Two-Dimensional Winding Loss Analytical Model for High-Frequency Multilayer Air-Core Planar Inductor

Air-cored planar inductors play an important part in enabling high power-density, low weight, and low-profile design of high-frequency switched-mode power applications. However, the absence of ferromagnetic core in these inductors makes the magnetic field distribution in them different from that in the cored inductors and the transformers. Due to this difference, the conventional winding loss calculation models like the one-dimensional Dowells model are not suitable for these inductors. Therefore, in this paper, an improved two-dimensional analytical winding loss model for multi-layered air-cored inductors with a single-turn per layer is proposed based on the fundamental electromagnetic field solution incorporating the two-dimensional boundary values and the edge effect in its formulation. The finite element method (FEM) simulation and experimental results validate the proposed model's high-accuracy and engineering precision over a wide frequency range (up to 10MHz). Furthermore, the results ensure the proposed analytical model to be an efficient, easier, and better substitute for the FEM based calculation approach.