Equivalent circuits for transformers based on one-dimensional propagation: accounting for multilayer structure of windings and ferrite losses

A Systematic Approach to Modeling Impedances and Current Distribution in Planar Magnetics

“…Here we highlight two branches of previous work to provide the background and clarify the differences between the modeling approach presented in this paper with those in the literature. Keradec and colleagues modeled multilayer windings in a magnetic component by adapting models for electromagnetic waves propagating in multilayered media, as is sometimes found in optical systems [22], [23], [25], [33], [34]. Analogies were made between the circuit domain and the optic domain.…”

“…However, the increasing skin and proximity effects and the resulted self and mutual impedances make the modeling challenging, especially when parallel windings are included. Previous modeling efforts have estimated ac resistance [8]- [12], predicted parasitics [13]- [15], estimated core losses [16]- [21], generated circuit representations [22], [23], extracted parameters by experimental measurements [24], [25], developed transmission line models [26], [27], [29]- [31], and investigated current sharing among parallel and interleaved windings [32]- [35]. These approaches have different focuses, rely on various assumptions, and sometimes are not easy to use.…”

Studying behavior of multilayer materials: A 1-D model correlated to magnetic domain walls through complex permeability

“…These multilayer media are modeled using one-dimensional (1-D) electromagnetic propagation wave equations. These models are suitable for copper conductors [1] but are not well known for magnetic materials. In our approach and for taking into account the non-homogeneity of the magnetic material, we investigate magnetic phenomena in the frame of domain-walls magnetization mechanism.…”

Wide frequency range lumped element equivalent circuit for HF planar transformer

“…Analytical studies related to this wide field are still in progress but, for simple shape planar transformers, needed theoretical material to do this is already available [6,7]. In this paper, we apply this theoretical work to deduce the equivalent circuit of such a planar transformer.…”