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FrequencyandPhaseModulation
SharleneKatzJamesFlynn
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Overview
• History• WhyFM?Noiseproblemswithlinearmodulationsystems:AM/SSB/DSB
• Definitions:Deviation,WBFM,NBFM
• VerypopularforVHFvoice
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DefinitionofanFMSignal
• Forabasebandsignal,x(t):
– kfisthefrequencydeviationconstantinHz/volt– Aconstantenvelopesignalwithvaryingfrequency/phase
– Theinstantaneousfrequencyis:
– Maximumfrequencydeviation=Δf=kf|x(t)|max
�
xFM (t) = Ac cos 2πfct + 2πk f x τ( )dτ−∞
t∫[ ]
�
fi(t) = fc + k f x(t)
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FMSignal‐TimeDomain
• Forapulsetrainbasebandsignal:
Basebandsignal,x(t)
FMsignal
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FMSignal‐TimeDomain
• Forasinusoidalbasebandsignal:
Basebandsignal,x(t)
FMsignal
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FMSignal–FrequencyDomain
• Fora1KHzsinusoidalbasebandsignal(tonemodulation)and10KHzcarrier
f(Hz)
10KHz
Spacing=1KHz
WiderthananAMorDSBsignal
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DeviationandBandwidth
• InstantaneousFrequency:fc+kfx(t)• Frequencydeviation:Δf=kfx(t)• Maximumfrequencydeviation,Δf=kf|x(t)|max– Fortonemodulation:Δf=kfAm
• DeviationRatio,D=Δf/W– For tone modulation: Modulation index, b = Df/fm – b<<1:narrowbandFM,NBFM– b>>1:widebandFM,WBFM
• Bandwidth,BW=2(D+1)W,orBW=2(b+1)fm
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FMMODULATION
• Spectrumvs.modulationindex,β– Spectrahaveatypicaltrapezoidalshapeinlinearfrequencyandamplitudeindecibels.
carrier
2xdeviation
≈‐3to‐6dBperfm ≈‐3to‐6dBperfm
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FMMODULATION
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FMMODULATION
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FMMODULATION
demos
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FMMODULATION
• ComparisontoAM/SSB/DSB
AM DSB SSB FMBANDWIDTH 2fm 2fm fm 2(β+1)fm
SNR LINEAR LINEAR LINEAR NON‐LINEAR
EFFICIENCY 33% 50% 100% ≤100%*
COMPLEXITY LOW MODERATE MODERATE HIGH
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FMMODULATION
• ThresholdEffect
• Captureeffect:Signalsmorethan6dBdownwillnotinterfere.
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FMMODULATION
• SDRProgramforNBFM
GUIINTERFACE(ptt_block)
TRANSMITtransmit_path
RECEIVEreceive_path
USRP
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FMMODULATION
• TRANSMITPATH(alwaysrunning)
AudioSource
AudioGain
3/2Resampler
48kS/s
48kS/s
32kS/s 320kS/sFM
ModulatorTransmitGain
TransmitEnablefromGUI
320kS/sTo
USRP
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FMMODULATION
• RECEIVEPATH(alwaysrunning)
256kS/sfromUSRP
LowPassFilter
64kS/sFM
Demodulator
32kS/sSquelch
32kS/s
AudioGain
ReceiveEnablefromGUI
32kS/s2/3Resampler
48kS/sAudioSink
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DefinitionofaPMSignal
• Forabasebandsignal,x(t):
– kpisthefrequencydeviationconstantinrad/volt– Aconstantenvelopesignalwithvaryingfrequency/phase
– Theinstantaneousphaseis:
– Theinstantaneousfrequencyis:
�
xPM (t) = Ac cos 2πfct + kp x(t)[ ]
�
θi(t) = 2πfct + kp x(t)
�
fi(t) = fc +kp2π
dx(t)dt
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PMSignal‐TimeDomain
• Forapulsetrainbasebandsignal:
Basebandsignal,x(t)
PMsignal
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PMSignal‐TimeDomain
• Forasinusoidalbasebandsignal:
Basebandsignal,x(t)
PMsignal
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PMSignal–FrequencyDomain
• Fora1KHzsinusoidalbasebandsignal(tonemodulation)and10KHzcarrier
f(Hz)
10KHz
Spacing=1KHz
WiderthananAMorDSBsignal
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BandwidthComparisonforFM/PM
• Bandwidth,BW=2(D+1)W,orBW=2(b+1)fm• FM:• For tone modulation: Modulation index, b = Df/
fm • BW = 2(kfAm + fm)
• PM:• Fortonemodulation:Modulationindex,b = kpAm • BW = 2(kpAm+1)fm
• Increasing frequency has a more profound effect on the BW of PM
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