directivity

[الدكتور عبد الكريم]

In electromagnetics, directivity is a figure of merit for an antenna. It measures the power density an actual antenna radiates in the direction of its strongest emission, relative to the power density radiated by an ideal isotropic radiator antenna radiating the same amount of total power. Mathematically, the directivity is defined as the maximum of the directive gain:

where
• θ and φ are the standard spherical coordinates angles
• Radiated power density is the power per unit solid angle such that
• 4π is the total solid angle for a sphere (also the surface area of a unit sphere, similar to 2π ****g the total angle for a circle and the perimeter of a unit circle).
• The denominator, , represents the average radiated power density
The directivity is rarely expressed as a unitless number. Usually, the directivity is expressed in dBi, so that

The reason the units are dBi (decibel relative to an isotropic radiator) is that for an isotropic radiator, the radiated power density is a constant, and therefore equals the average radiated power density (the denominator). This isotropic radiator is not directive at all but has nevertheless a directivity stricto senso equal to 1. This can be misleading and is much better described in dBi.

The word directivity is also sometimes used as a synonym for directive gain. This usage is readily understood, as the direction will be specified, or directional dependence implied. Later editions of the IEEE Dictionary[1] specifically endorse this usage; nevertheless it has yet to be universally adopted.
The peak directivity of an actual antenna can vary from 1.76 dB for a short dipole, to as much as 50 dB for a large dish antenna[2].