The only 3 dimensional omnidirectional antenna is the unity gain isotropic antenna, a theoretical construct derived from actual antenna radiation patterns and used as a reference for specifying antenna gain and radio system effective radiated power. Antenna gain (G) is defined as antenna efficiency (e) multiplied by antenna directivity (D) which is expressed mathematically as: . A useful relationship between omnidirectional radiation pattern directivity (D) in decibels and half-power beamwidth (HPBW) based on the assumption of a pattern shape is:
Practical antennas approach omnidirectionality by providing uniform radiation or response only in one reference plane, usually the horizontal one parallel to the earth's surface.
Common low gain omnidirectional antennas are the whip antenna, a vertically orientated dipole antenna, the discone antenna, and the horizontal loop antenna (or halo antenna) (Sometimes known colloquially as a 'circular aerial' because of the shape).
Omnidirectional antennas are generally realized using colinear dipole arrays. These arrays consist of half-wavelength dipoles with a phase shifting method between each element that ensures the current in each dipole is in phase. The Coaxial Colinear or COCO antenna uses transposed coaxial sections to produce in-phase half-wavelength radiatiors. A Franklin Array uses short U-shaped half-wavelength sections whose radiation cancels in the far-field to bring each half-wavelength dipole section into equal phase.