FEM tuned analytical approximation for fringing permeances Vencislav Valchev 1 , Alex Van den Bossche 2 , Todor Filchev 1 1 Department of Electronics, Technical University of Varna, Studenska 1, Bulgaria 2 Department of Electrical Energy, Systems and Automation, Ghent University, Sint-Pietersnieuwstraat 41, Belgium Abstract. This paper presents a novel analytical approach for calculating fringing per- meances in gapped inductors. For most of the gapped inductors, the permeance of other field paths out of the air gap (the fringing paths) is not negligible. Existing three- dimensional modeling techniques using finite element analysis for magnetic components are accurate, but require prohibitive amount of simulation time. Two-dimensional models are often used, but the accuracy is low as a 2D simulation fails taking into account impor- tant 3D effects. We propose an analytical approximation for fringing permeance calculation for the most usual field patterns, denoted as basic cases. These fringing coefficients can be used to present all symmetrical cases and cases with multiple air gaps. The derived equa- tions are sufficient for a normal engineering accuracy. 1 Introduction Gapped inductors are widely used in power electronics equipment. In most of the designs the additional inductance because of the fringing flux path around the air gaps is important and should be taken in account. There are many discretisation methods such as Finite Difference Method (FDM), Finite Difference in Time Domain (FDTD), Finite Elements Method (FEM), Boundary Element Method (BEM) which allow an accurate presentation and calculation of the field in a gapped core inductor. The advantages of the nu- merical methods are the flexibility for modelling irregular field geometry and boundaries and the possibility to handle non-linearly of the material. The air gap effects have been discussed by discretisation methods in several papers [1,2] and 2-D and 3-D solutions have been given. An improved computer-aimed optimisa- tion of inductor design considering air gap effects has been proposed is [3]. Other general methods for calculating gapped inductors are presented in [4, 5, 6], all of them having their advantages and disadvantages. Analytical solutions based on the Schwartz-Christoffel transformation [7] have been proposed. Although the mathematical base is promising, the accuracy is low as a field problem is solved where the conductors are placed far away from the air gap, which is usually not the case in practical arrangements. The analytical methods have their advantages: