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AM, FM, and Digital Modulated Systems Chap. 5
m(t)
Integrator
gain=D f
¨(t)
NBFM
signal
out
A c sin( c t)
Oscillator
(frequency=f c )
–90°
phase shift
A c cos( c t)
(a) Generation of NBFM Using a Balanced Modulator
NBFM
signal in
from part (a)
Limiter
Frequency
multiplier
Limiter
Frequency
multiplier
WBFM
signal
out
(b) Generation of WBFM From a NBFM Signal
Figure 5–12
Indirect method of generating WBFM (Armstrong method).
Example 5–7 NARROWBAND APPROXIMATION
SINUSOIDAL MODULATION
OF A PM SIGNAL WITH
Using the narrowband approximation, plot the waveform for a PM signal that has a modulating
signal of m(t) = sin(2pt). Assume that the carrier frequency is 5 Hz and the modulation index is
0.8. Compare the waveform of the narrowband PM signal with the actual PM signal and the
carrier signal. See Example5_07.m for the solution.
From Eqs. (5–62) and (5–49), the spectrum of the narrowband angle-modulated signal is
where
S(f) = A c
2 {[d(f - f c) + d(f + f c )] + j[(f - f c ) - (f + f c )]}
(f) = [u(t)] = d
D P M(f),
D f
M(f ),
j2pf
for PM signaling
for FM signaling
(5–64)
(5–65)
Wideband Frequency Modulation
A direct method of generating wideband frequency modulation (WBFM) is to use a voltagecontrolled
oscillator (VCO), as illustrated in Fig. 5–8b. However, for VCOs that are designed