Analysis of mutual coupling in finite planar arrays of dielectric covered rectangular waveguides

The merits of phased array antennas in communications and radar applications are well known. In the design of such an array, the mutual coupling between closely spaced apertures must be taken into account since this affects the radiation pattern shape and the active reflection coefficient of the radiating aperture. These apertures are usually covered with some dielectric material for environmental protection. Therefore the mutual coupling effects between these apertures must be calculated in the presence of the dielectric sheet. These apertures have usually been circular, rectangular or square. Expressions for the coupling between elements in a finite planar array of circular apertures, without the dielectric coverings have been given by Bird (1987) and have subsequently been verified elsewhere. Various methods are available to compute the mutual coupling, even with the higher order mode coupling between them but without the dielectric covering. A number of publications have included the effect of the dielectric covering but the coupling values are an approximation based on an infinite array approach. We present exact expressions for the mutual coupling between rectangular apertures, with or without the dielectric sheet. The analysis allows any orientation of the rectangular apertures as well as the coupling between any number of waveguide modes.