Generalized-scattering-matrix analysis of a class of finite arrays of coupled antennas by using 3-D FEM and spherical mode expansion

A rigorous method for characterizing, in terms of a multimode scattering matrix, a finite array of antennas where each antenna can be described by means of spherical waves is presented in this paper. The procedure provides the impedance, coupling and radiating characteristics of the arrays and comprises two steps. First, the generalized scattering matrix (GSM) of each single antenna is numerically calculated over a wide band of frequencies. For this purpose we use a previously-developed methodology that combines the domain segmentation technique, the three-dimensional finite element method (3D-FEM), spherical mode expansion and a reduced order model obtained using a symmetric matrix Pade´-Via-Lanczos (SyMPVL) algorithm. Second, the overall GSM of the finite array is calculated starting from the GSM of each antenna and using rotation and translation of spherical waves. A closed-form expression for the overall GSM is given and different examples are shown in order to validate the proposed method.