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Parabolic reflector diameter: 85%, 3 GHz

Short answer

For f=3 GHz, λ=0.1 m. P_t=500 W gives 26.99 dBW; with 2.5 dB loss and EIRP 46 dBW, gain is 21.51 dB (ratio 141.6). Using G=η(πD/λ)² with η=0.85 gives D=0.411 m.

A parabolic reflector antenna having the antenna efficiency 85% 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.

The EIRP of a transmitting system is the transmitter power minus feeder (waveguide) loss plus antenna gain (all in dB). From EIRP we find the gain, then the diameter from the parabolic gain formula G = η(πD/λ)².

Given: η = 0.85, 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(dBW) = 10 log₁₀(500) = 26.99 dBW

Step 3: Antenna gain from EIRP

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

Step 4: Diameter

G = η (πD/λ)²
D = (λ/π) √(G/η)
  = (0.1/π) √(141.59/0.85)
  = 0.03183 × √166.58
  = 0.03183 × 12.906
  = 0.4108 m

Check: 0.85 × (π × 0.4108/0.1)² = 0.85 × 166.58 ≈ 141.6 → 21.51 dB. ✓

Beamwidth for interest: HPBW ≈ 70λ/D = 70 × 0.1/0.4108 ≈ 17°.

Answer: Antenna gain = 21.51 dB (141.6); required dish diameter D ≈ 0.411 m (41.1 cm).

✓ Answer checked by Claude Opus 5.5 (high effort)

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