Lossy Spherical Cavity Resonators for Stress-Testing Arbitrary 3D Eigenmode Solvers

A lossy metal-wall cavity resonator that extends well beyond perturbation theory limits is studied. An exact analytical solution is employed for the spherical cavity resonator, having walls transformed from being a perfect electrical conductor (PEC) to free space. This model then acts as an ideal benchmark reference standard. A plane-wave approximation is then derived. Independent full-wave numerical modeling of the spherical cavity resonator is undertaken using eigenmode solvers within two well-known commercial, industry-standard, simulation software packages (HFSSTMand COMSOL). It has been found that the plane-wave approximation model accurately characterizes the results generated by these solvers when equivalent finite conductivity boundary (FCB) and layered impedance boundary (LIB) conditions are used. However, the impedance boundary (IB) condition is accurately characterized by the exact model, but the precise value of complex wave impedance at the wall boundary for the specific resonance mode must first be known a priori. Our stress-testing results have profound implications on the usefulness of these commercial solvers for accurately predicting eigenfrequencies of lossy arbitrary 3D structures. For completeness, an exact series RLC equivalent circuit model is given specifically for a spherical cavity resonator having arbitrary wall losses, resulting in the derivation of an extended perturbation model.