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Planar magnetic components using printed circuit board (pcb) windings are attractive due to their high repeatability, good thermal performance, and usefulness for realizing intricate winding patterns. To enable higher system integration at high switching frequency, more sophisticated methods that can rapidly and accurately model planar magnetics are needed. This paper develops a systematic approach to modeling impedances and current distribution in planar magnetics based on a lumped circuit model named as the modular layer model (MLM). Stacked pcb layers are modeled as repeating modular impedance networks, with additional modular impedances representing the magnetic core, air gaps, and vias. The model captures skin and proximity effects, and enables accurate predictions of impedances, losses, stored reactive energy, and current sharing among windings. The MLM can be used to simulate circuits incorporating planar magnetics, to visualize the electromagnetic fields, and to extract parameters for magnetic models by simulations, among many other applications. The modeling results are checked with results of previous theories and finite-element-modeling approaches, with good matching presented. A group of planar magnetic devices, including transformers and inductors with various winding patterns, are prototyped, and measured to validate the proposed approach and clarify the boundaries of its applicability.
Chen et al. (Wed,) studied this question.