(S)PEEC: Time- and frequency-domain surface formulation for modeling conductors and dielectrics in combined circuit electromagnetic simulations

The partial element equivalent circuit (PEEC) formulation is an integral-equation-based approach for the solution of combined circuit and electromagnetic (EM) problems. In this paper, a surface-based PEEC formulation is presented to complement the existing volume-based method. With the rise in the operating, frequencies and the increasing complexity of test structures on boards, packages, and chips, a surface-based formulation is more efficient for many problems in terms of the number of unknowns generated. The composite conductor dielectric modeling is based on the PMCHWT formulation which is transformed into a PEEC representation using equivalent magnetic and electric circuits connected by mutual coupling. Both time- and frequency-domain analyses are discussed, similar to a Spice-type circuit solver. The new formulation is compared with the volume-based PEEC approach in terms of accuracy and the number of unknowns generated.