Finite element solution of dielectric-ferrite resonators

Planar ferrite resonators are widely used in microwave and millimeter-wave junction circulators. Recent trends toward broadbanding and miniaturization of devices have led to interest in novel inhomogeneous structures. To simplify design procedures, a finite element package for the calculation of modal resonant frequencies in terms of a specified applied bias field and material magnetization has been developed. The frequency dependence of the ferrite tensor components is included in the analysis, and so the resulting eigenvalue problem is nonlinear. An iterative finite element scheme is used to solve this problem for resonators with arbitrary geometries, making full use of the symmetry of the modes. For the special case of homogeneous resonators of arbitrary shape the calculations may be simplified through the use of normalized parameters. To illustrate the technique and the limitations of the use of normalized parameters, a homogeneous ferrite ring resonator and an inhomogeneous dielectric-ferrite ring resonator have been analyzed. In both cases, good agreement with the exact solution is obtained. Calculations are also presented for a practical circulator geometry with threefold symmetry: a dielectric triangle inserted within a ferrite disk.