B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

4.3 Amplitude Modulation (AM) 155
In this case, mmax = b and mmin -b. Hence the modulation index according to Eq.
(4.10a) is
b - (-b) b
µ =
2A + b + (-b) A
Hence, b = µA and
Therefore,
m (
t )
= b COS W m t = µA COS W m t
'PAM (t) = [A + m (
t )
] COS W e t = A[l +µCOS W m t] COS W e t
Figure 4.9
Tone-modulated
AM. (a) µ = 0.5.
(b) µ = 1.
Figure 4.9 shows the modulated signals corresponding to µ = 0.5 and µ = 1, respectively.
A
. (
µ = 0.5
1 + 0.5 COS W 111 t
I --;. ··· IA/2
. . . . . ;, ... A/2
'
\
µ = I
1 + COS W,nt
, ,/ '
\
\
........I.
A
A
1-
1-
(a)
(b)
Sideband and Carrier Power
The advantage of envelope detection in AM comes at a price. In AM, the carrier term does not
carry any information, and hence, the carrier power is wasteful from this point of view:
'PAM (t) = A COS W e
t + m (
t )
COS W e t
'-,--'
carrier
'--.-'
sidebands
The carrier power P c is the mean square value of A cos w e t, which is A 2 /2. The sideband
power P s is the power of m (
t )
cos w e t, which is 0.5 m 2 ( t ) [see Eq. (3.93)] . Hence,
A 2
P c = - 2
and
The useful message information resides in the sideband power, whereas the carrier power is
the used for convenience in modulation and demodulation. The total power is the sum of the
carrier (wasted) power and the sideband (useful) power. Hence, rJ, the power efficiency, is
useful power P s
rJ - - total power Pc + P s
m 2 ( t )
---- 100%
A 2 + m 2 (t)
For the special case of tone modulation,
m (
t )
= µA cos W m t
and
- ( A)
2
m 2 ( t )
= _µ_
2