Matrix Analysis of 2-D Eddy-Current Magnetic Fields

We present an accurate equivalent circuit model to represent a 2-D eddy-current magnetic field. The magnetic field can be coupled with stranded windings and solid conductors. For use in developing formulations of impedance computation, we present two systematic matrix analysis methods based on the system equations, one using the loop method and the other using the nodal method. In the model, each solid conductor is represented by circuit branches. With this approach, the effect of eddy currents can be fully included. We also present the formulations for the computation of the total power loss for magnetic field-circuit coupled problems. We discuss a common mistake in many applications.