Electromagnetic Characterization of magnetic ring: Case of square cross section shape
For researchers and engineers in magnetic materials characterization, this work offers an analytical method to replace computationally expensive FEM simulations, but it is incremental as it extends existing analytical approaches to a specific geometry.
This paper develops a 2D analytical model for a toroidal magnetic ring with square cross-section under sinusoidal excitation, deriving exact expressions for internal magnetic field, flux, impedance, and losses. The model separates eddy current, hysteresis, and winding losses while accounting for skin effect and complex permeability, providing a computationally efficient alternative to FEM for standardized material characterization.
This paper presents a comprehensive 2D analytical model of a toroidal magnetic ring with a square cross-section, subjected to sinusoidal excitation. By applying Maxwell's equations in local Cartesian coordinates and utilizing a complex permeability framework, the exact analytical expressions for the internal magnetic field, flux, complex impedance, and losses are derived. The model rigorously separates eddy current losses, hysteresis losses, and winding losses, explicitly accounting for the skin effect and complex permeability within the conductive core using separation of variables and hyperbolic functions. Furthermore, parameter for apparent permeability is expressed to map the core behavior onto simplified linear material models. The derivations establish a mathematical foundation highly suitable for standardized material characterizations, such as Brockhaus and Iwatsu ring measurements, by avoiding the heavy computational cost of 2D and 3D Finite Element Analysis.