Characteristics of circular patch on thick substrate and superstrate

Accurate formulation for the wall admittance of a circular patch on a thick substrate/superstrate is presented. The principle of equivalence is invoked at the physical aperture of the patch, which yields equivalent electric and magnetic surface currents for the outside fields. The unknown electric current, in terms of the aperture electric field, is obtained from the field continuity condition on the aperture surface. Numerical results reveal that for a small substrate thickness, the equivalent electric current may be ignored. It should, however, be included in the analysis for larger substrate thicknesses. Numerical results for the wall conductance, wall susceptance, and radiation efficiency of a patch with various substrates and superstrates are presented