am technique

Fall 2001 Copyright 2001 ©Andreas Spanias I-1

Communication SystemsAM Modulation/Demodulation Techniques

Lecture 5

Andreas SpaniasDept. of Electrical Engineering

Arizona State University

email: [email protected]://www.eas.asu.edu/~spanias


Demodulators

• AM Demodulation is done using mixer circuits and filters

• In most cases it requires synchronization circuits usually involving a Phase Locked Loop (PLL)

• DSB-SC requires synchronization while conventional DSB can be done with simple envelope detectors

• Demodulators are often more complex than modulators


DSB-SC Modulation and Demodulation

ModulatorModulatorDeDe--modulator /modulator /

MixerMixer

)2cos( ϕπ +tfc

r(t)r(t)m(t)m(t)

)2cos( cctf ϕπ +

LPFLPF

TransmitterTransmitter ReceiverReceiver

y(t)y(t) y’(t)y’(t)


Demodulation of DSB-SC

Assumptions:• Received signal r(t) is noise free• Ideal Channel r(t) = u(t)

Demodulate by multiplying r(t) with a cos(.) signal. This is called a “mixer”

)2cos()()()( ccc tftmAtutr ϕπ +==


)2cos()( ϕπ +tftr cgenerally different from cϕ

)2cos()2cos()()( ϕπϕπ ++= tftftmAty cccc

The Mixer in DSB-SC

Xr(t)r(t) y(t)y(t)

)2cos( ϕπ +tfc

MixerMixer


)])[cos((2

)(' ϕϕ −= cc tmAty

The LPF will cancel the component)4cos( ϕϕπ ++ cctf

Apply the trigonometric identity )cos(21)cos(

21cos.cos βαβαβα ++−=

)]4cos())[cos((2

)( ϕϕπϕϕ +++−= cccc tftmAty

Use a LPF after the mixer

The Mixer in DSB-SC (2)

)cos(2

)()]([ ϕϕ −= cc tmAtyLPF

High High freqfreq. . componentcomponent


Synchronization RequirementNote that if ; receiver is synchronized

)cos(2

)()(' ϕϕ −= cc tmAty

°=− 45ϕϕ c 21)cos( =−ϕϕ c

°=− 0ϕϕ c

1)cos( =−ϕϕ c

if °=− 90ϕϕ c 0)cos( =−ϕϕ c ; no signal !

The Need for synchronization in DSB-SC


DSB-SC time-domain waveforms

m(t)m(t)

u(t)u(t)

y(t)y(t)


DSB-SC frequency-domain waveforms

M(f)M(f)

U(f)U(f)

Y(f)Y(f)


DSB-SC frequency-domain waveforms

•The mixer produces the baseband and translated spectra at twise fc

•LPF removes the double frequency component

•Demodulator requires phase synchronization

•Transmission bandwidth is 2W

•Efficient relative to conventional DSB


AM – Conventional Modulation

• This is the similar to DSB-SC except that the carrier signal is also transmitted

• The presence of the carrier signal at the receiver simplifies the demodulation circuit

• The carrier signal is transmitted by adding a D.C. bias to the message signal m(t)


AM – Conventional Modulation (2)

DSB-AMAdvantages:• Simplifies the receiver• No need for synchronization

Disadvantages:• Inefficient in the sense that we expend

power to transmit the carrier that does not carry information


Conventional Modulation

)(1 tm+

A D.C. bias is added to the messageA D.C. bias is added to the message

This signal then modulates a sinusoidThis signal then modulates a sinusoid

)2cos()](1[)( ccc tfAtmtu ϕπ ++=


Conventional Modulation

)2cos( cctf ϕπ +

m(t)m(t) u(t)u(t)1+m(t)1+m(t)

Constant D.C., e.g., 1Constant D.C., e.g., 1

This transmitted signal includes the carrierThis transmitted signal includes the carrier

)2cos()()2cos()( cccccc tftmAtfAtu ϕπϕπ +++=


Conventional Modulation Waveforms

m(t)m(t)

u(t)u(t)


1)( ≤tmIf

Simple demodulation (detector) circuit

We normalize the message so that we can usean envelope detector

then 0)](1[ ≥+ cAtm

Therefore an envelope detector can be usedTherefore an envelope detector can be usedto detect m(t)to detect m(t)


Envelope Detector Circuit

•• The diode acts as a rectifier and the capacitor discharges and iThe diode acts as a rectifier and the capacitor discharges and interpolatesnterpolates

•• In practice, the time constant of the RC circuit is chosen relatIn practice, the time constant of the RC circuit is chosen relative to the carrier ive to the carrier frequency and the message bandwidthfrequency and the message bandwidth

•• For proper operation of conventional modulation the carrier is aFor proper operation of conventional modulation the carrier is at least 10 times the t least 10 times the bandwidth of the message signalbandwidth of the message signal


Envelope Detection Waveformsenvelopeenvelope

••Diode leaves only positive half cyclesDiode leaves only positive half cycles••Capacitor fills in between the Capacitor fills in between the hald hald cyclescycles


Normalized Message Signal

1)( ≤tm

Since it is desirable to have

We can use a normalized message signal, i.e.,

))(max()()(

tmtmtmn =


Conventional Modulation with a Normalized Signal

)2cos()](1[)( ccnc tftmaAtu ϕπ ++=

a is called the modulation index

If a<1 then

0)](1[ >+ cn Atma


The Frequency Spectrum of Conventional AM

)]([.)( tuTFfU =

)()(.[2 cn

ju

jc ffMaefcfMaeAcc ++−= − ϕϕ

)]()( cj

cj ffeffe cc ++−+ − δδ ϕϕ


|U(f)|

f(Hz)f(Hz)--fcfc+W+W--fcfc--WW fcfc+W+Wfcfc--WW

The Frequency Spectrum of Conventional AM (2)

carriercarrier

|M(f)|

......f(Hz)f(Hz)WW--WW


For a sinusoid

)2cos()( tftm mπ= where cm ff <<

)2cos()](1[)( ccc tfAtmtu ϕπ ++=

)2cos()2cos()2cos( ccmcccc tftfAtfA ϕππϕπ +++=

)])(2cos())(2[cos(2

)2cos()( cmccmcc

ccc fftfftAtfAtu ϕπϕπϕπ ++++−++=

)()( fUtu ↔

Conventional AM with a single tone (1)


LSB LSBUSB USB

cf− cf

)]()([2

)( cj

cjc ffeffeAfU cc ++−= − δδ ϕϕ

)]()([4 mc

jmc

jc fffefffeAcc −+++−+ − δδ ϕϕ

)]()([4 mc

jmc

jc fffefffeAcc +++−−+ − δδ ϕϕ

mc ff +−mc ff −− mc ff − mc ff +

Conventional AM with a single tone (2)

carriercarrier

am technique

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