Directivity

In electromagnetics, directivity is a parameter of an antenna or optical system which measures the degree to which the radiation emitted is concentrated in a single direction. It measures the power density the antenna radiates in the direction of its strongest emission, versus the power density radiated by an ideal isotropic radiator (which emits uniformly in all directions) radiating the same total power. An antenna's directivity is a component of its gain; the other component is its (electrical) efficiency. Directivity is an important measure because many antennas and optical systems are designed to radiate electromagnetic waves in a single direction or over a narrow angle. Directivity is also defined for an antenna receiving electromagnetic waves, and its directivity when receiving is equal to its directivity when transmitting. The directivity of an actual antenna can vary from 1.76 dBi for a short dipole, to as much as 50 dBi for a large dish antenna. The directivity, D {displaystyle D} , of an antenna is the maximal value of its directive gain. Directive gain is represented as D ( θ , ϕ ) {displaystyle D( heta ,phi )} and compares the radiant intensity (power per unit solid angle) U ( θ , ϕ ) {displaystyle U( heta ,phi )} that an antenna creates in a particular direction against the average value over all directions: Here θ {displaystyle heta } and ϕ {displaystyle phi } are the zenith angle and azimuth angle respectively in the standard spherical coordinate angles; U ( θ , ϕ ) {displaystyle U( heta ,phi )} is the radiation intensity, which is the power per unit solid angle; and P tot {displaystyle P_{ ext{tot}}} is the total radiated power. The quantities U ( θ , ϕ ) {displaystyle U( heta ,phi )} and P tot {displaystyle P_{ ext{tot}}} satisfy the relation that is, the total radiated power P tot {displaystyle P_{ ext{tot}}} is the power per unit solid angle U ( θ , ϕ ) {displaystyle U( heta ,phi )} integrated over a spherical surface. Since there are 4π steradians on the surface of a sphere, the quantity P tot / ( 4 π ) {displaystyle P_{ ext{tot}}/(4pi )} represents the average power per unit solid angle. In other words, directive gain is the radiation intensity of an antenna at a particular ( θ , ϕ ) {displaystyle ( heta ,phi )} coordinate combination divided by what the radiation intensity would have been had the antenna been an isotropic antenna radiating the same amount of total power into space. Directivity, then, is the maximal directive gain value found among all possible solid angles: