563489578934

Sec. 4–19 Study-Aid Examples 301
Note: An alternative method of computing (P s ) norm is to calculate the area under the PDF for s(t).
That is, by using Eq. (4–125),
2
(P s ) norm = (V s ) rms
q
= P s (f) df = 165 kW
L
-q
(4–126b)
Using Eq. (4–126a) or Eq. (4–126b), we obtain the actual average power dissipated in the
50-Ω load: † (4–127)
(P s ) actual = (V s) rms
=
R L
2
1.65 * 105
50
= 3.3 kW
SA4–4 PEP for an AM Signal If the AM voltage signal of SA4–1 appears across a
50-Ω resistive load, compute the actual peak envelope power (PEP).
Solution.
Using Eq. (4–18), we get the normalized PEP:
(P PEP ) norm = 1 2 [ max |g(t)|]2 = 1 2 A c 2 [1 + max m(t)] 2
= 1 2 (500)2 [1 + 0.8] 2 = 405 kW
(4–128)
Then the actual PEP for this AM voltage signal with a 50-Ω load is
(P PEP ) actual = (P PEP) norm
R L
=
4.50 * 105
50
= 8.1 kW
(4–129)
SA4–5 Sampling Methods for Bandpass Signals Suppose that a bandpass signal s(t) is
to be sampled and that the samples are to be stored for processing at a later time. As shown
in Fig. 4–32a, this bandpass signal has a bandwidth of B T centered about f c , where f c B T and
B T 7 0. The signal s(t) is to be sampled by using any one of three methods shown in Fig. 4–32. ‡
For each of these sampling methods, determine the minimum sampling frequency (i.e., minimum
clock frequency) required, and discuss the advantages and disadvantages of each method.
Solution.
Method I Referring to Fig. 4–32a, we see that Method I uses direct sampling as described in
Chapter 2. From Eq. (2–168), the minimum sampling frequency is (f s ) min = 2B, where B is the
highest frequency in the signal. For this bandpass signal, the highest frequency is B = f c + B T 2.
Thus, for Method I, the minimum sampling frequency is
(f s ) min = 2f c + B T Method I
(4–130)
For example, if f c = 100 MHz and B T = 1 MHz, a minimum sampling frequency of (f s ) min =
201 MHz would be required.
† If s(t) is a current signal (instead of a voltage signal), then (P s ) actual = (I s ) 2 rms R L .
‡ Thanks to Professor Christopher S. Anderson, Department of Electrical and Computer Engineering,
University of Florida, for suggesting Method II.