Antenna gain

Antenna gain is the dimensionless ratio G = 4π U_max/P_rad, where U_max is the maximum radiation intensity (power per unit solid angle) and P_rad is the total power radiated by the antenna. It quantifies the extent to which an antenna concentrates its radiated power in its peak direction compared with a hypothetical isotropic radiator that would spread the same total power uniformly over 4π steradians. Gain is usually expressed in decibels relative to isotropic (dBi): G_dBi = 10 log₁₀(G).

Representative values: an isotropic radiator has G = 1 (0 dBi) by definition. A Hertzian dipole has G = 1.5 (1.76 dBi). A centre-fed half-wave dipole has G ≈ 1.64 (2.15 dBi). A three-element Yagi for VHF television has about 7 dBi. A large parabolic dish for satellite downlink has G up to 40–60 dBi, with its gain-aperture relation G = 4π A_eff/λ². The reciprocity theorem guarantees that an antenna's gain is the same for transmission and reception — a high-gain dish that concentrates outgoing power into a narrow beam equally collects incoming power from that same narrow beam and rejects signals from elsewhere. The gain enters the Friis transmission formula P_r = P_t G_t G_r (λ/4πr)² that governs radio link budgets, and the effective aperture A_eff = G λ²/(4π) gives the equivalent collecting area for reception. Gain above isotropic is always paid for by pattern narrowness: no antenna can have G > 1 in every direction; high gain in one direction requires nulls elsewhere.