Directivity

Directivity is a property of a radiating source that describes how its radiated power is distributed over directions. It quantifies how strongly the source concentrates energy in particular directions relative to an ideal isotropic radiator.

Mathematically, directivity D is defined as D = 4π Umax / P_rad, where U(θ,φ) is the radiation intensity in a given direction and P_rad is the total power radiated. An equivalent expression is D = 4π / Ω_A, where Ω_A is the solid angle over which the source radiates with significant power. By convention, an isotropic radiator has D = 1, while real antennas with focused beams have D > 1.

Directivity is related to, but distinct from, antenna gain. Gain G equals the product of directivity and radiation efficiency (G = ηD). Thus a directive but inefficient antenna may have the same or lower gain than a less directive, more efficient one.

The concept is illustrated by the radiation pattern, which includes the main lobe, beamwidth, side lobes, and nulls. Directivity is determined from measurements or simulations of the far-field pattern U(θ,φ). Higher directivity is achieved by larger apertures or specialized structures, such as parabolic dishes, horn antennas, or Yagi arrays in radio frequency applications; in acoustics, horn-loaded loudspeakers and arrays can produce directional sound.

Directivity is important in radar, wireless communications, and audio design to optimize coverage, signal-to-noise ratio, and interference management. It does not account for losses due to inefficiency or mismatches, which are captured separately by gain.