Page 292 - Satellite Communications, Fourth Edition

272 Chapter Nine

9.6.4 Signal-to-noise ratio
The term signal-to-noise ratio introduced in Sec. 9.6.3 is used to refer
to the ratio of signal power to noise power at the receiver output. This
ratio is sometimes referred to as the postdetector or destination signal-
to-noise ratio. In general, it differs from the carrier-to-noise ratio at the
detector input (the words detector and demodulator may be used inter-
changeably), the two ratios being related through the receiver process-
ing gain as shown by Eq. (9.9). Equation (9.9) may be written in decibel
form as

S C
10 log 10 10 log 10 10 log G P (9.11)
10
N N
As indicated in App. G, it is useful to use brackets to denote decibel
quantities where these occur frequently. Equation (9.11) therefore may
be written as

c S d c C d [G ] (9.12)
P
N N
This shows that the signal-to-noise in decibels is proportional to the
carrier-to-noise in decibels. However, these equations were developed for
the condition that the noise voltage should be much less than the car-
rier voltage. At low carrier-to-noise ratios this assumption no longer
holds, and the detector exhibits a threshold effect. This is a threshold
level in the carrier-to-noise ratio below which the signal-to-noise ratio
degrades very rapidly. The threshold level is shown in Fig. 9.12 and is
defined as the carrier-to-noise ratio at which the signal-to-noise ratio is
1 dB below the straight-line plot of Eq. (9.12). For conventional FM
detectors (such as the Foster Seeley detector), the threshold level may
be taken as 10 dB. Threshold extension detector circuits are available
which can provide a reduction in the threshold level of between 3 and
7 dB (Fthenakis, 1984).
In normal operation, the operating point will always be above thresh-
old, the difference between the operating carrier-to-noise ratio and the
threshold level being referred to as the threshold margin. This is also
illustrated in Fig. 9.12.

Example 9.4 A 1-kHz test tone is used to produce a peak deviation of 5 kHz in an
FM system. Given that the received [C/N] is 30 dB, calculate the receiver pro-
cessing gain and the postdetector [S/N].
Solution Since the [C/N] is above threshold, Eq. (9.12) may be used. The modula-
tion index is
5 kHz/1 kHz 5