Magnetic Component Model for Planar Structures Based on Transmission Lines

Magnetic component models are quite complex if they take into consideration the variation of the field distribution in a three-dimensional (3-D) space. However, if the field distribution can be assumed to be one-dimensional (1-D), the magnetic component models can be drastically simplified because it is feasible to obtain accurate analytical expressions based on the solution of the Maxwell equations for a 1-D field distribution. The field distribution in magnetic components can be assumed to be 1-D when the field depends on one of its coordinates and the dependence on the other coordinates is negligible. Therefore, classical 1-D models have to be modified in order to be applied to planar transformers because their magnetic field vector has a constant direction, but its magnitude is not constant along that direction. This paper presents a 1-D model for planar magnetic transformers. Some comparisons between 2-D approaches and the proposed 1-D model have been carried out in order to show the accuracy of the proposed method.