Rigorous dc Solution of Partial Element Equivalent Circuit Models Including Conductive, Dielectric, and Magnetic Materials

• Published in: IEEE transactions on electromagnetic compatibility 2020-06, Vol.62 (3), p.870-879
• Main Authors: Romano, Daniele, Kovacevic-Badstubner, Ivana, Parise, Mauro, Grossner, Ulrike, Ekman, Jonas, Antonini, Giulio
• Format: Article
• Language: English
• Subjects: <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> dc</tex-math> </inline-formula> </named-content> solution; Computer simulation; Conductors; dc solution; Dielectrics; Electronic systems; Elektroniksystem; Equivalent circuits; Fast Fourier transformations; Finite element method; Fourier transforms; Impulse response; Integrated circuit modeling; Magnetic materials; Mathematical model; Maxwell's equations; Method of moments; Nonlinear programming; partial element equivalent circuit (PEEC) method; Well posed problems
• ISSN: 0018-9375; 1558-187X; 1558-187X
• DOI: 10.1109/TEMC.2019.2919759

This paper presents a rigorous derivation of the dc solution of three-dimensional partial element equivalent circuit (PEEC) formulation extended to include simultaneously conductive, dielectric, and magnetic materials. The circuit interpretation of Maxwell's equations provided by the PEEC method allows to reformulate the dc modeling task in such a way that physical phenomena are fully exploited. Indeed, since the displacements currents are identically zero in dielectrics, Kirchhoff's current law is enforced in terms of charge conservation internally to dielectrics or at the interface between dielectrics and other materials. A well-posed problem is achieved by adding the charges as new unknowns and identifying the disconnected objects. Two numerical examples are presented demonstrating the accuracy of the proposed method when compared to the dc solution as extracted by the fast Fourier transform of the impulse response and a finite element method simulation.