563489578934

246
Bandpass Signaling Principles and Circuits Chap. 4
Also, from Eq. (4–16),
or
But |g(t)| is always real, so
R v (0) = 1 2 Re{R g(0)} = 1 2 Re{8g* (t)g(t + 0)9}
R v (0) = 1 2 Re{8|g(t)|2 9}
R v (0) = 1 2 8|g(t)|2 9
Another type of power rating, called the peak envelope power (PEP), is useful for transmitter
specifications.
DEFINITION. The peak envelope power (PEP) is the average power that would be obtained
if |g(t)| were to be held constant at its peak value.
This is equivalent to evaluating the average power in an unmodulated RF sinusoid that
has a peak value of A p = max [v(t)], as is readily seen from Fig. 5–1b.
THEOREM.
The normalized PEP is given by
P PEP = 1 2 [ max |g(t)|]2
(4–18)
A proof of this theorem follows by applying the definition to Eq. (4–17). As described
later in Chapters 5 and 8, the PEP is useful for specifying the power capability of AM, SSB,
and television transmitters.
Example 4–3 AMPLITUDE-MODULATED SIGNAL
Evaluate the magnitude spectrum for an amplitude-modulated (AM) signal. From Table 4–1, the
complex envelope of an AM signal is
so that the spectrum of the complex envelope is
g(t) = A c [1 + m(t)]
G(f) = A c d(f) + A c M(f)
(4–19)
Using Eq. (4–9), we obtain the AM signal waveform
s(t) = A c [1 + m(t)] cos v c t
See Example4_3.m for a plot of an AM signal that is modulated by a sinusoid.
Using Eq. (4–12), we get the AM spectrum
S(f) = 1 2 A c[d(f - f c ) + M(f - f c ) + d(f + f c ) + M(f + f c )]
(4–20a)