Antenna efficiency

Antenna (radiation) efficiency is the ratio of the power radiated by the antenna to the power accepted at its input terminals. It accounts for conductor and dielectric losses.

η = P_rad / P_in = P_rad / (P_rad + P_loss)
  = Rr / (Rr + RL)

where Rr = radiation resistance and RL = loss resistance.

The total efficiency also includes mismatch loss:

e0 = e_r · e_c · e_d,   e_r = 1 − |Γ|²

(e_r reflection, e_c conductor, e_d dielectric efficiency).

Example: Rr = 73 Ω, RL = 2 Ω → η = 73/75 = 0.973 (97.3 %). With |Γ| = 0.2, e_r = 0.96 and total efficiency ≈ 0.934 (93.4 %).

Efficiency links gain and directivity: G = η D. Electrically short antennas have very small Rr, so their efficiency is low.