A systematic approach to modeling impedances and current distribution in planar magnetics

Planar magnetic components using printed-circuit-board 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 lumped circuit model that captures the impact of skin and proximity effects on current distribution and electromagnetic fields in planar magnetics. This enables accurate predictions of impedances, losses, stored reactive energy and current sharing among parallel windings. This lumped model is also a circuit domain representation of electromagnetic interactions. It can be used to simulate circuits incorporating planar magnetics, to visualize the electromagnetic fields, and to extract parameters for magnetic models by simulations. The modeling results match with previous theories and finite-element-modeling results. A group of planar magnetic devices, including transformers and inductors with various winding patterns, are prototyped and measured to validate the proposed approach.