Page 392 - Satellite Communications, Fourth Edition

372 Chapter Twelve

In Eq. (12.53) the values to be used are the satellite EIRP, the earth-
station receiver feeder losses, and the earth-station receiver G/T.The
free space and other losses are calculated for the downlink frequency.
The resulting carrier-to-noise density ratio given by Eq. (12.53) is that
which appears at the detector of the earth station receiver.
Where the carrier-to-noise ratio is the specified quantity rather
than carrier-to-noise density ratio, Eq. (12.38) is used. This becomes,
on assuming that the signal bandwidth B is equal to the noise band-
width B :
N
c C d [EIRP] c G d [LOSSES] [k] [B] (12.54)
D
D
N D T D

Example 12.12 A satellite TV signal occupies the full transponder bandwidth of
36 MHz, and it must provide a C/N ratio at the destination earth station of 22 dB.
Given that the total transmission losses are 200 dB and the destination earth-
station G/T ratio is 31 dB/K, calculate the satellite EIRP required.
Solution Equation (12.54) can be rearranged as

[EIRP] D c C d c G d [LOSSES] D [k] [B]
N D T D

Setting this up in tabular form, and keeping in mind that [k] 228.6 dB
and that losses are numerically equal to 200 dB, we obtain

Quantity Decilogs
[C/N] 22
[G/T] 31
[LOSSES] 200
[k] 228.6
[B] 75.6
[EIRP] 38

The required EIRP is 38 dBW or, equivalently, 6.3 kW.
Example 12.12 illustrates the use of Eq. (12.54). Example 12.13 shows
the use of Eq. (12.53) applied to a digital link.

Example 12.13 A QPSK signal is transmitted by satellite. Raised-cosine fil-
tering is used, for which the rolloff factor is 0.2 and a bit error rate (BER) of
10 5 is required. For the satellite downlink, the losses amount to 200 dB, the
1
receiving earth-station G/T ratio is 32 dBK , and the transponder bandwidth
is 36 MHz. Calculate (a) the bit rate which can be accommodated, and (b) the
EIRP required.