Page 402 - Satellite Communications, Fourth Edition

382 Chapter Twelve

Equation (12.61) shows that to obtain the combined value of C/N , the
0
reciprocals of the individual values must be added to obtain the N /C
0
ratio and then the reciprocal of this taken to get C/N . Looked at in
0
another way, the reason for this reciprocal of the sum of the reciprocals
method is that a single signal power is being transferred through the
system, while the various noise powers, which are present are additive.
Similar reasoning applies to the carrier-to-noise ratio, C/N.

Example 12.18 For a satellite circuit the individual link carrier-to-noise spectral
density ratios are: uplink 100 dBHz; downlink 87 dBHz. Calculate the combined
C/N 0 ratio.
Solution

N 0 10 8.7 9
10 10 2.095 10
C
Therefore,

s C t 10 log(2.095 10 )
9
N 0
86.79 dBHz

Example 12.18 illustrates the point that when one of the link C/N 0
ratios is much less than the other, the combined C/N ratio is approxi-
0
mately equal to the lower (worst) one. The downlink C/N is usually (but
not always) less than the uplink C/N , and in many cases it is much less.
0
This is true primarily because of the limited EIRP available from the
satellite.
Example 12.19 illustrates how BO is taken into account in the link-
budget calculations and how it affects the C/N ratio.
0
Example 12.19 A multiple carrier satellite circuit operates in the 6/4-GHz band
with the following characteristics.
Uplink:
2
Saturation flux density 67.5 dBW/m ; input BO 11 dB; satellite G/T 11.6
1
dBK .
Downlink:
Satellite saturation EIRP 26.6 dBW; output BO 6 dB; free-space loss 196.7 dB;
1
earth station G/T 40.7 dBK . For this example, the other losses may be ignored.
Calculate the carrier-to-noise density ratios for both links and the combined value.
Solution As in the previous examples, the data are best presented in tabular form,
and values are shown in decilogs. The minus signs in Eqs. (12.50) and (12.55) are
attached to the tabulated numbers: