The partial element equivalent circuit (PEEC) method provides an electromagnetic model of interconnections and packaging structures in terms of standard circuit elements. The surface-based PEEC (S-PEEC) formulation can reduce the number of unknowns compared to the standard volume-based PEEC (V-PEEC) method. This reduction is of particular use in the case of high-speed circuits and high-switching power electronics, where the bandwidth extends from low frequencies to the GHz range. In this article, the S-PEEC formulation is revised and cast in a matrix form. The main novelty is that the interaction integrals involving the curl of the magnetic and electric vector potentials are computed through the Taylor series expansion of the full-wave Green’s function, leading to analytical forms that are rigorously derived. Therefore, the numerical integration is avoided, with a consequent reduction of the computation time. The proposed formulas are studied in terms of the frequency, size of the mesh, and distance between the basis function domains. Three examples are presented, confirming the accuracy of the proposed method compared to the V-PEEC method and surface-based numerical methods from literature.

The Partial Element Equivalent Circuit (PEEC) method is widely used to model a large variety of electrical systems ranging from interconnects to antennas and packaging. A key aspect in the development of the method is the computation of interaction integrals, namely partial inductances and coefficients of potential. In this work, a novel semi-analytical approach to the computation of the self-interaction integral over rectangular domains is proposed for the zero thickness case as it occurs in the case of the coefficients of potential and partial inductances of very thin conductors and in the surface integral equation based formulation. The proposed semi-analytical formula is verified by comparison with more standard integration schemes.