One-Dimensional Non-Uniform Dielectric Structure as Tunable Resonator

Abstract

The paper presents research on the composite dielectric resonators. This type of resonator consists of dielectric parts, which can move with respect to each other using an external actuator. The air discontinuity between dielectric parts perturbs the electromagnetic field of the resonator and as a result, shifts resonance frequency. As an analytical solution for this kind of structure does not exist, most practical techniques resort to approximate numerical solutions. The electromagnetic field problem for an inhomogeneous dielectric structure consisting of two infinite plates separated by a dielectric layer with a different dielectric constant is solved rigorously. The problem is reduced to a nonlinear eigenvalues and vectors problem. The eigenvalues determine the resonant frequencies, and the vectors represent the electromagnetic field of the resonance structure. It is shown, that the resonant frequency of the basic LM-mode has a high sensitivity to the change of the air layer between dielectric plates. Displacement of the plates in a few percent of its thickness leads to a change in the resonant frequency by tens of percent, depending on the dielectric constant of the plate. The sensitivity of the resonant frequency shift and the tuning range increases as the dielectric constant grows up and the plate thickness decreases. Another factor affected on resonant frequency tuning sensitivity and range is the distribution of the electromagnetic field along the dielectric plate plane. The increase of the electromagnetic field variation in such directions leads to growing sensitivity but reducing the tuning range. Resonant frequencies of LE-mode are less sensitive to a displacement of resonator's parts. The main reason for such a difference is the direction of E-field in inhomogeneity regions. E-field of LM-modes is directed normally to the border between the dialectic plate and air, but the E-field of LE-modes is located parallel to the border. The correlation characteristics of the tuning with the geometric and electrophysical parameters of the plates were established. It has been shown, that resonance frequency tuning occurs without degradation of the resonator's unloaded Q-factor. Moreover, the Q-factor increases due to the redistribution of electromagnetic field energy into the air region where the loss is almost absent. It has been demonstrated, that the regularities for a one-dimensional inhomogeneous structure are valid for inhomogeneous cylindrical dielectric resonators.