Frequency and Phase Modulation

FrequencyandPhaseModulation

SharleneKatzJamesFlynn

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

FMMODULATION

FMMODULATION

FMMODULATION

demos

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

FMMODULATION

•  ThresholdEffect

•  Captureeffect:Signalsmorethan6dBdownwillnotinterfere.

FMMODULATION

•  SDRProgramforNBFM

GUIINTERFACE(ptt_block)

TRANSMITtransmit_path

RECEIVEreceive_path

USRP

FMMODULATION

•  TRANSMITPATH(alwaysrunning)

AudioSource

AudioGain

3/2Resampler

48kS/s

48kS/s

32kS/s 320kS/sFM

ModulatorTransmitGain

TransmitEnablefromGUI

320kS/sTo

USRP

FMMODULATION

•  RECEIVEPATH(alwaysrunning)

256kS/sfromUSRP

LowPassFilter

64kS/sFM

Demodulator

32kS/sSquelch

32kS/s

AudioGain

ReceiveEnablefromGUI

32kS/s2/3Resampler

48kS/sAudioSink

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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