Page 297 - Satellite Communications, Fourth Edition

Analog Signals 277

used. Denoting the decibel value as gdB, then the voltage ratio is
obtained from

gdB
g 5 10 / 20 (9.17)
The peak deviation also will depend on the number of channels, and
this is taken into account through use of a loading factor, L. The rele-
vant CCITT formulas are

For n 240: 20logL 15 10logn (9.18)
For 12 n 240: 20logL 1 4logn (9.19)

Once L and g are found, the required peak deviation is obtained from
the tabulated rms deviation as

# #
F g L F rms (9.20)
The required IF bandwidth can now be found using Carson’s rule,
Eq. (9.1), and the processing gain from Eq. (9.16). The following example
illustrates the procedure.

Example 9.5 The carrier-to-noise ratio at the input to the demodulator of an
FDM/FM receiver is 25 dB. Calculate the signal-to-noise ratio for the top chan-
nel in a 24-channel FDM baseband signal, evaluated under test conditions for
which Table 9.1 applies. The emphasis improvement is 4 dB, noise weighting
improvement is 2.5 dB, and the peak/rms factor is 13.57 dB. The audio channel
bandwidth may be taken as 3.1 kHz.
Solution Given data: n 24; gdB 13.57; b 3.1 kHz; [P] 4; [W] 2.5;
[C/N] 25

From Eq. (9.17):
gdB
g 5 10 / 20 5 4.77
From Eq. (9.19):
s2114 log nd
L 5 10 / 20 5 1.683
From Table 9.1, for 24 channels ΔF rms 35 kHz, and using Eq. (9.20),
# #
F g L F rms > 281 kHz
Assuming that the baseband spectrum is as shown in Fig. 9.4a, the top frequency is

f m 108 kHz
and Carson’s rule gives
B IF 2s F f m d 778 kHz