The edge admittance of a wide microstrip patch as seen by an obliquely incident wave

The reflection coefficient of a transverse electromagnetic wave, obliquely incident on the truncated upper edge of a slab-loaded parallel-plate waveguide, is calculated using the knowledge of both the tangential electric field and normal magnetic field on the top of the slab beyond the truncated edge. A suitable approximation of these aperture fields is obtained from the corresponding static fields, resulting in the correct value of the reflection coefficient to first order when the substrate is electrically thin. This development can be considered as a canonical problem on which several promising techniques in the analysis of microstrip patch antennas as circuit elements are based