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Problems 405
5–25 A transmitter produces a quadrature modulated (QM) signal. The complex envelope is
g(t) = A c [m 1 (t) + j m 2 (t)]
Let the carrier frequency be 50 kHz and A c = 100. The transmitter is tested using two sinusoidally
modulated waveforms that are m 1 (t) = 3cos(v 1 t) and m 2 (t) = 4cos(v 2 t) where f 1 = 2 kHz and
f 2 = 5 kHz. Using MATLAB, plot the output voltage waveform for this transmitter.
5–26 Using MATLAB, calculate the actual PEP for the transmitter described in Prob. 5–25 if the resisitive
load on the transmitter is 50 Ω.
★ 5–27 A sinusoidal signal m(t) = cos 2pf m t is the input to an angle-modulated transmitter, where the
carrier frequency is f c = 1 Hz and f m = f c 4.
(a) Plot m(t) and the corresponding PM signal, where D p = p.
(b) Plot m(t) and the corresponding FM signal, where D f = p.
5–28 A sinusoidal modulating waveform of amplitude 4 V and frequency 1 kHz is applied to an FM
exciter that has a modulator gain of 50 HzV.
(a) What is the peak frequency deviation?
(b) What is the modulation index?
5–29 An FM signal has sinusoidal modulation with a frequency of f m = 15 kHz and modulation index
of b = 2.0.
(a) Find the transmission bandwidth by using Carson’s rule.
(b) What percentage of the total FM signal power lies within the Carson rule bandwidth?
★ 5–30 An FM transmitter has the block diagram shown in Fig. Fig. P5–30. The audio frequency
response is flat over the 20-Hz-to-15-kHz audio band. The FM output signal is to have a carrier
frequency of 103.7 MHz and a peak deviation of 75 kHz.
(a) Find the bandwidth and center frequency required for the bandpass filter.
(b) Calculate the frequency f 0 of the oscillator.
(c) What is the required peak deviation capability of the FM exciter?
FM exciter
f c =5.00 MHz
Bandpass
filter
× 8
Frequency
multiplier
Class C
amplifier
FM
output
Oscillator
f o =?
Figure P5–30
5–31 Analyze the performance of the FM circuit of Fig. 5–8b. Assume that the voltage appearing
across the reverse-biased diodes, which provide the voltage variable capacitance, is v(t) = 5 +
0.05 m(t), where the modulating signal is a test tone, m(t) = cos v 1 t, v 1 = 2pf 1 , and f 1 = 1 kHz.
The capacitance of each of the biased diodes is C d = 10021 + 2v(t) pF. Assume that C 0 = 180
pF and that L is chosen to resonate at 5 MHz.
(a) Find the value of L.
(b) Show that the resulting oscillator signal is an FM signal. For convenience, assume that the
peak level of the oscillator signal is 10 V. Find the parameter D f .