Rigorous analysis of coupling in dielectric resonators

A theoretical analysis is presented of a shielded dielectric resonator (DR) structure consisting of a DR placed on a dielectric substrate with a very low dielectric constant spacer in-between and enclosed by a metallic shielding. The field equations are obtained by using both the axial mode-matching method and the radial mode-matching method. The technique used in the analysis is based on dividing the resonator structure into partial regions and regarding these as sections of dielectrically loaded waveguides. The resulting transcendental equation is obtained by enforcing the continuity of the tangential field components inside each partial region as well as the condition of vanishing tangential electric field on the metallic enclosure. As an example, a simplified version of the DR configuration has been solved and numerically evaluated using the theory of the mode matching method to obtain the coupling coefficient between a microstrip line and the magnetically coupled DR. The results are in good agreement with the experimental values