General Formulation of Fringing Fields in 3-D Cylindrical Structures Using Fourier Analysis

Soft and hard-magnetic material improvements give rise to ever more complex electromagnetic devices that require fast and accurate modeling in the three-dimensional domain. This paper is the first to present a semianalytical 3-D modeling technique based on Fourier analysis that is able to calculate the fringing fields in 3-D slotted cylindrical structures assuming linear material properties. The magnetic field distribution is obtained by subdividing such structures into concentric regions and by selecting the appropriate boundary conditions. The complete model is introduced and a generic magnetic field formulation in the cylindrical coordinate system is obtained. Furthermore, the boundary conditions are extensively discussed and the numerical implementation is presented. The method is described in a general manner to enable modeling of a wide range of electromagnetic devices. By means of an example, the modeling technique is validated with a finite element analysis.