Electric Circuit Element Boundary Conditions in the Finite Element Method for Full-Wave Frequency Domain Passive Devices

A natural coupling of a circuit with an electromagnetic (EM) device is possible if special boundary conditions, called Electric Circuit Element (ECE), are used for the EM field formulation. This contribution shows how these ECE boundary conditions can be implemented into the finite element method for the solving of coupled full-wave EM field-circuit problems in the frequency domain. The implementation is based on a weak formulation that uses the electric field strength strictly inside the domain and a scalar potential defined solely on the boundary. Edge elements are used inside the three-dimensional domain and nodal elements are used on its two-dimensional boundary surface. The weak formulation is given and its discrete form is validated on a 2D example, with known analytic solution.