The Unified Approach to the Analysis of Spherical Multilayer Structures and its Applications

Abstract

This work presents a unified 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 air 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 spherical multilayer 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. The verification process of this approach is done on some test structures. For dielectric resonators, the system equation of a two-layer dielectric resonator is analytically verified with literature, the resonant frequencies of a resonator with two dielectric substrates covering a metallic core agree well with commercial software. For microstrip antennas, the dyadic Green’s function of a microstrip antenna on a spherical structure of one dielectric layer covering a metallic one is identical to literature and very good agreement of the input impedance and radiation pattern of the antenna with commercial software codes is achieved. The agreement of the calculated input impedance of microstrip antennas with measured data is also obtained. The effects of the curvature and ground plane on the input impedance and radiation pattern are shown. Furthermore, the derivation of system equations of some commonly used radial waveguides and the dyadic Green’s function of some more complex microstrip structures are presented.