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).

2 DmDDtmdttdmDDtmtfpfppfpf = =)()()()(Couch, 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 , 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.

3 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: 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.

4 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.

5 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))

6 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. All rights reserved. 0-13-142492-0 Figure 5 11 Magnitude spectra for FM or PM with sinusoidal Modulation for various Modulation indexes.

7 1(2cos()1()2cos()1())1(2cos()1(11011tffJ AtfJAtffJAcccccc ==+= 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.))

8 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()(ffmouttftnfjt jnntfjtjondmnDtneeeetscc ==== 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.

9 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.

10 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+().