Evaluation of the lagrangian method for deriving equivalent circuits of integrated magnetic components: A case study using the integrated winding coupled inductor

Recently, Lagrangian dynamics have been applied to transforming integrated magnetic components into equivalent circuits of transformers and inductors. This Lagrangian method is expected to yield an equivalent circuit with few components, when applied to an integrated magnetic component with few flux paths that can be magnetized independently. However, properness of this method has not been verified. As a case study, this paper derives the equivalent circuit of the integrated winding coupled inductor using the Lagrangian method to evaluate consistency with the magnetic circuit model and experimental behavior. As a result, the Lagrangian method yielded a simpler equivalent circuit than those by the conventional methods. Additionally, the equivalent circuit of the Lagrangian method is found to be functionally equivalent to the magnetic circuit model and consistent with the experiment. These results support that the Lagrangian method provides proper equivalent circuits and is useful for deriving simple equivalent circuits in some cases.