COMS3100/7100 I t d ti to Introduction t Communications
Lecture12: GenerationandDetectionofFMandPM
Thislecture: DirectFMandVCO PhaseModulatorsandIndirectFM OpticalPhaseModulatorsandindirectAM FrequencyDetection
Ref: Carlson,Chapter5;Haykin,Chapter2.7
PhaseModulation(PM)
c (t ) = c t + (t )
PMdefined:Phasemodulationis thatformofanglemodulationin (t ) = x(t ); 180o whichtheanglec(t)isvaried linearlywiththemessagesignalx(t) I Instantaneous phase h varies i directly di l withthemodulatingsignal Ph modulation Phase d l ti index i d orphase h deviation isthemaximumphase x (t ) = A cos[ t + x(t )] c c c shiftproducedbyx(t) 180o < <180o
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FrequencyModulation (FM)
Totalphaseangleconsistsofthe constantrotationaltermct and(t)
c (t ) = c t + (t )
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Instantaneousrateofrotation 1 d c (t ) 1 d (t ) orinstantaneousfrequency f(t) f (t ) = = fc + 2 dt 2 dt isgivenby FMdefined:Frequency f c + f x(t ), f < f c modulationisthatformofangle f (t ) = modulationinwhichthe instantaneousfrequencyf(t)is variedlinearlywiththemessage signalx(t) NB:instantaneousfrequency f isfrequencydeviation or f(t) isnotthespectral maximumshiftfromcarrierfc frequencyf
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GenerationandDetectionof fFMandPM
Todaywewilldiscussthebasicmethodsforgenerationanddetection ofFMandPM Communicationsystemsareelectrical(RFandMicrowave)and optical.Differentenablingtechnologyisinvolvedforangle modulationinthesetwofields. fields However,operationprinciplesareexactlythesame. Inbothcasesweneedtoestablishamethodforlinearchangeofthe instantaneousphase(PM)orfrequency(FM)withthemessagesignal Thisrequiresdevicesthatwillproducephaseorfrequency deviationinalinearfashion. fashion Suchdevicesaretypicallyhardtoobtaininpractice,especiallyover awideoperatingrange(freq.). However,constantamplitudepropertyisadvantagetohardware implementation Constantpowerinputsignal Canuselimiters/zerocrossingdetection
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FMProcessing gwithhardlimiter
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(a) ( )Signal g (b) ( )Signal g +noise(c) ( )output p oflimiter(d) ( )output p ofLPF
Hardlimiter (0vcomparator)
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DirectFM voltage g andcurrentcontrolledoscillators
Optical
frequency eque cyof o the t equantum qua tu oscillator osc ato (laser) ( ase )ca canbechanged c a gedby changingthecurrentthroughthedevice.Thisfrequentlyoccursas asideeffectoftheAMcausingfrequencychirp. directFMmodulationisstraightforward;itrequiresonlyavoltage controlledoscillator(VCO) whoseoscillationfrequencyisalinear functionoftheappliedvoltage
RF&Mi Microwave
Theoutputvoltageneedstobeoftheform:
V0 (t ) = V0 cos(c t + K v Vmessage (t )dt )
Th i The instantaneousf frequencyis i then: h as f (t ) =
d (t ) = (c t + K v Vmessage (t )dt ) = c + K v Vmessage (t ) dt f (t ) = f c + f Vmessage (t )
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1 dc (t ) 2 dt
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DirectFMandVCOs
InRF/microwaveregionthiscanbedoneusingavariable reactance elementasp partoftheLCresonantcircuit.
RFC=RFchoke(blockshighfrequencies) VB =VoltagebiassoCv(t) = Cx(t) - voltagecontrolledcapacitor
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DirectFMandVCOs
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Thisisdirectfrequencymodulationwithf=(C/2C0)fc Theapproximationisgoodto1%when C/C0<0.013; <0 013;theattainable frequencydeviationis C i.e.,Cx(t) issmall f = f c 0.006 f c IfW <<fc then h 2C0 Cx(t) isslow COMS3100
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DirectFMandVCOs
TypicalvaractorVCcurve isfarfromlinearandcan beapproximatedby Below:aHartleyoscillator withtuningbetween74 and105MHz
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DirectFMof fasemiconductorlaser
Mostofthetimethisisexactlywhatyouwanttoavoid
Detrimentaltolonghaulopticalcommunications causeswavelength chirp hi
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However,FMoflasercarrierfrequencycanbeefficientlyusedinlaser rangefinders
Lasercurrentmodulationis appliedtochangethelaserpower andatthesametimethe instantaneousfrequency Differentiatedpowerwaveform producesseriesofsharppeaks duetointerferencewithreflection Distanceisproportionaltothe averagetimeseparationbetween thepeaks Notabsolute(liketimeof flight)
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PhaseModulation/IndirectFMmodulation
Implementationisrelativelyeasy Carriercanbesuppliedbyafixedfrequencysource, source e e.g., g a microwavePLLsynthesiser/distributedfeedback(DFB)laser Integratingtheinputsignaltoaphasemodulatorproduces theFMoutput
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fc = | |nf fc1 fLO|
f1 (t ) = f c1 + x(t ) 2 T
f 2 = nf1 = nf c1 + f x(t ),
f = n 2T
Theintegratorandthephasemodulatorconstitutea narrowband b dfrequency f modulator d l
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NarrowbandPhaseModulator
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Basedonapproximation xc(t) Ac cos(wct) - Ac x(t) sin(wct) validif| x(t) | << 1 radian
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Switching gcircuitPM
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FlipflopPMsquarewave BPFisPMoutput
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Frequency q yDetection
Frequencydetector(discriminator),producesanoutput voltagethatshouldvarylinearlywiththeinstantaneous frequencyoftheinput. Discriminatorcircuitscanbetypicallyclassifiedasoneofthe following
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FMtoAMconversion Phaseshiftdiscrimination Zerocrossingdetection Frequencyfeedback
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FMtoAMconversion
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AM
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