Antenna Gain - Relative to a Dipole


In electromagnetics, an antenna’s power gain or simply gain is a key performance figure which combines the antenna’s directivity and electrical efficiency. As a transmitting antenna, the figure describes how well the antenna converts input power into radio waves headed in a specified direction. As a receiving antenna, the figure describes how well the antenna converts radio waves arriving from a specified direction into electrical power. When no direction is specified, “gain” is understood to refer to the peak value of the gain. A plot of the gain as a function of direction is called the radiation pattern.

Antenna gain is usually defined as the ratio of the power produced by the antenna from a far-field source on the antenna’s beam axis to the power produced by a hypothetical lossless isotropic antenna, which is equally sensitive to signals from all directions. Usually this ratio is expressed in decibels, and these units are referred to as “decibels-isotropic” (dBi). An alternative definition compares the antenna to the power received by a lossless half-wave dipole antenna, in which case the units are written as dBd. Since a lossless dipole antenna has a gain of 2.15 dBi, the relation between these units is: gain in dBd = gain in dBi – 2.15 dB . For a given frequency, the antenna’s effective area is proportional to the power gain. An antenna’s effective length is proportional to the square root of the antenna’s gain for a particular frequency and radiation resistance. Due to reciprocity, the gain of any antenna when receiving is equal to its gain when transmitting.

Directive gain or directivity is a different measure which does not take an antenna’s electrical efficiency into account. This term is sometimes more relevant in the case of a receiving antenna where one is concerned mainly with the ability of an antenna to receive signals from one direction while rejecting interfering signals coming from a different direction.

A true isotropic radiator cannot be built, so in practice a different antenna is used. This will often be a half-wave dipole, a very well understood and repeatable antenna that can be easily built for any frequency. The directive gain of a half-wave dipole is known to be 1.64 and it can be made nearly 100% efficient. Since the gain has been measured with respect to this reference antenna, the difference in the gain of the test antenna is often compared to that of the dipole. The “gain relative to a dipole” is thus often quoted and is denoted using “dBd” instead of “dBi” to avoid confusion. Therefore in terms of the true gain (relative to an isotropic radiator) G, this figure for the gain is given by the formula shown here.

Related formulas


GdBdantenna gain relative to a dipole (in dB) (dimensionless)
Gtrue gain (dimensionless)