563489578934

316
AM, FM, and Digital Modulated Systems Chap. 5
which is a distorted AM signal. The bandwidth of this signal is much wider than that of the
undistorted AM signal, as is easily demonstrated by spectral analysis. This is the overmodulated
condition that the FCC does not allow. An AM transmitter that uses pulse width modulation is
an example of a circuit that acts as a two-quadrant multiplier (see Fig. 5–2 and the discussion of
this figure that follows Example 5–3). This produces the product A c [1 + m(t)] cos v c t, provided
that m(t) Ú -1, but produces no output when m(t) 6-1.
Example 5–2 AM SIGNAL WITH 150% MODULATION
Let an AM signal with a carrier frequency of 10 Hz be modulated with a sinusoidal signal
having a frequency of 1 Hz and 150% modulation. Assume that the AM transmitter uses a
two-quadrant multiplier. Plot the AM signal at the transmitter output. See Example5_02.m for
the solution.
If the percentage of negative modulation is less than 100%, an envelope detector
may be used to recover the modulation without distortion, since the envelope, |g(t)| =
|A c [1 + m(t)]|, is identical to A c [1 + m(t)]. If the percentage of negative modulation is over
100%, undistorted modulation can still be recovered provided that the proper type of
detector—a product detector—is used. This is seen from Eq. (4–76) with u 0 = 0.
Furthermore, the product detector may be used for any percentage of modulation. In
Chapter 7, we will see that a product detector is superior to an envelope detector when the
input signal-to-noise ratio is small.
From Eq. (4–17), the normalized average power of the AM signal is
8s 2 (t)9 = 1 2 8|g(t)|2 9 = 1 2 A c 2 8[1 + m(t)] 2 9
= 1 2 A c 2 81 + 2m(t) + m 2 (t)9
= 1 2 A c 2 + A c 2 8m(t)9 + 1 2 A c 2 8m 2 (t)9
(5–8)
If the modulation contains no DC level, then 8m(t) 9 = 0 and the normalized power of the AM
signal is
8s 2 (t)9 = 1 2 A c 2
⎧
⎨⎩
⎧
⎪⎨⎪⎩
discrete
carrier power
+ 1 2 A c 2 8m 2 (t)9
sideband power
(5–9)
DEFINITION. The modulation efficiency is the percentage of the total power of the
modulated signal that conveys information.
In AM signaling, only the sideband components convey information, so the modulation
efficiency is
E =
8m 2 (t)9
1 + 8m 2 (t)9 * 100%
(5–10)