Optimum directivity coverage of fan-beam antennas

Cellular and point-to-multipoint wireless communication systems use fan-beam antennas for sector coverage from the central station. The ratio of the azimuth-to-elevation half-power beamwidth typically ranges from two for sites requiring low-gain antenna values to 25 or greater for sites covering large cells. This article presents an approximate formula for the antenna directivity of the fan-beam antenna using two parameters to describe the azimuth pattern shape, and two parameters for the elevation pattern. The directivity formula presented includes minor lobes. A variation of the fan-beam directivity formula is presented for the omnidirectional antenna. The directivity formula presented in this note is developed from separable-pattern functions, and uses a pattern-shape parameter in addition to the half-power-beamwidth value.