Page 372 - Satellite Communications, Fourth Edition

352 Chapter Twelve

EIRP is often expressed in decibels relative to 1 W, or dBW. Let P be
S
in watts; then
[EIRP] [P ] [G] dBW (12.3)
S
where [P ] is also in dBW and [G] is in dB.
S
Example 12.1 A satellite downlink at 12 GHz operates with a transmit power of
6 W and an antenna gain of 48.2 dB. Calculate the EIRP in dBW.

Solution
[EIRP] 10 loga 6W b 48.2
1W
56 dBW

For a paraboloidal antenna, the isotropic power gain is given by Eq.
(6.32). This equation may be rewritten in terms of frequency, since this
is the quantity which is usually known.

2
G (10.472fD) (12.4)
where f is the carrier frequency in GHz, D is the reflector diameter in
m, and is the aperture efficiency. A typical value for aperture effi-
ciency is 0.55, although values as high as 0.73 have been specified
(Andrew Antenna, 1985).
With the diameter D in feet and all other quantities as before, the
equation for power gain becomes

2
G (3.192fD) (12.5)

Example 12.2 Calculate the gain in decibels of a 3-m paraboloidal antenna oper-
ating at a frequency of 12 GHz. Assume an aperture efficiency of 0.55.
Solution
2
G 0.55 (10.472 12 3) > 78168
Hence,
[G] 10 log 78168 48.9 dB

12.3 Transmission Losses
The [EIRP] may be thought of as the power input to one end of the
transmission link, and the problem is to find the power received at the
other end. Losses will occur along the way, some of which are constant.