Using the Darwin Approximation for Equivalent Circuit Parameter Extraction with Frequency-dependent Linear Materials

In this work, a simulation methodology is introduced, aimed at constructing an equivalent circuit (EC) for a device under investigation, specifically a common-/differential-mode ferrite choke. This methodology comprehensively incorporates resistive, inductive and capacitive effects by employing Darwin's approximation of Maxwell's equations and using Finite Element (FE) simulations, thus eliminating the need for time-consuming and costly measurement campaigns. This approach enables the efficient extension of classical and well-established eddy current simulations to include capacitive effects, while circumventing the complexities associated with electromagnetic wave phenomena such as the necessity of open domain boundary conditions. Especially in power electronic applications, the signal spectrum typically remains below the threshold frequency where wave effects become dominant, precisely the region covered by the Darwin model. Moreover, a frequency-dependent heuristic permeability model for the choke material is used, which enables the incorporation of typical quantities provided by manufacturers of ferrite materials.