Gain, efficiency and polarization

Antenna gain

Gain is the ratio of the radiation intensity in a given direction to the radiation intensity that would be obtained if the input power were radiated isotropically:

G(θ,φ) = 4π U(θ,φ) / P_in
P_rad = η P_in   →   G = η D
G(dBi) = 10 log10 G

It includes losses, so G ≤ D. Example: λ/2 dipole, D = 1.64; if η = 0.97, G = 1.59 (2.0 dBi). For aperture antennas G = 4πAe/λ².

Antenna efficiency

Radiation efficiency is the ratio of power radiated to power accepted at the terminals:

η = P_rad / P_in = Rr / (Rr + RL)

Rr = radiation resistance, RL = ohmic/dielectric loss resistance. Total efficiency also includes mismatch: e0 = (1 − |Γ|²) · η.

Example: Rr = 73 Ω, RL = 2 Ω → η = 73/75 = 97.3 %.

Antenna polarization

Polarization is the orientation of the E-field vector traced with time at a fixed far-field point in the direction of maximum radiation. Write the field as two orthogonal components:

Ex = Ex0 cos(ωt − kz)
Ey = Ey0 cos(ωt − kz + δ)

• Linear: δ = 0 or π (or one component zero).
• Circular: Ex0 = Ey0 and δ = ±90° (RHCP / LHCP).
• Elliptical: all other cases.

Axial ratio AR = major/minor axis (1 for circular, ∞ for linear). Polarization loss factor PLF = |ρ̂w · ρ̂a|² = cos²ψ.