Nonlinear Analytical Model of an Inductance Considering Saturation and Temperature Variation

This paper presents an analytical model of air gapped inductor considering the nonlinear magnetic behavior of the core along with temperature variation. First, a nonlinear magnetic behavior is represented by a mathematical function, which contains three coefficients and defines magnetic flux density (B) as a function of magnetic field strength (H). Using Matlab curve fitting toolbox, these coefficients are defined as a function of temperature. After that, B and H relation is transformed into magneto motive force (MMF) and flux relation by the geometry of the core. This procedure yields a magnetic equivalent circuit. The nonlinear equation is solved by LambertW function. Validation of the proposed model is proved by fmite element analysis (FEA).