A unified approach to the analysis of radial waveguides, dielectric resonators, and microstrip antennas on spherical multilayer structures

This paper presents a uniform procedure to analyze radial waveguides, dielectric resonators, dielectric resonator antennas, and microstrip antennas on spherical structures. It can be applied to any type of spherical multilayer closed and sector structures, which also include hemispherical structures. The arbitrary layers may be airgaps or dielectric substrates with or without metallizations in the interfaces. The inner layer can be a metallic or dielectric core. The kernel of this approach is the derivation of the spectral- and space-domain dyadic Green´s function of multilayer spherical structures by using an equivalent circuit and simple network analysis techniques. The relations between the spectral and space domains are derived using the vector-Legendre transformation. For the demonstration of the applicability of this approach, the dyadic Green´s functions and the system equations of some commonly used spherical structures are presented, among which the system equation of a two-layer dielectric resonator is verified analytically with the literature. As an example, the resonant frequencies of a spherical resonator with two dielectric layers covering a metallic inner layer are calculated and verified with commercial software.