Fringing Field Analytical Calculation of High Frequency Planar Magnetic Components

When the switching frequency is above 100 kHz, the winding loss of the round wire magnetic component will increase sharply due to skin effect and proximity effect, which greatly limits its wide application. On the contrary, the planar magnetic component can not only work at such high frequency, but also suitable for high power density applications for its low profile. However, in order to avoid core saturation and change the inductance, the air gap is usually required in the design of the planar magnetic component, which will produce fringing effect and further increase the winding loss. Based on Roshen’s assumptions, this paper analyzes the planar magnetic component with center air gap. Firstly, the Schwartz-Christoffel mapping is used to establish the mapping relationship between the air gap fringing region and the strip region. Then the magnetic field intensity in complex form is obtained by the complex potential function and the one in vector form is given, which is represented by the strip region coordinate. Finally, the magnetic field intensity verification and the thermal verification are carried out. The method proposed in this paper provides effective guidance for the design of planar magnetic components operating at high frequency.