In electromagnetics, an antenna's gain is a key performance parameter which combines the antenna's directivity and radiation efficiency. The term power gain has been deprecated by IEEE. In a transmitting antenna, the gain describes how well the antenna converts input power into radio waves headed in a specified direction. In a receiving antenna, the gain 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, the gain in the direction of the antenna's main lobe. A plot of the gain as a function of direction is called the antenna pattern or radiation pattern. It is not to be confused with directivity, which does not take an antenna's radiation efficiency into account. Gain or 'absolute gain' is defined as "The ratio of the radiation intensity in a given direction to the radiation intensity that would be produced if the power accepted by the antenna were isotropically radiated". Usually this ratio is expressed in decibels with respect to an isotropic radiator (dBi). An alternative definition compares the received power 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(dBd) ≈ Gain(dBi) − 2.15. For a given frequency, the antenna's effective area is proportional to the 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.
Gain Gain is a unitless measure that multiplies an antenna's radiation efficiency η {\displaystyle \eta } and directivity D {\displaystyle D} :
G = η D {\displaystyle G=\eta D}
Radiation efficiency The radiation efficiency η {\displaystyle \eta } of an antenna is "The ratio of the total power radiated by an antenna to the net power accepted by the antenna from the connected transmitter."
η = P R P O {\displaystyle \eta ={P_{\mathrm {R} } \over P_{\mathrm {O} }}}
A transmitting antenna is supplied with power by a transmission line connecting the antenna to a radio transmitter. The power accepted by the antenna P O {\displaystyle P_{\mathrm {O} }} is the power supplied to the antenna's terminals. Losses prior to the antenna terminals are accounted for by separate impedance mismatch factors which are therefore not included in the calculation of radiation efficiency.
Gain in decibels Published numbers for antenna gain are almost always expressed in decibels (dB), a logarithmic scale. From the gain factor G {\displaystyle G} , one finds the gain in decibels as:
G d B i = 10 log 10 ( G ) . {\displaystyle G_{\mathrm {dBi} }=10\log _{10}\left(G\right).}
Therefore, an antenna with a peak power gain of 5 would be said to have a gain of 7 dBi. 'dBi' is used rather than just 'dB' to emphasize that this is the gain according to the basic definition, in which the antenna is compared to an isotropic radiator. When actual measurements of an antenna's gain are made by a laboratory, the field strength of the test antenna is measured when supplied with, say, 1 watt of transmitter power, at a certain distance. That field strength is compared to the field strength found using a so-called reference antenna at the same distance receiving the same power in order to determine the gain of the antenna under test. That ratio would be equal to G {\displaystyle G} if the reference antenna were an isotropic radiator ("irad"). However 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 with respect to the isotropic radiator 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 {\displaystyle G} , this figure for the gain is given by:
G dBd ≈ 10 log 10 ( G 1.64 ) . {\displaystyle G_{\text{dBd}}\approx 10\log _{10}\left({\frac {G}{1.64}}\right).}
For instance, the above antenna with a gain G {\displaystyle G} = 5 would have a gain with respect to a dipole of 5/1.64 ≈ 3.05, or in decibels one would call this 10 log(3.05) ≈ 4.84 dBd. In general:
G dBd ≈ G dBi − 2.15 dB {\displaystyle G_{\text{dBd}}\approx G_{\text{dBi}}-2.15\,{\text{dB}}}
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