Page 389 - Satellite Communications, Fourth Edition

The Space Link 369

Since frequency rather than wavelength is normally known, it is left
as an exercise for the student to show that with frequency f in gigahertz,
Eq. (12.43) can be rewritten as

[A 0 ] (21.45 20 log f) (12.44)

Combining this with Eq. (12.42) and rearranging slightly gives the
EIRP as

] [A ] [FSL]
[EIRP] [ M 0 (12.45)
Equation (12.45) was derived on the basis that the only loss present
was the spreading loss, denoted by [FSL]. But, as shown in the pre-
vious sections, the other propagation losses are the atmospheric
absorption loss, the polarization mismatch loss, and the antenna
misalignment loss. When allowance is made for these, Eq. (12.45)
becomes

[EIRP] [ ] [A ] [FSL] [AA] [PL] [AML] (12.46)
M
0
In terms of the total losses given by Eq. (12.12), Eq. (12.46) becomes

] [A ] [LOSSES] [RFL]
[EIRP] [ M 0 (12.47)
This is for clear-sky conditions and gives the minimum value of [EIRP]
which the earth station must provide to produce a given flux density
at the satellite. Normally, the saturation flux density will be specified.
With saturation values denoted by the subscript S, Eq. (12.47) is
rewritten as
] [ ] [A ] [LOSSES] [RFL] (12.48)
[EIRP S U S 0 U

Example 12.10 An uplink operates at 14 GHz, and the flux density required to sat-
2
urate the transponder is 120 dB(W/m ). The free-space loss is 207 dB, and the other
propagation losses amount to 2 dB. Calculate the earth-station [EIRP] required for
saturation, assuming clear-sky conditions. Assume [RFL] is negligible.
Solution At 14 GHz,

[A 0 ] (21.45 20 log14) 44.37 dB
The losses in the propagation path amount to 207 2 209 dB. Hence,
from Eq. (12.48),

[EIRP ] 120 44.37 209
S U
44.63 dBW