Accurate determination of antenna directivity

The derivation of a formula for accurate estimation of the total radiated power from a transmitting antenna for which the radiated power density is known in a finite number of points on the far-field sphere is presented. The main application of the formula is determination of directivity from power-pattern measurements. The derivation is based on the theory of spherical wave expansion of electromagnetic fields, which also establishes a simple criterion for the required number of samples of the power density. An array antenna consisting of Hertzian dipoles is used to test the accuracy and rate of convergence of the derived formula. Its performance is compared to that of numerical integration using Simpson's formula.