Modelling a spherical patch antenna axisymmetrically excited by a radial probe

Existing theories for the patch antenna radiation on dielectric layered substrates, especially, for spherical patches are not complete. A mathematically complete theory must have the capability of establishing the existence of an exact solution to the boundary value problem, and result in an algorithm for finding it with a guaranteed accuracy. The method of analytical regularization, exploiting a partial inversion of the basic equations, offers a way of building such a theory. In this paper the problem of modelling a spherical conformal antenna is considered. These antennas are frequently excited by a radial coaxial probe, which can be modelled by an electric dipole located at the surface of the metallic sphere