Analysis of a circular microstrip disk antenna with a thick dielectric substrate

The problem of a circular microstrip disk excited by a probe is solved using rigorous analysis. The disk is assumed to have zero thickness, and the current on the probe is taken to be uniform. Using vector Hankel transforms the problem is formulated in terms of vector dual-integral equations, from which the unknown current can be solved for. Due to the singular nature of the current distribution arising from probe excitation, the direct applications of Galerkin's basis function expansion method gives a slowly convergent result. Therefore the singular part of the current is removed since the singularity is known a priori. The unknown current to be solved for is then regular and tenable to Galerkin's method of analysis. It is shown that this analysis agrees with the single-mode approximation when the dielectric substrate layer is thin, and that it deviates from the single-mode approximation when the substrate layer is thick. Excellent agreement of both the computed real and imaginary parts of the input impedance with experimental data is noted. The radiation patterns and the current distributions on the disk are also presented.