Mutual Coupling of Antennas with Overlapping Minimum Spheres Based on the Transformation between Spherical and Plane Vector Waves

Abstract

Mutual coupling in finite arrays of antennas with strongly overlapping minimum spheres is quickly calculated by computing the general translation matrix between spherical modes. This matrix is obtained by using the transformation properties of spherical and plane vector waves. Although this approach is less efficient than the classical one, which is based on addition theorems, it allows to overcome the well-known limitation of addition theorems that requires nonintersecting minimum spheres. Symmetry relations are provided for the translation coefficients that greatly increase the speed of computation of the general translation matrix. By computing the reflection and the transmission submatrices of the generalized scattering matrix of a finite antenna array, accurate results are obtained for the S-parameters and the radiation patterns of arrays, in comparison with commercial software or a purely numerical in-house full-wave method. For this purpose, different types of antennas with strongly overlapping hemispheres in an array environment on a ground plane are used, such as apertures, monopoles, cavity-backed patch antennas, or dielectric resonator antennas.