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Determination of complex resonant frequencies of resonators loaded with dielectric materials

A variational technique is employed to determine complex resonant frequencies of cavity resonators for isotropic dielectric material measurements. Effects of lossy walls and the filling hole of the resonator on the resonant frequency are taken into account by using surface impedance boundary condition. Magnetic fields in the variational expression are expanded into loss-free modes of the cavity to reduce the problem to a matrix equation. The resulting equation is in fact a nonlinear eigenvalue problem in terms of wavenumber. Starting with an initial guess, it is firstly approximated by a quadratic eigenvalue problem that is transformed to a generalized eigenvalue problem and then solved. For validation, the results obtained by the proposed method are compared with measured data.