Analytical Modelling of Current Sharing and Eddy Current Losses in PCB Windings of Stacked Transformers

This paper establishes mathematical models to analyze uneven current sharing behaviors among paralleled secondary PCB windings and eddy current losses in stacked transformers proposed for high-efficiency LLC resonant converters. Decomposition of the models simplifies the complex individual current calculation of paralleled PCB windings by exciting each of the interleaved primary windings separated. The current sharing is then calculated based on the leakage flux passing through the loop formed by analyzed paralleled PCB windings. The observation that how the biased magnetic-motive force (MMF) affects the current sharing behaviors are quantitatively explained, respectively, in one-stack, two-stack and modular four-stack transformer structures. The eddy current losses are analyzed according to the uneven shared currents among the paralleled PCB windings and with a particular consideration of a distance factor between the primary and secondary windings. Although the modelling is based on 1-D assumption, the analytical prediction matches 3-D finite-element analysis (FEA) simulation results well, verifying the accuracy.