563489578934

PROBLEMS
Problems 305
4–1 Show that if v(t) = Re{g(t)e jvct }, Eqs. (4–1b) and (4–1c) are correct, where g(t) = x(t) + jy(t) =
R(t)e ju(t) .
4–2 An AM signal is modulated by a waveform such that the complex envelope is
g(t) = A c {1 + a[0.2 cos(p250t) + 0.5 sin(p2500t)]}
where A c = 10. Find the value of a such that the AM signal has a positive modulation percentage
of 90%. Hint: Look at Ex. 4–3 and Eq. (5–5a).
★ 4–3 A double-sideband suppressed carrier (DSB-SC) signal s(t) with a carrier frequency of 3.8 MHz
has a complex envelope g(t) = A c m(t). A c = 50 V, and the modulation is a 1-kHz sinusoidal test
tone described by m(t) = 2sin (2p 1,000t). Evaluate the voltage spectrum for this DSB-SC signal.
4–4 A DSB-SC signal has a carrier frequency of 900 kHz and A c = 10. If this signal is modulated by
a waveform that has a spectrum given by Fig. P3–3. Find the magnitude spectrum for this DSB-
SC signal.
4–5 Assume that the DSB-SC voltage signal s(t), as described in Prob. 4–3 appears across a 50-Ω
resistive load.
(a) Compute the actual average power dissipated in the load.
(b) Compute the actual PEP.
4–6 For the AM signal described in Prob. 4–2 with a = 0.5, calculate the total average normalized
power.
4–7 For the AM signal described in Prob. 4–2 with a = 0.5, calculate the normalized PEP.
4–8 A bandpass filter is shown in Fig. P4–8.
L
C
v 1 (t)
R
v 2 (t)
Figure P4–8
(a) Find the mathematical expression for the transfer function of this filter, H( f ) = V 2 ( f )V 1 ( f ),
as a function of R, L, and C. Sketch the magnitude transfer function |H( f )|.
(b) Find the expression for the equivalent low-pass filter transfer function, and sketch the corresponding
low-pass magnitude transfer function.
★ 4–9 Let the transfer function of an ideal bandpass filter be given by
where B T is the absolute bandwidth of the filter.
H(f) =
L
1, ƒ f + f c ƒ 6 B T >2
1, ƒ f - f c ƒ 6 B T >2
0, f elsewhere