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Analytical calculation method for the non-linear characteristic of ferrite-cored inductors with stepped air gap
Abstract
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 calcu-lated. 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
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