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Sec. 5–1 Amplitude Modulation 315
m(t)
t
(a) Sinusoidal Modulating Wave
A C [1+m(t)]
s(t)
A min
A C
A max
t
(b) Resulting AM Signal
Figure 5–1
AM signal waveform.
Equation (5–6) may be obtained by averaging the positive and negative modulation as given by
Eqs. (5–5a) and (5–5b). A max , A min , and A c are illustrated in Fig. 5–1b, where, in this example,
A max = 1.5A c and A min = 0.5A c , so that the percentages of positive and negative modulation are
both 50% and the overall modulation is 50%.
Example 5–1 AM SIGNAL WITH 50% AND 100% MODULATION
Let an AM signal with a carrier frequency of 10 Hz be modulated with a sinusoidal signal having
a frequency of 1 Hz. Furthermore, let the percentage of modulation be 50% over the time interval
0 6 t 6 2 sec and then changed to 100% over 2 6 t 6 4 sec. Plot the AM signal waveform over
the interval of 0 6 t 6 4 sec. See Example5_01.m for the solution.
The percentage of modulation can be over 100% (A min will have a negative value),
provided that a four-quadrant multiplier † is used to generate the product of A c [1 + m(t)] and
cos v c t so that the true AM waveform, as given by Eq. (5–4), is obtained. ‡ However, if the
transmitter uses a two-quadrant multiplier that produces a zero output when A c [1 + m(t)] is
negative, the output signal will be
s(t) = e A c[1 + m(t)] cos w c t, if m(t) Ú -1
0, if m(t)6 -1
(5–7)
† A four-quadrant multiplier multiplies for the two inputs having any polarity. A two-quadrant multiplier multiplies
only if one of the inputs has a single polarity (e.g. for x 7 0) and it produces zero output if x 6 0.
‡ If the percentage of modulation becomes very large (approaching infinity), the AM signal becomes the doublesideband
suppressed carrier signal that is described in the next section.