Using Spherical Harmonics to Model Mutual Coupling Effects on Embedded Element Patterns

Abstract

The reconstruction of Embedded Element Patterns (EEP) in an array of antennas is presented as an attempt to understand the effects of Mutual Coupling (MC) among the antenna elements. The EEP far fields are modeled with a weighted sum of orthonormal spherical harmonic basis functions (explained by their mode numbers). The weight of each significantly contributing mode is estimated by the Singular Value Decomposition (SVD) approach. A practical example of a non-uniform array of circular patch antennas is considered for analyzing the significant contributing modes. Although the values of the weights of the modes are different for each antenna element in the array, the contributing modes remain very similar for all the elements, indicating that the mutual coupling can be sufficiently explained by a limited number of variables (weights) corresponding to limited spherical harmonic modes. The reconstructed patterns are validated by comparing them with full-wave simulation results.