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PRlNCKPUi\:S OF COMMUl\UCA,TlON
SYSTEM - 4[.SEM ECE
MODULE 1: AMPLITUDE MODULATION
Time domain representation of AM
Amplitude Modulation may be defined as a process in which the amplitude of the carrier
wave is varied to the instantaneous value (amplitude) ofthe modulating or base band
signal.
Let us consider a sinusoidal carrier wave CCt)given as :
C(t) = Ac
CDS Wet
= Ac CDS 2nfet
(1)
Here Ac is the maximum amplitude of the carrier wave and Weis the carrier frequency.
For simplicity here we have assumed that the phase of the carrier wave is zero in
equation (1).
Let M(t) denote the modulating or base band signal.
Then according to amplitude modulation, the maximum amplitude Ac of the carrier will
have to be made proportional
M(t).
to the instantaneous
amplitude of the modulating signal
The standard equation for amplitude modulated (AM) wave may be expressed as :
Set) = Ac cos wet + KaM(t) Ac cos wet
Or,
Set)
= Ac[l + KaM(t)]
CDS Wet
(2)
••••••••••••••••••
(3)
Figure 1 shows the modulating signal or base band signal, carrier signal and modulated
signal.
Mo'dulatihgrsignal;
".-."
C(i:)
Mr.RAVIKlRAN
M.Tech,
Dept OF ECE, CBIT KOLAR
Page 1

--PIUNCIPl"ES OF COMMUNKCAtflON SYSTEM - 4 SEM ECE
Points about Amplitude
1.
It may be observed
of amplitude
2.
Modulation
that equation
modulated
It may be noted that carrier
The
modulating
the time-domain
behaviour
signal.
signal having frequency
3.
(1) or (2) describe
=
signal [i.e C(t)
Ae cos wet]
is a fixed frequency
We .
or baseband
signal
M(t)
contains
the
information
to be
is super imposed
upon
transmitted.
4.
In the process
the carrier
of amplitude
of amplitude
The
6.
variations
resulting
amplitude
modulation
7.
Equation
from
the information
process
whereas
modulation,
the
amplitude
modulated
varies
according
to the
with the value of the modulating
amplitude
unchanged
and is equal to
called as the envelope
of AM wave consists
signal. This means that the unique property
carrier
and phase of the carrier
Ae [1 +K, M(t)] . This implies that the amplitude
1 shows that the envelope
of the modulated
is called
wave. This wave has a constant
of the AM signal remains
The AM wave has time-varying
baseband
in the form
signal.
an amplitude
cos wet and amplitude
the frequency
maximum
value of the information
signal M(t). The frequency
Figure
is transmitted
signal. In
of amplitude-modulation
of the wave is changing around Ae in accordance
8.
of the carrier
signal of simply AM wave.
(3) represents
frequency
the
of amplitude
constant
instantaneous
modulation,
variations
of the carrier signal.
signal
In the process
remain
this information
signal in the form of amplitude
other words, in amplitude
5.
modulation,
We
of the AM wave.
of the modulating
or
of AM is that the envelope
has the same shape as the message
signal or baseband
signal.
Mr.RAVIKIRAN MTech, Dept OF ECE, CBIT KOLAR
Page 2

-----------~
-------------------
PRINCIPLES OF COMMUN!CATlON SYSTEM - 4-SEM ECE
Frequency - Domain Representation
or
Spectrum of AM Waves
Frequency
Mathematical Expression and Waveforms
Let met) is the modulating signal and the carrier signal is given by the expression:
C(t) = Accos 2nfct
...................(1)
Then the equation for the AM will be
set)
= Accos Zrtf-t
+ Accos 2nfc t Ksmjt]
(2)
This equation describes the AM wave in time-domain. However, if we want to know the
frequency description or frequencies present in AM wave, we will have to find its
spectrum or frequency-domain representation.
For this purpose, first we have to take the Fourier transform of AM wave.
Let Set) or S( co) denote the Fourier transform of set),
C(t) or C(w) denotes the Fourier transform of c(t)
M(t) or M(w) denoted the Fourier transform of met).
Let the modulating signal met) and its Fourier transform M(t) be shown in figure 1 (a) .
f'!l(tJ
o~------~------~----t
--_1:
-·\ro
----r----~
~rn
Let the modulating signal or message signal met) be band-limited to the interval:
Mr.RAVIKIRAN
M.Tech,
Dept OF ECE, CBIT KOLAR
Page 3

PIUNClPLES OF COMMUNICATION
SYSTEM - 4\-SEM IEeE
This means that the modulating signal does not have any frequency component outside
the interval
(-Wrn,
Wrn).
It may be noted at this point that in figure 1 (a) the modulating signal frequency ranges
extend from -Wrn to Wrn i.e. it includes negative frequencies also from -Wrn to 0 .
Practically there is no meaning of negative frequency. In fact, the negative frequency is
used for mathematical convenience only.
Hence we can say that the modulating signal contains frequencies
simply the bandwidth of modulating signal is
of a cosine signal cos
wet
Wrn .
from 0 to
consists of two impulse at
n[,B(w+ we) +o{w- wd]
We
and -
We
as :
Ccs ')..rr-tc.-t
.•............... (3)
I
~
nA[o(w+ wc)+.S(lu-wdl
~i[6
Clt):: Ac. c.o~
Since the carrier signal is C(t)= Ac;(lS'Wct, therefore
Acoswct
or
We know that the Fourier transform
oR
--'
COSWct ~
Wrn
...•.•....•..... (4t
[f+-tJ +& [of --t=J}
~lTtc. t
AcCb'\:tITtc.{ ~
~c{OC-t+-~c.)--\-o(-t-+e-)J
Figure 1 (b) shows the carrier signal Aecos 2nfe t and its Fourier transform.
C(w)
Figure 1 (b)
Now, the Am wave is given as:
set)
= Ac cos2nfc
t + ,AcKa m(t)cos
2nfc t
(5)
To find the spectrum of AM wave, we take its Fourier transform.
Mr.RAVIKIRAN
M.Tech,
Dept OF ECE, CBIT KOLAR
Page 4

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