckFm +(), 1 ()kJn k M,() ffckFm (), + =+ :=Modulation_index M:=n9=Bandwidth2 n Fm :=2 * n is the number of significant sidebands per Carsons rulenround M1+():=Mx10:=Modulating Frequency - single sinewaveFm100:=fc0104 :=Ac1:=79FM/PM Modulation index: set to /2 for peak Phase dev of /2set to f/fm for Frequency Modulation . spectrumis the same for : avo 09/21/04last edit date:2/27/07 =.4, Sideband Level = /2 for Narrowband FM210 1 Sided SpectrumPeak J01st Sidebands J12nd Sidebands J2 Bessel FunctionsModulation_index24 =.9, Sideband Level = /2 for Narrowband Sided SpectrumPeak J01st Sidebands J12nd Sidebands J2 Bessel FunctionsModulation_index = , Carrier Null420 2 Sided SpectrumPeak J01st Sidebands J12nd Sidebands J2 Bessel FunctionsModulation_index25 = , first sideband Sided SpectrumPeak J01st Sidebands J12nd Sidebands J2 Bessel FunctionsModulation_index = , second sideband Sided SpectrumPeak J01st Sidebands J12nd Sidebands J2 Bessel FunctionsModulation_index26 Power vs BW, = term includes power in +Jn and power in -Jn, the upper and lower sideband pairsPMn,()J0 M()221nkJn k M,()2 =+ := power vs bandwidthNumber of Sideband pairsPMk,()Ac22100 2=HzPMn,()Ac22100 100=Power vs BW, = power vs bandwidthNumber of Sideband pairsPMk,()Ac22100 4=HzPMn,()Ac22100 vs BW, = 123456785060708090100% power vs bandwidthNumber of Sideband pairsPMk,()Ac22100 ,()Ac22100