Quasi-static partial element equivalent circuit models of magneto-dielectric materials

This study aims to present the formulation of the partial element equivalent circuit (PEEC) for dispersive and lossy linear magneto-dielectric materials under the quasi-static hypothesis. The magnetic permeability and dielectric permittivity are usually available as tabulated data at different frequency samples. They are incorporated in the time-domain PEEC formulation by resorting to a rational approximation of their frequency-dependent constitutive relations. Thus, a set of ordinary differential equations is obtained besides those obtained by enforcing Kirchoff voltage and current laws to the PEEC equivalent circuit. The resulting augmented model preserves the circuit structure of the usual PEEC model and, hence, can be run in Spice-like circuit solvers. The robustness and accuracy of the proposed time-domain approach is tested by comparison with its frequency-domain counterpart despite the larger number of unknowns.