A descriptor form implementation of PEEC models incorporating dispersive and lossy dielectrics

With rising frequencies involved in electronics, losses and dispersion exhibited by dielectrics become important to consider in electromagnetic modeling. The Partial Element Equivalent Circuit (PEEC) method is suitable for a mixed electromagnetic and circuit setting, forming equivalent circuits that can be interconnected with circuit elements. In this paper, a descriptor form representation of PEEC models incorporating dispersive and lossy dielectrics is developed. By representing the electrical permittivity with a Debye-Lorentz model equivalent circuits can be synthesized. The synthesized circuits for the permittivity are included in the PEEC equations by formulating the circuit equations for the additional circuit unknowns. This yields an input/output formulation that can handle an arbitrary number of finite dielectrics and be integrated by any kind of integration scheme. Furthermore, it offers a straightforward way to incorporate lossy and dispersive dielectrics into a PEEC solver compared to using recursive convolution. The proposed descriptor form representation is tested for a setup consisting of three microstrips over a ground plane, separated by a dielectric substrate. Both the ideal and the lossy and dispersive case are tested and compared. Furthermore, the proposed formulation is verified against an existing implementation in the frequency-domain. Good agreement between the proposed formulation and the existing frequency-domain PEEC formulation is obtained.