Analytical Formulas for the Computation of the Electric Field in the Partial Element Equivalent Circuit Method With Conductive, Dielectric, and Magnetic Media

In this paper, analytical formulas for the electric field generated by currents, charges, and magnetization in conductive, dielectric, and magnetic media are presented in the framework of the partial element equivalent circuit (PEEC) method. Under the quasi-static hypothesis, assuming a Manhattan-type tessellation of the geometries and rectangular basis functions, the electric field is exploited in its contributions due to charges, currents, and magnetization. These different contributions require the computation of different type of integrals which are evaluated analytically. The mathematical derivations and the treatment of the singularities are described in detail. Two numerical examples are presented proving the accuracy of the proposed analytical formulas and their speed-up with respect to the numerical computation.