Loss Modeling and Magnetic Shielding Effect Analysis of Litz-Wire Windings in High-Frequency Transformers Based on Complex Permeability

Accurate evaluation of winding loss in high-frequency transformers is of great significance for improving power density and operating efficiency. However, under the influence of high-frequency leakage magnetic fields, the proximity-effect loss in Litz wire remains considerable, while traditional fine-scale models suffer from high modeling complexity and computational cost. To address this issue, a homogenized loss modeling method for Litz wire based on complex permeability is proposed, and the effect of magnetic shielding is further analyzed. Equivalent models for single-turn and multi-turn Litz-wire windings considering the geometric filling factor are established. High-frequency loss is calculated by combining finite-element magnetic field analysis with numerical integration, and the proposed method is validated by a compact multi-turn winding model and wide-frequency impedance measurements. The results show that the proposed method agrees well with fine-scale finite-element results, with errors within 5%. In addition, magnetic shielding can reduce the magnetic field intensity around the winding and exhibits certain potential for loss reduction.