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Sec. 5–6 Phase Modulation and Frequency Modulation 335
From Fig. 5–9, it is obvious that an increase in the amplitude of the modulation signal
V p will increase ∆F. This in turn will increase the bandwidth of the FM signal, but will not
affect the average power level of the FM signal, which is A 2 c >2. As V p is increased, spectral
components will appear farther and farther away from the carrier frequency, and the spectral
components near the carrier frequency will decrease in magnitude, since the total power in the
signal remains constant. (For specific details, see Example 5–6.) This situation is distinctly
different from AM signaling, where the level of the modulation affects the power in the AM
signal, but does not affect its bandwidth.
In a similar way, the peak phase deviation may be defined by
¢u = max [u(t)]
(5–45)
which, for PM, is related to the peak modulating voltage by
¢u = D p V p
(5–46)
where V p = max [m(t)].
DEFINITION. † The phase modulation index is given by
b p =¢u
where ∆u is the peak phase deviation.
The frequency modulation index is given by
(5–47)
b f = ¢F
(5–48)
B
where ∆F is the peak frequency deviation and B is the bandwidth of the modulating
signal, which, for the case of sinusoidal modulation, is f m , the frequency of the
sinusoid. ‡
For the case of PM or FM signaling with sinusoidal modulation such that the PM and
FM signals have the same peak frequency deviation, b p is identical to b f .
Example 5–5 FM SIGNAL WITH SINUSOIDAL MODULATION
Plot the waveform for an FM signal that has a modulating signal of m f (t) = cos(2pt). Assume
that the carrier frequency is 5 Hz and the modulation index is 3. See Example5_05.m for the
solution.
† For digital signals, an alternative definition of modulation index is sometimes used and is denoted by h in
the literature. This digital modulation index is h = 2∆u p, where 2∆u is the maximum peak-to-peak phase deviation
change during the time that it takes to send one symbol, T s . [See Eq. (5–82).]
‡ Strictly speaking, the FM index is defined only for the case of single-tone (i.e., sinusoidal) modulation.
However, it is often used for other waveshapes, where B is chosen to be the highest frequency or the dominant frequency
in the modulating waveform.