The fundamental characteristics of an antenna are its gain and half-power beamwidth. According to the Reciprocity theorem (a generic theorem for transmission processes), the transmitting and receiving patterns of an antenna are identical at a given radio frequency. The gain quantifies the amount of input power that is concentrated in a particular direction. It is expressed with respect to a hypothetical isotropic antenna, which radiates equally in all directions. (Isotropic means radiating in all directions.)
Thus, in a given direction (q, f ), the gain is as follows:
G(q,f) = (dP / dW)/(Pin/4π)
where Pin is the total input power, and dP is the increment of radiated output power in solid angle dW. ...