Page 288 - Satellite Communications, Fourth Edition

268 Chapter Nine

results usually give a good indication of what to expect with an arbitrary
signal.

Example 9.2 A test tone of frequency 800 Hz is used to frequency modulate a car-
rier, the peak deviation being 200 kHz. Calculate the modulation index and the
bandwidth.
Solution

200
250
0.8
B 2(200 0.8) 401.6 kHz

Carson’s rule is widely used in practice, even though it tends to give
an underestimate of the bandwidth required for deviation ratios in the
range 2 < D < 10, which is the range most often encountered in practice.
For this range, a better estimate of bandwidth is given by
2s F 2F d
B IF M (9.4)

Example 9.3 Recalculate the bandwidths for Examples 9.1 and 9.2.
Solution For the video signal,
B IF 2(10.75 + 8.4) 38.3 MHz

For the 800 Hz tone:
B IF 2(200 + 1.6) 403.2 kHz

In Examples 9.1 through 9.3 it will be seen that when the deviation
ratio (or modulation index) is large, the bandwidth is determined mainly
by the peak deviation and is given by either Eq. (9.1) or Eq. (9.4).
However, for the video signal, for which the deviation ratio is relatively
low, the two estimates of bandwidth are 29.9 and 38.3 MHz. In practice,
the standard bandwidth of a satellite transponder required to handle
this signal is 36 MHz.
The peak frequency deviation of an FM signal is proportional to the
peak amplitude of the baseband signal. Increasing the peak amplitude
results in increased signal power and hence a larger signal-to-noise
ratio. At the same time, ΔF, and hence the FM signal bandwidth, will
increase as shown previously. Although the noise power at the demod-
ulator input is proportional to the IF filter bandwidth, the noise power
output after the demodulator is determined by the bandwidth of the
baseband filters, and therefore, an increase in IF filter bandwidth does
not increase output noise. Thus an improvement in signal-to-noise ratio