An array is simply a group of objects, and the array factor is a measure of how much a specific characteristic changes because of the grouping. This phenomenon is observed when antennas are grouped together. The radiation (or reception) pattern of the antenna group is considerably different from that of a single antenna. This is due to the constructive and destructive interference properties of radio waves. A well designed antenna array, allows the broadcast power to be directed to where it is needed most. These antenna arrays are typically one dimensional, as seen on collinear dipole arrays, or two dimensional as on military phased arrays. In order to simplify the mathematics, a number of assumptions are typically made: 1. all radiators are equal in every respect 2. all radiators are uniformly spaced 3. the signal phase shift between radiators is constant. The array factor

AF

is the complex-valued

far-field The near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative ''near-field'' behaviors dominate close to the ante ...

radiation pattern In the field of antenna design the term radiation pattern (or antenna pattern or far-field pattern) refers to the ''directional'' (angular) dependence of the strength of the radio waves from the antenna or other source.Constantine A. Balanis: “A ...

obtained for an array of

N

isotropic radiators located at

coordinates In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...

\vec_n

, as determined by:

AF(\hat) = \sum_^N a_n e^,

where

a_n

are the complex-valued excitation coefficients, and

\hat

is the direction

unit vector In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in \hat (pronounced "v-hat"). The term ''direction vecto ...

. The array factor is defined in the transmitting mode, with the time convention

e^

. A corresponding expression can be derived for the receiving mode, where a negative sign appears in the exponential factors, as derived in reference.

References

See also