Determination of Far Fields of Wire Antennas on a PEC Sphere Using Spherical Harmonic Expansion

Far-field patterns of wire antennas on a PEC sphere are calculated from quasi-static near fields using spherical harmonic expansion. Three cases of the wire antennas - F-antenna, dipole, and resonant loop on the PEC sphere - are considered. With the assumed sinusoidal current distribution on the antenna, the method of images is employed to obtain currents and charges on the antenna's image against the sphere. Only from the charge density and current distributions of the wire antenna and its image, ignoring the sphere, the quasi-static near fields are calculated using Coulomb's and Biot-Savart's laws. The fields in a source-free region are expressed in spherical harmonic expansion with the coefficients obtained from the radial components of the calculated quasi-static electric and magnetic near fields. The far fields thus obtained from the expansion match well with that of the simulated patterns. Deviations between simulation and theory are discussed and explained.