Shielded Composite Dielectric Spherical Resonator

Abstract

Electromagnetics theoretic analysis of composite Shielded dielectric resonator has been made. Charactersticequation for the TE and TM dielectric sphere of radic of the order of mm size are found suitable for the optical frequency reason where as for the microwave reason. Radic of the order of mm size are founds suitable. Expressions for the quality factor for realistic resonator i.e for a composite shielded dielectric resonator with a non zero conductivity and a metal shield with a finite conductivity have also been derived for TE and TM modes. Computations for the quality factors have been made for resonators with parameter suitable for the optical and micro wave reason. Keywords Spherical resonator quality factors eigen modes.

The electromagnetic field analysis of the shielded spherical diectric resonators starting fromthe maxwells equations The problem has been treated using spherical coordinates geometry. Assuming and idealized situation in which the shield is perfectly conducting (Loss less) and the dielectric is (loss less) the problem has been treated separately for the TE and TM modes. The field for the expression has been derived. And using the boundry conditions.Characteristics equations have been derived. Since the characteristic equation are transcendental equation these have been solved numerically to calculate resonant frequency. In fact the shield as well as dielectric arelossy due to their finite conductivities. Hence, the quality factor for a realistic resonator is finite.

Expressions for the quality factor have been derived by using expressions for the dielectric loss. In order to calcite quality factor the resonant frequency for the ideal resonator have been used. Effect of variation of the sphere radius on the resonant frequency and quality factor has been study in this paper.