Page 373 - Satellite Communications, Fourth Edition

The Space Link 353

Other losses can only be estimated from statistical data, and some of
these are dependent on weather conditions, especially on rainfall.
The first step in the calculations is to determine the losses for clear-
weather or clear-sky conditions. These calculations take into account the
losses, including those calculated on a statistical basis, which do not vary
significantly with time. Losses which are weather-related, and other
losses which fluctuate with time, are then allowed for by introducing
appropriate fade margins into the transmission equation.
12.3.1 Free-space transmission
As a first step in the loss calculations, the power loss resulting from the
spreading of the signal in space must be determined. This calculation is sim-
ilar for the uplink and the downlink of a satellite circuit. Using Eqs. (12.1)
and (12.2) gives the power-flux density at the receiving antenna as
EIRP
(12.6)
M
4 r 2
The power delivered to a matched receiver is this power-flux density
multiplied by the effective aperture of the receiving antenna, given by
Eq. (6.15). The received power is therefore

P A eff
M
R
2
EIRP l G R

4 r 2 4 (12.7)
2
)a l b
(EIRP)(G R
4 r
Recall that r is the distance, or range, between the transmit and
is the isotropic power gain of the receiving
receive antennas and G R
antenna. The subscript R is used to identify the receiving antenna.
The right-hand side of Eq. (12.7) is separated into three terms asso-
ciated with the transmitter, receiver, and free space, respectively. In
decibel notation, the equation becomes

2
[P ] [EIRP] [G ] 10 loga 4 r b (12.8)
R
R
l
The received power in dBW is therefore given as the sum of the trans-
mitted EIRP in dBW plus the receiver antenna gain in dB minus a third
term, which represents the free-space loss in decibels. The free-space loss
component in decibels is given by
2
[FSL] 10 loga 4 r b (12.9)
l