Page 374 - Satellite Communications, Fourth Edition

354 Chapter Twelve

Normally, the frequency rather than wavelength will be known, and
8
the substitution l c/f can be made, where c 10 m/s. With frequency
in megahertz and distance in kilometers, it is left as an exercise for the
student to show that the free-space loss is given by
[FSL] 32.4 20 log r 20 log f (12.10)

Equation (12.8) can then be written as
] [EIRP] [G ] [FSL] (12.11)
[P R R
] will be in dBW when the [EIRP] is in dBW, and
The received power [P R
[FSL] in dB. Equation (12.9) is applicable to both the uplink and the
downlink of a satellite circuit, as will be shown in more detail shortly.

Example 12.3 The range between a ground station and a satellite is 42,000 km.
Calculate the free-space loss at a frequency of 6 GHz.

Solution
[FSL] 32.4 20 log 42,000 20 log 6000 200.4 dB
This is a very large loss. Suppose that the [EIRP] is 56 dBW (as calcu-
lated in Example 12.1 for a radiated power of 6 W) and the receive antenna
gain is 50 dB. The receive power would be 56 50 200.4 94.4 dBW.
This is 355 pW. It also may be expressed as 64.4 dBm, which is 64.4 dB
below the 1-mW reference level.
Equation (12.11) shows that the received power is increased by
increasing antenna gain as expected, and Eq. (6.32) shows that antenna
gain is inversely proportional to the square of the wavelength. Hence,
it might be thought that increasing the frequency of operation (and
therefore decreasing wavelength) would increase the received power.
However, Eq. (12.9) shows that the free-space loss is also inversely pro-
portional to the square of the wavelength, so these two effects cancel.
It follows, therefore, that for a constant EIRP, the received power is
independent of frequency of operation.
If the transmit power is a specified constant, rather than the EIRP,
then the received power will increase with increasing frequency for
given antenna dish sizes at the transmitter and receiver. It is left as an
exercise for the student to show that under these conditions the received
power is directly proportional to the square of the frequency.

12.3.2 Feeder losses
Losses will occur in the connection between the receive antenna and the
receiver proper. Such losses will occur in the connecting waveguides,
filters, and couplers. These will be denoted by RFL, or [RFL] dB, for receiver