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The copper loss of planar transformers is a major consideration in high-efficiency and high-power-density converter design. The traditional copper loss optimization is based on the offsetting of the magnetomotive force of the transformer’s primary and secondary sides. However, the magnetizing current in most converters cannot be neglected, and the traditional copper loss model, as well as the traditional optimization methods, are not applicable, especially in the case of large magnetizing current. In this paper, the traditional 1D copper loss model is improved into a new form that considers the magnetizing current revealing the influence of the magnetizing current and the layer arrangement on the copper loss. The model indicates that the copper loss will increase significantly with the rise of magnetizing current and elucidates that certain interleaving structures, previously regarded as identical, are, in fact, distinct from one another. The OPM (optimal path method) is proposed to help design the minimum copper loss layer arrangement when considering the magnetizing current. Both simulations and experiments verify the effectiveness of the proposed copper loss model as well as the OPM by measuring the winding resistance. The experiments also compare the efficiency of 2 LLC converters with different winding structures, demonstrating that the transformer designed by the OPM has lower copper loss.
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Wei et al. (2025) studied this question.
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