Quasi-Static Partial Element Equivalent Circuit Models of Linear Magnetic Materials

This paper presents a 3-D partial element equivalent circuit (PEEC) model of linear magnetic materials under the quasi-static hypothesis. Rigorous analytical formulas are proposed for integrals accounting for flux density due to both current and magnetization densities for Manhattan-type discretizations. Such closed-form formulas remove the singularities exhibited by existing formulas and completely avoid numerical integration. The resulting model preserves the circuit interpretation of standard PEEC models and, thus, can be easily integrated in a SPICE-like circuit solver. Numerical results are presented showing that the proposed closed formulas outperform the numerical schemes and guarantee an excellent agreement with existing results available in the literature.