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Fast and accurate evaluation of the antenna directivity via sampling expansion

A simple, fast and accurate closed form formula for evaluating the total radiated power, and then the antenna directivity, is proposed in this work. The derivation of such a formula is based on the spatial band limitation properties and nonredundant sampling representations of the electromagnetic field radiated by a transmitting antenna, so that a sampling expansion of the radiation intensity is adopted to reduce the surface integral in summations. The peculiarity of the proposed technique consists in reducing the number of samples over each parallel when moving from the equatorial circumference to the poles. This allows one to reduce significantly the number of required data with respect to the Dich's (1997) approach without loosing the accuracy of the total radiated power evaluation. It must be stressed that in the here proposed approach, according to the results of Bucci, Gennarelli and Savarese (see IEEE Trans. Antennas Propagat., vol.46, p.351-59, 1998), the number of samples over each parallel is related to the maximum transverse dimension of the antenna. Therefore the reduction in the number of data becomes very remarkable in the case of elongated antennas.