Partial Element Equivalent Circuit Models of Three-Dimensional Geometries Including Anisotropic Dielectrics

During recent years anisotropic materials have received an increasing interest and found important applications in the field of shielding and antennas. The anisotropy may be due to intrinsic properties, or as a consequence of mixing. Intentionally or not, the anisotropy impacts the electromagnetic (EM) behavior of a system. Therefore, it is desirable to be able to incorporate the anisotropic effects in an EM model, to allow design tasks and analysis. In this paper, the partial element equivalent circuit (PEEC) formulation is extended to handle nondispersive linear anisotropic dielectrics. The anisotropic dielectric PEEC cell is derived and the resulting PEEC equations are developed into a descriptor system form, which is well suited for implementation in SPICE-like solvers, and for reduction by model-order reduction techniques. A verification of the model is given by a numerical example of a patch antenna situated on an anisotropic substrate and the results are in good agreement with a finite-difference time-domain implementation. The proposed PEEC model is of interest for further work, i.e., in the modeling of setups involving mixtures of materials, with an orientational alignment, and engineered materials, encountered in different EM compatibility applications.