Resonant patch antennas on spherical ground planes and the need for fractional order associated legendre functions

Summary form only given. The traditional cavity model has been a valuable tool for the estimation of resonant modes of patch antennas since its inception nearly 30 years ago. This model is frequently used for planar antenna structures having canonical shapes in Cartesian, cylindrical, and elliptical coordinates. However, there is no limitation on the cavity model that requires the ground plane to be planar. As such, the cavity model can be useful for determining resonant modes of patch antennas having canonical shapes in spherical coordinates on a spherical ground plane. Indeed, the resonant modes readily follow by solving for the internal fields (underneath the patch) with the presumption of fictitious magnetic walls around the perimeter of the patch and electric walls on the top and bottom. Using a classical TE/TM decomposition of the fields, the resonant modes may be found.