Analytical calculation method for the non-linear characteristic of ferrite-cored inductors with stepped air gap - Stenglein, Erika; Albach, Manfred (Electrical Engineering, 2017)
Magnetic devices are essential components in the field of power electronics. Exploiting the non-linear behavior of inductors and transformers offers the great merit of increasing the performance of switch mode power supplies. For instance, the light-load efficiency of a buck voltage regulator can be improved by using a non-linear inductor with stepped air gap. Moreover, non-linear chokes can be used for passive power factor correction or are employed in solar PV systems. For an optimal design, however, a controlled decrease in inductance at a larger current is required. Such a characteristic is displayed by inductors with stepped air gaps. To optimize the gap geometry, the knowledge of the exact behavior of the non-linear choke is crucial. As simulation tools require rather long computation times to calculate the non-linear characteristic, the authors chose a different approach. This paper demonstrates the analytical calculation of the current depending inductance of pot cores with stepped air gap. By solving a boundary value problem the magnetic vector potential inside the winding area is obtained assuming linear core material. Subsequently, the non-linearity of the core material is incorporated by decomposing the original non-linear problem into linear subproblems. Following this, the solution of the original problem is composed using the solutions of the linear subproblems. Once the magnetic vector potential as a function of inductor current has been determined, the current depending inductance can be calculated. Results derived from both simulations with COMSOL Multiphysics and measurements show good agreement with the theoretical predictions.
Keywords: Inductive component; Nonlinear inductance; Stepped air gap; Boundary value problem; Measurement