New method of modeling electronic circuits coupled with 3D electromagnetic finite element models

New zero-dimensional or scalar electromagnetic finite elements, that have the time integral of electric scalar potential as their nodal variable are presented. There are three zero-dimensional element types, representing resistors, capacitors, and inductors. These elements can be easily combined with two- or three-dimensional elements, with three components of magnetic vector potential and the time integral of electric scalar potential as nodal variables. Constant current sources are directly modeled by inhomogeneous Neumann excitations, and constant voltage sources are modeled by use of Norton´s theorem. By the addition of dependent current and voltage sources, electronic circuits can be modeled. Example finite-element analyses include an R-L circuit, a transistor circuit driving a wire loop modeled with three-dimensional finite elements, and a circuit impedance on the secondary of a saturable three-dimensional transformer model.