Antenna directivity

Directivity (D) is the ratio of the radiation intensity of an antenna in a given direction to the radiation intensity averaged over all directions. Usually the maximum value is quoted:

D = U_max / U_avg = 4π U_max / P_rad

where U = radiation intensity (W/sr) and U_avg = P_rad/4π (isotropic source).

• It depends only on the shape of the pattern, not on losses.
• Isotropic antenna D = 1 (0 dBi); short dipole 1.5 (1.76 dBi); λ/2 dipole 1.64 (2.15 dBi).
• For a pencil beam with half-power beamwidths θ1, θ2:

D ≈ 4π / (θ1 θ2)   (radians)
  ≈ 41253 / (θ1° θ2°)

Example: θ1 = θ2 = 30° → D ≈ 41253/900 ≈ 45.8 (16.6 dBi).

Relation with gain: G = η D, where η is the radiation efficiency.