Improved approximation for fringing permeances in gapped inductors

The purpose of this paper is to propose new analytical approximations for fringing flux calculations around the air gaps of inductor cores, including multiple gap cases and different symmetrical cases. Existing 3D techniques using finite element analysis are accurate but require a prohibitive amount of simulation time and special software. We propose an improved analytical approximation for fringing permeance calculation for the most usual field patterns. The approach is extended form 2D to 3D giving analytical solutions for corner effects, thus providing a better accuracy of the approximation. The derived fringing coefficients are used to present all symmetrical cases and cases with multiple air gaps. The accuracy of the proposed equations is sufficient for a normal engineering design. The advantages of analytical approximations are the possibility of generating diagrams, of solving the reverse problems and optimizing more complex problems.