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Receiving antenna gain

Short answer

Receiving antenna gain Gr expresses how well an antenna captures power from an incoming wave compared with an isotropic antenna. By reciprocity it equals transmitting gain and relates to effective aperture as Gr = 4πAe/λ². A 1.2 m dish at 12 GHz with 55% efficiency gives about 41.0 dBi.

Explain the antenna parameter: receiving antenna gain (Gr).

Receiving antenna gain (Gr) expresses how well an antenna captures power from an incoming wave in its direction of maximum response compared with an isotropic antenna. By reciprocity it equals the transmitting gain, and it is related to the effective aperture Ae:

Gr = 4π Ae / λ²
Ae = η_a × A_physical  (aperture antennas)
Pr = PFD × Ae = Pt Gt Gr (λ / 4πd)²

Example: 1.2 m dish at 12 GHz (λ = 0.025 m), η_a = 0.55: Ae = 0.55 × π(0.6)² ≈ 0.622 m²; Gr = 4π × 0.622/0.025² ≈ 12 507 ≈ 41.0 dBi.

Gr is higher for larger aperture and higher frequency; it appears in the receiver term G/T of satellite links.

✓ Answer checked by Claude Opus 5.5 (high effort)

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