Page 179 - Fundamentals of Communications Systems

Chapter
6

Amplitude Modulation

Amplitude modulation (AM) was historically the first modulation developed
and conceptually the easiest to understand. Consequently, AM is developed
first in this text.

6.1 Linear Modulation
The simplest analog modulation is to make m (m(t)) = A c m(t), i.e., a linear
function of the message signal. The complex envelope and the spectrum of this
modulated signal are given as

2
x z (t) = A c m(t) G x z (f ) = A G m (f )
c
This modulation has x I (t) = A c m(t) and x Q (t) = 0, so the imaginary portion
of the complex envelope is not used in a linear analog modulation. The resulting
bandpass signal and spectrum are given as
√ √
x c (t) =
2x z (t) exp[ j 2π f c t] = A c m(t) 2 cos(2π f c t) (6.1)
A 2 c A 2 c A 2 c A 2 c
(f ) = G m ( f − f c ) + G m (− f − f c ) = G m ( f − f c ) + G m ( f + f c )
G x c
2 2 2 2
(6.2)
where the fact that m(t) was real was used to simplify Eq. (6.2). Figure 6.1
shows the complex envelope and an example bandpass signal for the message
√
signal shown in Figure 5.1 with A c = 1/ 2. It is quite obvious from Figure 6.1
that the amplitude of the carrier signal is modulated directly proportional to the
absolute value of the message signal (hence the name amplitude modulation).
Figure 6.2 shows the resulting energy spectrum of the linearly modulated signal
for the message signal shown in Figure 5.2. A very important characteristic
of this modulation is that if the message signal has a bandwidth of W Hz
then the bandpass signal will have a transmission bandwidth of B T = 2W.

6.1
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