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Concept
Directivity
Summary
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 is the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions. Therefore, the directivity of a hypothetical isotropic radiator is 1, or 0 dBi.
An antenna's directivity is greater than its gain by an efficiency factor, radiation 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. By the principle of reciprocity, the directivity of an antenna 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, , of an antenna is defined for all incident angles of an antenna. The term "directive gain" is deprecated by IEEE. If an angle relative to the antenna is not specified, then directivity is presumed to refer to the axis of maximum radiation intensity.
Here and are the zenith angle and azimuth angle respectively in the standard spherical coordinate angles; is the radiation intensity, which is the power per unit solid angle; and is the total radiated power. The quantities and satisfy the relation
that is, the total radiated power is the power per unit solid angle integrated over a spherical surface. Since there are 4π steradians on the surface of a sphere, the quantity represents the average power per unit solid angle.
In other words, directivity is the radiation intensity of an antenna at a particular 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, if a direction is not specified, is the maximal directive gain value found among all possible solid angles:
In an antenna array the directivity is a complicated calculation in the general case.
Official source
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