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Parabolic reflector diameter: 75%, 5 GHz

Short answer

Wavelength is 0.06 m at 5 GHz. Antenna gain from EIRP is 25.22 dB (332.5). Diameter equals (λ/π)√(G/η) = 0.402 m (40.2 cm).

A parabolic reflector antenna having antenna efficiency 75% is designed for 5 GHz resonance frequency with 3 dB waveguide loss. If Effective Isotropic Radiated Power (EIRP) is calculated 50 dBW and transmitting power is 600 W, calculate its diameter.

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

Given: η = 0.75, f = 5 GHz, waveguide loss L = 3 dB, EIRP = 50 dBW, Pₜ = 600 W.

Step 1: Wavelength

λ = c/f = (3 × 10⁸)/(5 × 10⁹) = 0.06 m

Step 2: Transmit power in dBW

Pₜ = 10 log₁₀(600) = 27.78 dBW

Step 3: Antenna gain

EIRP = Pₜ − L + G
G    = 50 − 27.78 + 3 = 25.22 dB
G    = 10^(2.522) = 332.54

Step 4: Diameter

D = (λ/π) √(G/η)
  = (0.06/π) √(332.54/0.75)
  = 0.019099 × √443.39
  = 0.019099 × 21.057
  = 0.4022 m

Check: 0.75 × (π × 0.4022/0.06)² = 0.75 × 443.4 ≈ 332.5 → 25.22 dB. ✓

HPBW ≈ 70λ/D = 70 × 0.06/0.4022 ≈ 10.4°.

Answer: G = 25.22 dB (332.5); diameter D ≈ 0.402 m (40.2 cm).

✓ Answer checked by Claude Opus 5.5 (high effort)

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