Three-Dimensional Frequency-Dependent Thermal Model for Planar Transformers in LLC Resonant Converters

In this paper, a thorough thermal analysis is carried out in order to find an analytical three-dimensional (3-D) frequency-dependent thermal model of planar transformers (PTs) used in high-frequency power converters. Because of the tendency of having higher power density as well as miniaturization of power converters, the components have to work near their thermal limit margins. This issue is more critical for planar magnetics in LLC converters due to their variable high-frequency operation, making thermal modeling and heat transfer analysis tools necessary. The proposed 3-D frequency thermal model is obtained based on the lumped parameters network (LPN) according to different thermal resistances of the PT including convection, conduction, and radiation heat exchanges. It should be noted that not only the 3-D geometry effect of the core is applied to the proposed model, but thermal surface resistances are also considered to model the highfrequency operation effect. Moreover, the lumped capacitance thermal model is used to analyze the transient thermal variation of the transformer. The LLC resonant converter with two PTs, including EE58/11/38 and ER51/10/38 planar cores, is considered to show the compatibility of the proposed 3-D-frequency LPN model. In addition, the temperature distribution of different parts of the transformers is evaluated using finite element method modeling and compared with the proposed 3-D frequency-dependent LPN model. Experimental results confirm the improved accuracy of the proposed LPN model and show the proposed model predicts the temperature distribution in PTs with an error of less than 3%. Considering the improved accuracy and low computational time of the method, the proposed 3-D frequency-dependent model is a powerful and fast design tool to evaluate the temperature distribution for different designs, and so can be used to effectively optimize the transformer from thermal point of view.