Page 287 - Satellite Communications, Fourth Edition

Analog Signals 267

12 transponders as described in Sec. 7.7. The individual transponder
bandwidth is typically 36 MHz. In contrast, the baseband bandwidth for
a telephony channel is typically 3.1 kHz.
In theory, the spectrum of a frequency-modulated carrier extends to
infinity. In a practical satellite system, the bandwidth of the transmit-
ted FM signal is limited by the intermediate-frequency amplifiers. The
IF bandwidth, denoted by B , must be wide enough to pass all the sig-
IF
nificant components in the FM signal spectrum that is generated. The
required bandwidth is usually estimated by Carson’s rule as

B 2s F F d (9.1)
M
IF
where ΔF is the peak carrier deviation produced by the modulating
baseband signal, and F M is the highest frequency component in the
baseband signal. These maximum values, ΔF and F , are specified in
M
the regulations governing the type of service. For example, for com-
mercial FM sound broadcasting in North America, ΔF 75 kHz and
F 15 kHz.
M
The deviation ratio D is defined as the ratio
F
D (9.2)
F M

Example 9.1 A video signal of bandwidth 4.2 MHz is used to frequency modulate
a carrier, the deviation ratio being 2.56. Calculate the peak deviation and the signal
bandwidth.
Solution
D × F 2.56 × 4.2 10.752 MHz

B IF 2(10.752 + 4.2) 29.9 MHz
A similar ratio, known as the modulation index, is defined for sinu-
soidal modulation. This is usually denoted by ß in the literature. Letting
Δf represent the peak deviation for sinusoidal modulation and f the
m
sinusoidal modulating frequency gives
f
(9.3)
f m
The difference between b and D is that D applies for an arbitrary mod-
ulating signal and is the ratio of the maximum permitted values of devi-
ation and baseband frequency, whereas b applies only for sinusoidal
modulation (or what is often termed tone modulation). Very often the
analysis of an FM system will be carried out for tone modulation rather
than for an arbitrary signal because the mathematics is easier and the