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specifically that the uplink is being considered. Thus Eq. (12.38) becomes c C d N0 U [EIRP]U c G d T U [LOSSES]U [k] (12.39)
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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.
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12.7.1 Saturation ux density
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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 saturation flux density is a specified quantity in link budget calculations, and knowing it, one can calculate the required EIRP at the earth station. To show this, consider again Eq. (12.6) which gives the flux density in terms of EIRP, repeated here for convenience:
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(12.40)
But from Eq. (12.9) for free-space loss we have [FSL] 10 log l2 4 10 log 1 4 r2
(12.41)
Substituting this in Eq. (12.40) gives [
[EIRP]
[FSL]
10 log
(12.42)
The l2/4 term has dimensions of area, and in fact, from Eq. (6.15) it is the effective area of an isotropic antenna. Denoting this by A0 gives [A0] 10 log l2 4 (12.43)
The Space Link
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 [A0] (21.45 20 log f) (12.44)
Combining this with Eq. (12.42) and rearranging slightly gives the EIRP as [EIRP] [
[A0]
[FSL]
(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 previous 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] [
[A0]
[FSL]
[AA]
[PL]
[AML]
(12.46)
In terms of the total losses given by Eq. (12.12), Eq. (12.46) becomes [EIRP] [
[A0]
[LOSSES]
[RFL]
(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 [EIRPS]U [
[A0]
[LOSSES]U
[RFL]
(12.48)
Example 12.10 An uplink operates at 14 GHz, and the flux density required to sat-
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, [A0] (21.45 20 log 14) 44.37 dB
The losses in the propagation path amount to 207 from Eq. (12.48), [EIRPS]U 120 44.37 209
209 dB. Hence,
44.63 dBW
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12.7.2 Input backoff
As described in Sec. 12.7.3, where a number of carriers are present simultaneously in a TWTA, the operating point must be backed off to a linear portion of the transfer characteristic to reduce the effects of intermodulation distortion. Such multiple carrier operation occurs with frequencydivision multiple access (FDMA), which is described in Chap. 14. The point to be made here is that backoff (BO) must be allowed for in the linkbudget calculations. Suppose that the saturation flux density for single-carrier operation is known. Input BO will be specified for multiple-carrier operation, referred to the single-carrier saturation level. The earth-station EIRP will have to be reduced by the specified BO, resulting in an uplink value of [EIRP]U [EIRPS]U [BO]i (12.49)
Although some control of the input to the transponder power amplifier is possible through the ground TT&C station, as described in Sec. 12.7.3, input BO is normally achieved through reduction of the [EIRP] of the earth stations actually accessing the transponder. Equations (12.48) and (12.49) may now be substituted in Eq. (12.39) to give c C d N0 U [
[A0]
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