Vector complex eigenmode analysis of microwave cavities

A vector complex eigenmode analysis procedure of microwave cavities is presented. The resonance problem of arbitrary shaped microwave cavities loaded with lossy dielectric material is formulated with the finite-element method in either E or H fields through a Galerkin-weighted residual procedure. Discretisation of the problem results in a very large, highly sparse, complex symmetric generalised eigenvalue problem. Inverse iteration with shifting in combination with a preconditioned conjugate gradient procedure is employed for the efficient solution of the complex eigenvalue problem. The method, being very efficient in terms of time and memory, is applied in the determination of the resonance of a cylindrical cavity loaded with lossy dielectric material. The obtained results are in very good agreement with experimental ones. A duality in the resonant frequencies is observed between the E and H formulations. Furthermore, the method can be used in the solution of the inverse problem of determining the dielectric properties of the loaded material