Analytical Model for HF-Losses Caused by 2D Magnetic Fields in Litz Wire

Abstract

The 2D magnetic field effect arises when the winding height is lower than the window height due to isolation requirements and mechanical constraints. In this situation, most analytical models for calculating HF-losses in Litz wire fail to predict the winding losses accurately since they are normally based on a 1D magnetic field assumption. Although numerical or semi-numerical methods can accurately calculate the winding losses, they are too time-consuming to be integrated into the converter optimization routines. This article provides a new loss model, which is validated to have a much lower error (<10%) than 1D field loss models (up to −45%) by numerical calculations and experiments. The model is presented for two winding transformers with layered windings and non-gapped cores with high permeability in the frequency range, where the strand diameter to skin depth ratio is equal to 1.2. Moreover, the model can also be extended for interleaved windings by separating the windings to multiple blocks. Furthermore, the computation time is less than 300µs using the algorithm provided in this article. This new model achieves a good balance between accuracy and computational time and has great potential to improve the transformer as well as the converter design.

Keywords

• 2D magnetic field
• high frequency losses
• Litz wire
• transformer