A Closed-Form Method for Predicting Mutual Coupling Between Base-Station Dipole Arrays

A simple approach is developed to compute mutual coupling (or isolation) between base-station antenna arrays of N dipoles. This method is more practical compared to direct field measurement of the mutual coupling between two antennas as a function of the separation distance. The approach utilizes a closed-form expression for the self and mutual impedances for two slanted dipoles in free space. Two arrays of these dipoles are then assembled together. The elements of the 2Ntimes2N Z matrix of the resulting system are the self-impedance of individual dipoles as well as the mutual impedance between every two dipoles within each array as well as between the two arrays. The input impedance of each array and the mutual impedance between the two arrays are derived through simultaneous solution of the 2N-port antenna system and two (N+1)-port feed networks feeding the two arrays. Two types of feed networks are introduced: One comprised of a cascade of two-way power dividers, often referred to as a corporate feed (CF), and the other is a virtual feed network based on the parallel connection of all antenna elements in each array, which will be referred to as the parallel feed (PF). The two types of feed networks were compared and found equivalent. However, the PF type is much less tedious to use from a network analysis standpoint. It is further shown that the S parameters for the CF type may be deduced from the PF type using duality. The above approach for computing mutual coupling between antenna arrays cannot directly account for the effect of a finite ground plane that is usually utilized in the base-station arrays to provide higher gains and a nearly one-sided beam. A correction method is suggested, whereby the mutual coupling between two arrays without a ground plane is adjusted to provide a reasonable estimate for the coupling between two arrays with a finite ground plane. This correction approach is based on the far-field coupling predicted by the Friis transmission formula. The mutual coupling between the two arrays predicted by this method agrees reasonably well with the measured results for arrays in both broadside and collinear configurations