Estimation of High-Frequency Magnetic Fringing Losses of Planar Transformers Using Finite Element Analysis

In this work, fringing effect is studied on planar transformers for various frequencies, air gap lengths, core materials and core geometries to aid engineers in choosing the best transformer design with least fringing losses. Using finite element modelling, fringing losses were analysed for four different core geometries, namely EE, EI, ER and ETD, with varying core widths to estimate a generalized fringing losses equation. Emerging core materials like amorphous and nanocrystalline materials were analysed in addition to the common ferrite material for the core of the transformer. Simulations were performed for frequencies ranging from 50 to 400 kHz and air gap lengths varying from 0.05 mm to 0.25 mm. Using curve fitting, an equation was developed to estimate fringing losses. Fringing losses of a planar transformer were found to be directly dependent on its frequency, magnetic flux density, air gap length and core width. The fundamental difference of the proposed equation from the traditional fringing losses formula is that fringing losses were found to be proportional to the square of the frequency instead of the first power of frequency. Fringing losses were also calculated with the traditional formula, to analyse the improvement obtained with the proposed finite element modelling-based equation. It was observed that the proposed formula gave fringing losses results with a minimal error of about 9% for a range of lower and higher frequencies, whereas the traditional formula accounted for about 45% error for higher frequencies and around 11% error for lower frequencies.