Directive Gain and Directivity of Antenna

The Directive Gain (D_G) is defined as the ratio of radiation intensity due to the test antenna to isotropic antenna (hypothetical antenna that radiates uniformly in all direction).

                       

                                    D_G =     U        =    4πU 

                                                 U₀             P_rad

Where,

U   = radiation intensity due to test antenna, in watts per unit solid angle

U₀  = radiation intensity due to isotropic antenna, in watts per unit solid angle

P_rad =total power radiated in watts

Since U is a directional dependent quantity, the directive gain of an antenna depends on the angle θ and Φ. If the radiation intensity assumes its maximum value then the directive gain is called the Directivity (D₀).

i.e.                               D_G =     U_max    =   4πU_max

                                                   U₀              P_rad

Gain of an Antenna

Power Gain of an antenna is defined as the ratio of its radiation intensity at a point to the radiation intensity that results from a uniform radiation of the same input power.

i.e.                               Gain = 4π x radiation intensity           = 4π (θ, Φ)

                                                    Total input power                     P_in

Whereas, relative gain is defined as the ratio of power gain of the test antenna in a given direction to a power gain of reference antenna (whose gain can calculated or known). In most of cases reference antenna is a lossless isotropic source.

i.e.                               Gain =                  4π (θ, Φ)

                                                 P_in (lossless isotropic antenna)

 When the direction is not stated, the power gain is usually taken in the direction of maximum radiation.