Efficient computation for the general solution of a slot loaded by a hemispherical dielectric and/or backing cavity

The problem of a slot loaded by a hemispherical dielectric and/or a hemispherical backing cavity is solved using the method of moments (MoM). A novel recurrence formula is presented for fast calculations of the MoM admittance integrals associated with the spherical homogeneous solutions. The method enables the admittance integrals to be calculated without the need for any numerical integration. Measurements were carried out and good agreement between theory and experiment is obtained.