Page 388 - Satellite Communications, Fourth Edition

368 Chapter Twelve

specifically that the uplink is being considered. Thus Eq. (12.38)
becomes

c C d [EIRP] c G d [LOSSES] [k] (12.39)
U
U
N 0 U T U
In Eq. (12.39) the values to be used are the earth station EIRP, the
satellite receiver feeder losses, and satellite receiver G/T. The free-space
loss and other losses which are frequency-dependent are calculated for
the uplink frequency. The resulting carrier-to-noise density ratio given
by Eq. (12.39) is that which appears at the satellite receiver.
In some situations, the flux density appearing at the satellite receive
antenna is specified rather than the earth-station EIRP, and Eq. (12.39)
is modified as explained next.

12.7.1 Saturation flux density
As explained in Sec. 7.7.3, the traveling-wave tube amplifier (TWTA) in
a satellite transponder exhibits power output saturation, as shown in
Fig. 7.21. The flux density required at the receiving antenna to produce
saturation of the TWTA is termed the saturation flux density. The sat-
uration flux density is a specified quantity in link budget calculations,
and knowing it, one can calculate the required EIRP at the earth sta-
tion. To show this, consider again Eq. (12.6) which gives the flux den-
sity in terms of EIRP, repeated here for convenience:
EIRP

M
4 r 2
In decibel notation this is
1
[ M ] [EIRP] 10 log 2 (12.40)
4 r
But from Eq. (12.9) for free-space loss we have
l 2 1
[FSL] 10 log 10 log 2 (12.41)
4 4 r
Substituting this in Eq. (12.40) gives

l 2
[ M ] [EIRP] [FSL] 10 log (12.42)
4
2
The l /4 term has dimensions of area, and in fact, from Eq. (6.15) it
is the effective area of an isotropic antenna. Denoting this by A gives
0
l 2
[A ] 10 log (12.43)
0
4