Electric circuit element boundary conditions for electromagneto-quasistatic and full wave models in A, φ potentials and their finite element implementation

Abstract

Electric Circuit Element (ECE) boundary conditions (BC) defined for full-wave (FW) electromagnetic field allow a natural coupling between field devices and electric circuits. The novelty of this paper is that it shows how ECE BC can be implemented into a 3D-finite element method (FEM), when using A, a magnetic vector potential and φ, a scalar potential. Weak formulations are described and implemented in the free environment Open Numerical Engineering LABoratory(onelab). The validation is carried out on 3D examples solved both in frequency (FD) and time domain (TD), for FW formulations in potentials, as well as for corresponding Darwin approximations of Electromagneto-Quasistatic (EMQS) models. Results are compared with those obtained with a formulation in EV, where E is the electric field inside the domain and V is a scalar potential defined solely on the boundary. The results show that: 1) the use of potentials has some advantages over the EV formulation in TD only; 2) excitation type matters, the voltage excitation, here essential in FEM, proved to be the most robust one for the considered examples: a coplanar waveguide and a spiral inductor.