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Chapter 5
Amplitude Modulation
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InformationSource
SignalModulator
PropagationChannel
SignalDemodulator
InformationDestination
Analog Communication System
Analog signals may be transmitted directly via carrier modulation overthe propagation channel and to be carrier-demodulated at the receiver.
TransmitterModulator
Receiver Demodulator
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Modulation: The process by which some characteristics of a carrier
signal (i.e. modulated signal) is varied in accordance with message
signal (i.e. modulating signal)
f(t): message signal
A bandlimited signal whose frequency content is in the neighbourhoodoff=0 (DC) ? baseband signal
c(t): the carrier signal, independent off(t)
c(t)=Ac cos(2pfct+? c)Ac : Carrier amplitude
fc : Carrier frequency wc=2pfc (radian frequency)
? c : Carrier phase
f(t) modulates c(t) in either amplitude, frequency or phase. In effect,
modulation convertsf(t) to a bandpass form, in the neighborhood of the
center frequencyfc.
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Why is Modulation Required?
To achieve easy radiation: If the communication channel consists of
free space, antennas are required to radiate and receive the signal.
Dimension of the antennas is limited by the corresponding wavelength.
Example: Voice signal bandwidthf=3kHz
? /4=25000m!!
If we modulate a carrier wave @ fc = 100MHz with the voice signal
? /4=75cm
m10103
103 53
8
=
==f
c
m310100
1036
8
=
== fc
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Why is Modulation Required? (Contd)
s1
f
f
fC1
fC2
To accommodate for simultaneous transmission of several signals
f
fC3
Example: Radio/TV broadcasting
s2
s3
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Why is Modulation Required? (Contd)
To expand the bandwidth of the transmitted signal for better
transmission quality (to reduce noise and interference)
( )SNRBC += 1log 2
Channel capacity Bandwidth Signal-to-noise ratio
Channel capacity: Maximum achievable information rate that can be
transmitted over the channel
12 = BC
SNR
B The required SNR (for fixed noise level, corresponding signal
power) decreases
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Amplitude Modulation (AM)
(Ch. 5 in Textbook)
Objectives:
To study different amplitude modulation scheme
To study generation and detection of AM signals To study application of AM
Double Sideband Large Carrier (DSB-LC) Modulation: Commercialbroadcast stations use this type and it is commonly known as just
amplitude modulation (AM).
Double Sideband Suppressed Carrier (DSB-SC) Modulation
Single Sideband (SSB) Modulation Vestigial Sideband (VSB) Modulation
We will study
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Double Side Band Large Carrier (DSB-LC)(5.2 in Textbook)
( )tcjtcjc eet +=
2
1cos
( ) ( ){ }tfF F= ( ) ( ){ }t F=
( ) ( ) ( ) ( )[ ]ttftA ccc coscos += F
( ) ( )
+++= tjtjtjctjc cccc etfetfeAeA
2222F
( ) ( ) ( ) ( )cccccc FFAA +++++=2
1
2
1
Modulator ( ) ( )( ) tAtft cc cos+=
( ) tAtc cc cos=
( )tf
( ) tAttf ccc coscos +=
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t
f(t)
c+2B
passband
baseband
t
t
F [f(t) cosct]
cc-2B
F(0)/2
F()= F [f(t)]
F(0)
2B-2B
F [Ac cosct]pA
-c
c-c
Ac cosct
F [Ac cosct+ f(t)cosct]
c-c
pA
Ac cosct+ f(t)cosct envelope
t
f(t) cosct
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F()= F [f(t)]
F(0)
2B-2B
()=
F [Ac cosct+ f(t)cosct]
c-cc-2B c+2B
Bandwidth=B [Hz] Bandwidth=2B
F(0)/2 pA pA
Observations:
Modulation shifts the content ofF() to the neighbourhood ofc .
F() for[-2B, 0] is shifted to () for[c-2B, c] and called aslower sideband.
F() for[0, 2B] is shifted to () for[c, c+2B] and called asupper sideband.
Let B denote the highest frequency component off(t).
Assume fc >> B ? (t) is defined as a narrowbandsignal (i.e. its spectralcontent is located in the immediate vicinity of some high center frequency)
Upper
sideband
Lower
sideband
baseband passband
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Observations (contd)
The bandwidth of message signal isB. The transmission bandwidth
T=2B (i.e. DSB-LC is wasteful of bandwidth)
The carrier term does not carry any information and hence the carrier
power is wasted.
F(
)= F [f(t)]
F(0)
2B-2B
()= F [A
ccos
ct+ f(t)cos
ct]
c-cc-2B c+2B
Bandwidth=B [Hz] Bandwidth=2B
F(0)/2 pA pAUpper
sideband
Lower
sideband
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Zero crossings
Envelope has the
same shape of f(t)
Envelope distortion
Observations (contd)
If Ac+f(t)>0 for all t, the envelope of(t) of has essentially the same shapeas thef(t).
If Ac+f(t)
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overmodulated
? envelope dist.
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Carrier and Sideband Power in DSB-LC
( ) ( ) ( ) ( )ttftAt ccc coscos +=
( ) ( ) ( ) ( ) ( ) ( )ttfAttftAt ccccc 222222 cos2coscos ++=
( ) ( ) ( ) ( )ttftAt ccc 22222 coscos +=
( ) ( ) 22 222 tfAt c +=
( ) dttT
tT
Tc
Tc =
+
2/
2/
22 cos1limcos ( )dttT
T
Tc
T +=+
2/
2/
2cos1211lim
( )2
12cos1
1lim
2
1lim
2
1 2/
2/
2/
2/
= ++=+
dttTT
t T
Tc
T
T
TT
= 0
Assume and f(t) varies slowly with respect to ( )tccos( ) 0=tf
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( ) ( ) 22 222 tfAt c +=
Carrier Power Sideband Power (carries information)
Modulation (Power)Efficiency
useful powertotal power
=
( )
( ) 22
222
2
tfA
tf
c +=
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( )[ ]8
cos2
222
2
cmc
c AmtmA =+
( )[ ]
8
cos
2
222
2
cmc
c AmtmA
=
( ) ( ) ( )[ ] ( )[ ]tmA
tmA
tAt mcc
mcc
cc +++= cos2
cos2
cos
Example (Contd)
Upper sidebandpower
Lower sideband
power
total useful power
total power=
2
2
222
22
242
4
m
m
AmA
Am
cc
c
+
=
+
=
Form= 1 ? = 33%. Under the best condition, i.e. m=1, 67% of
the total power is used in the carrier and represents wasted power.
