Q4Satellite Communication

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Q.4. An earth station employs a power amplifier providing an output power of 100 W and antenna of 5 meter diameter for both transmission and reception. The transmit frequency is 6.25 GHz and the receive frequency is 4.5 GHz. System noise temperature is 140 K. Find the EIRP and G/T ratio for this station.

Answer 1

Given: Pout = 100 W, antenna diameter D = 5 m (same antenna for both Tx and Rx), transmit frequency ftx = 6.25 GHz, receive frequency frx = 4.5 GHz, system noise temperature Tsys = 140 K. Assume a typical aperture efficiency η = 0.55 (55%), a standard value for parabolic reflector antennas unless otherwise specified.

Transmit antenna gain (at 6.25 GHz): using the standard parabolic antenna gain formula G = η(πD/λ)², with wavelength λ = c/f = 3×10⁸/6.25×10⁹ = 0.048 m:

G_{t x} = η (\frac{π D}{λ})^{2} = 0.55 \times (\frac{π \times 5}{0.048})^{2}

G_{t x} (dB) = 10 lo g_{10} (G_{t x}) \approx 47.70 dB

EIRP calculation: first, convert the transmit power to dBW: Pout(dBW) = 10log₁₀(100) = 20 dBW. Then:

E I R P = P_{o u t} (dBW) + G_{t x} (dB) = 20 + 47.70 = 67.70 dBW

Receive antenna gain (at 4.5 GHz): with wavelength λ = 3×10⁸/4.5×10⁹ = 0.0667 m:

G_{r x} = η (\frac{π D}{λ})^{2} = 0.55 \times (\frac{π \times 5}{0.0667})^{2}

G_{r x} (dB) \approx 44.85 dB

G/T ratio: the figure of merit G/T (in dB/K) is calculated as the receive antenna gain minus the system noise temperature expressed in dB:

T_{sy s} (dB) = 10 lo g_{10} (140) \approx 21.46 dB

G / T = G_{r x} (dB) - T_{sy s} (dB) = 44.85 - 21.46 \approx 23.39 dB/K

Result: EIRP ≈ 67.70 dBW and G/T ≈ 23.39 dB/K for this earth station. Note that the receive antenna gain is lower than the transmit antenna gain despite using the same physical dish, because the receive (downlink) frequency of 4.5 GHz is lower than the transmit (uplink) frequency of 6.25 GHz — since parabolic antenna gain scales with the square of frequency for a fixed aperture size (G∝1/λ²∝f²), the lower-frequency downlink signal is captured with correspondingly lower gain by the same physical dish, which is consistent with the general link-budget principle discussed earlier that uplink frequencies are deliberately set higher than downlink frequencies.

Sensitivity of the result to aperture efficiency assumption: since the problem does not explicitly state an aperture efficiency, the assumed value of η=0.55 (a typical, commonly quoted figure for a well-designed prime-focus or Cassegrain parabolic reflector) directly affects the computed gain and hence the final EIRP and G/T values; because gain enters as G=η(πD/λ)², a change in efficiency shifts the gain in dB by 10log₁₀(η_new/η_old). For example, a lower-efficiency antenna (η=0.5) would reduce Gtx by about 10log₁₀(0.5/0.55)≈-0.41 dB, giving Gtx≈47.29 dB and EIRP≈67.29 dBW, while a higher-efficiency antenna (η=0.65) would increase Gtx by about +0.72 dB. This sensitivity is why aperture efficiency is always explicitly specified (or measured via antenna range testing) in real earth-station procurement and acceptance-testing specifications, rather than left to a generic assumed value.

G (dB) = 10 lo g_{10} (η) + 20 lo g_{10} (\frac{π D}{λ})

Cross-check using the alternative gain-frequency-diameter formula: the same transmit gain can be verified using the commonly tabulated engineering approximation G(dBi) ≈ 20log₁₀(f_GHz) + 20log₁₀(D_m) + 17.8 (which folds a typical 55% efficiency directly into the constant term), giving Gtx ≈ 20log₁₀(6.25)+20log₁₀(5)+17.8 = 15.92+13.98+17.8 = 47.7 dB, matching the value obtained from the fundamental η(πD/λ)² formula and confirming the calculation.

Practical design significance: an EIRP of 67.7 dBW (about 5.9 MW) is a substantial but realistic uplink EIRP for a medium-sized commercial C-band/extended-C-band earth station of this power and antenna size, sufficient to close a link to a typical GEO transponder with adequate margin under clear-sky conditions. The computed G/T of 23.39 dB/K is representative of a good standard-size commercial receive-only or transmit-receive earth station (by comparison, large international gateway stations with bigger antennas and cryogenically cooled LNAs achieve G/T values of 35-40 dB/K, while small VSAT terminals typically have G/T in the range of 10-20 dB/K); this station's combination of moderate transmit power (100 W) and moderate antenna size (5 m) situates it as a fairly typical business-grade or teleport-class earth station rather than either a high-end broadcast gateway or a low-cost consumer VSAT. If the same station instead needed to operate at Ku-band (where rain attenuation is more severe), the same G/T and EIRP figures would need to be supplemented with a considerably larger rain-fade power margin, or the antenna/HPA sized up accordingly, illustrating how the frequency band choice interacts with the basic EIRP/G/T design trade-off computed here.

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