Simultaneous Use of Addition Theorems for Cylindrical and Spherical Waves for the Fast Full-Wave Analysis of SIW-Based Antenna Arrays

This paper introduces a fast full-wave methodology for the analysis of antenna arrays placed on the top plate of substrate integrated waveguides (SIWs). The methodology is based on the generalized scattering matrix (GSM) of each array element in terms of spherical and cylindrical modes and plane-port feeding modes, and the simultaneous use of addition theorems for spherical and cylindrical waves. Addition theorems allow the analytical translation of spherical and cylindrical modes, so that the GSMs can be simultaneously connected in the SIW layer and in the radiation region, to obtain the full-wave response of the array. The proposed methodology is validated by means of full-wave simulations with commercial and in-house softwares.