Gain

Related wiki pages Antennas, Antenna Design, Decibels, Radiated Power Measurement, SWR

Gain compared to a half wave dipole - dBD
The gain of an antenna is the relative increase in radiation at the maximum point expressed as a value in dB  above a standard. The standard to which other antennas are compared is usually a ½-wavelength dipole. The standard antenna is given a reference gain of 0dBD (zero decibel referenced to dipole). This comes from:

$$ \mbox{gain} = 10 \times \log \left( \frac {Pe}{Pi} \right) $$

Where Pe is effective radiated power and Pi is input power

An antenna with the effective radiated power of three times the input power would therefore have a gain of:

Pe = 3, Pi = 1

$$ 10 \times \log \left( \frac {3}{1} \right) = 4.77\mbox{dBD} $$

Gain compared to an isotropic readiator = dBi
An isotropic radiator is a theoretical "point source" antenna that radiates the same amount of energy in all directions. Although an isotropic antenna cannot be constructed, it is sometimes useful to compare actual antennas to it.

Comparison of dBD and dBi
Graphically, the radiation patterns of isotropic and dipole antennas - for equal power inputs - can be represented thus:



The area between the isotropic radiator circle and the half wave circle radiator circle represents a gain difference of approximately 2.15dB

hence, $$ dBi = dBD + 2.15 $$