An isotropic antenna is an antenna that radiates all the received input power uniformly in all directions.
The gain of an antenna in a particular direction is the ratio between the power radiated by the antenna in this direction and the power that would be radiated by an isotropic antenna, then converted to decibel.
Antenna gain unit is dBi. dB because the power ratio is given in decibel, i for the isotropic reference. The gain of an isotropic antenna is then 0dBi in all directions. The gain of a perfect dipole is 2.15dBi at 0˚ elevation.
dBd is sometimes used for omnidirectional antennas application. Instead of the theoretical isotropic antenna, a theoretical dipole antenna is used as a reference. Here is how to convert from dBi:
Antenna Gain (dBd) = Max Antenna Gain (dBi) -2.15
For more details the best reference is 145-2013 – IEEE Standard for Definitions of Terms for Antenna.
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