Analytical Far-Zone Calculation of the Field Radiated From an Equilateral Triangular Aperture

Abstract

This communication contributes to the classical analytical models for computing the radiated electromagnetic fields from an aperture with a canonical shape by means of the equivalence principle. Analytical closed-form expressions are presented for the radiation pattern generated by the modes of an equilateral triangular aperture. The derived formulation is based on the use of a well-known equivalence principle, which provides the radiated far-field from the transversal field at the aperture. This equivalence principle, as well as the formulation of the modal field functions associated with an equilateral triangular aperture, are briefly described. The equivalence principle is then applied to these modal field functions to evaluate the closed-form expressions for the integrals required to obtain the radiation pattern associated with each mode. Different examples are shown, where the analytical results achieved by the formulation derived in this communication when compared with those provided by commercial software packages based on different numerical approaches show a very good agreement.