Analysis of finite-size phased arrays of circular waveguide elements

A derivation is presented for the calculation of the interelement mutual coupling in a finite-size planar array of waveguide-fed apertures covered by a multilayered dielectric and/or plasma. The general mutual admittance expression is evaluated for circular apertures and the mutual coupling calculations are verified experimentally for two transverse electric circular waveguide mode excited apertures. A parametric study of higher order mode aperture fields indicates that the only significant change in the circular aperture mutual coupling is due to the transverse magnetic mode, which introduces an additional phase shift. Qualitative agreement between calculations for a 183-element array of circular apertures and an infinite array establishes the validity of the finite-array theoretical model.