Thermal Modeling of Inductor and Transformer Windings Including Litz Wire

Design optimization of magnetic components, which considers both electrical and thermal performance, can help in designing power converters with a high power density. This paper proposes an approximate analytical model for thermal resistance of inductor and transformer windings, including litz wire, which only requires knowledge of thermal properties of constituent materials and geometric dimensions. The model is based on regular square and hexagonal packing of insulated wires and is derived by integration of infinitesimal thermal resistances along a specified heat flow path. The model closely agrees with finite-element analysis (FEA) and can be used in place of time-consuming FEA as part of larger thermal network models for magnetic components. The model is also experimentally validated using a toroidal inductor with a litz-wire winding; the model has less than 12% error compared to the experimental measurement. Application of the model for practical windings, including litz-wire windings, is also discussed. The model can be used during the design process of magnetic components of a switching power converter to evaluate the temperature and potential hot spots. The model provides closed-form results, hence fast computation times, and so can be used in design optimization procedures.