Q2Satellite Communication

Given: Tin=60K, TRF=60K, TM=600K, TIF=1200K, GRF=17dB, Gm=0dB, GIF=25dB (GIF is not needed in the standard three-stage formula since IF is the last, terminal stage here).

First convert the gain values from dB to linear ratios:

The system noise temperature, referred to the receiver input, is calculated using the Friis cascaded-noise formula:

Result: the overall system noise temperature is approximately 155.9 K. This calculation clearly illustrates the Friis formula's central insight — the first two terms (Tin=60K and TRF=60K), representing the antenna and first-stage RF amplifier noise contributions, together already account for 120 K (about 77%) of the total 155.9 K system noise temperature, while the mixer and IF stage contributions, though individually large in their own right (600K and 1200K respectively), are heavily suppressed (divided by the RF stage's gain of 50.12) once referred back to the system input, contributing only about 12 K and 24 K respectively — confirming why earth station receiver designers focus intensely on minimizing the noise temperature of the very first (RF/LNA) amplification stage, since it dominates the overall system noise performance regardless of how much noisier the later stages may be.

Cross-check by direct noise-figure conversion: the same result can be verified independently by first converting each stage's noise temperature into an equivalent noise figure using F = 1 + T/290 (with the reference temperature T0 = 290 K), then applying the standard cascaded Friis noise-figure formula, and finally converting the resulting overall noise figure back into an equivalent system noise temperature using Ts = (F-1)×290. Carrying this through for the given data yields FRF = 1+60/290 = 1.207, FM = 1+600/290 = 3.069, FIF = 1+1200/290 = 5.138, and the cascaded overall noise figure F = FRF + (FM-1)/GRF + (FIF-1)/(GRF·GM) = 1.207 + 2.069/50.12 + 4.138/50.12 = 1.207+0.0413+0.0826 = 1.331, which back-converts to Ts = (1.331-1)×290 = 96.0 K for the receiver chain alone (excluding the antenna's own Tin=60K contribution); adding this to Tin gives 60+96.0 = 156.0 K, matching the Friis-temperature-domain calculation of 155.9 K to within rounding error, confirming the arithmetic is self-consistent regardless of whether the calculation is carried out in the temperature domain or the noise-figure domain.

Practical significance for earth-station design: a system noise temperature of about 156 K is a realistic, respectable value for a good-quality 4 GHz C-band earth station receiver front-end, and this figure would subsequently be combined with the receive antenna gain to yield the station's G/T figure of merit, which together with the satellite's downlink EIRP and the free-space/atmospheric path loss determines the achievable carrier-to-noise ratio C/N = C/(kTsB) for the link. Because Ts appears directly (linearly) in the denominator of this C/N expression, every reduction in Ts translates directly into an equivalent improvement in link margin — for example, reducing TRF from 60 K to 30 K (a plausible improvement from upgrading to a lower-noise LNA) would reduce Ts to roughly 60+30+11.97+23.94 ≈ 125.9 K, an improvement of about 0.9 dB in G/T, which could be traded for a smaller receive antenna, a higher data rate, or additional rain-fade margin at Ku/Ka-band, illustrating why LNA noise-temperature specification is one of the most economically significant design parameters in earth-station procurement.

Effect of changing operating conditions: if the antenna were instead pointed at a lower elevation angle, Tin would rise (due to increased atmospheric noise contribution and greater ground-noise pickup through antenna sidelobes near the horizon), directly increasing Ts and degrading G/T even though the receiver hardware itself is unchanged — this is why link budgets specify a minimum operating elevation angle, and why antenna sites are chosen to maximize elevation angle to the target satellite wherever geographically possible. Similarly, if rain were present along the propagation path, the sky noise temperature contribution to Tin would increase further (since a lossy, absorptive medium such as a rain cell radiates thermal noise in proportion to its own physical temperature and its attenuation), simultaneously degrading the received carrier power (via rain attenuation) and increasing the system noise temperature — a double penalty that is precisely why rain-fade link margins at higher frequency bands must be sized generously to cover both effects together, not merely the attenuation of the wanted signal alone.