Analytical Thermal Model for Inductor and Transformer Windings and Litz Wire

Design optimization of inductors and transformers, considering both electrical and thermal performance, can help in the design process of converters with a high power density. Such optimization requires accurate thermal models for conduction inside the inductors and transformers, especially for conduction across the winding. Existing winding thermal models lack accuracy for litz-wire windings, use time-consuming finite element analysis, or require experimental measurements for calibration. An approximate analytical model of winding thermal resistance is presented, which only requires knowledge of material thermal properties and geometric dimensions. The model is based on regular square and hexagonal packing of insulated wires and is derived by integration of infinitesimal thermal resistance along specified paths of heat flow. Accuracy assessment using finite element analysis shows that the model has a maximum 15% error over a wide range of material and geometric parameters. Application of the model for practical windings, including litz wire windings, is also discussed.