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Parabolic reflector diameter: 75%, 3 GHz

Short answer

EIRP = P_t_dB - L + G. P_t = 500 W = 26.99 dBW, L = 2.5 dB, EIRP = 46 dBW → G_dB = 46 - 26.99 + 2.5 = 21.51 dB, G = 141.6. λ = 0.1 m, η = 0.75. Diameter D = (λ/π)√(G/η) = (0.1/π)√(141.6/0.75) ≈ 0.437 m (43.7 cm).

A parabolic reflector antenna having antenna efficiency 75% is designed for 3 GHz resonant frequency with 2.5 dB waveguide loss. Find out the antenna diameter if effective isotropic radiated power (EIRP) is calculated 46 dBW and transmitting power is 500 W.

EIRP = transmitter power − feeder (waveguide) loss + antenna gain (in dB). Find the gain from EIRP, then the diameter from G = η(πD/λ)².

Given: η = 0.75, f = 3 GHz, waveguide loss L = 2.5 dB, EIRP = 46 dBW, Pₜ = 500 W.

Step 1: Wavelength

λ = c/f = (3 × 10⁸)/(3 × 10⁹) = 0.1 m

Step 2: Transmit power in dBW

Pₜ = 10 log₁₀(500) = 26.99 dBW

Step 3: Antenna gain

EIRP = Pₜ − L + G
G    = 46 − 26.99 + 2.5 = 21.51 dB
G    = 10^(2.151) = 141.59

Step 4: Diameter

D = (λ/π) √(G/η)
  = (0.1/π) √(141.59/0.75)
  = 0.03183 × √188.79
  = 0.03183 × 13.740
  = 0.4374 m

Check: 0.75 × (π × 0.4374/0.1)² = 0.75 × 188.8 ≈ 141.6 → 21.51 dB. ✓

With lower efficiency (75 % instead of 85 %), a slightly larger dish is needed for the same gain.

Answer: G = 21.51 dB (141.6); diameter D ≈ 0.437 m (43.7 cm).

✓ Answer checked by Claude Opus 5.5 (high effort)

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