Analytical Modeling of High-Frequency Winding Loss in Round-Wire Toroidal Inductors

Toroidal inductors are used in many industrial applications in which they are key components regarding cost and volume. In the inductor design process, it is paramount to accurately estimate its high-frequency winding loss. Finite-element analysis (FEA) software and analytical models can be used for this purpose. However, the former employs too much time and the latter lacks accuracy when applied to toroidal windings, leading to an overestimation that can exceed 200%. As a consequence, designers would benefit from a reliable method to calculate high-frequency loss in toroidal windings. This article proposes an analytical model that considers the 2-D characteristic of the magnetic field and the geometrical particularities of toroidal windings. Furthermore, it provides an easy-to-use method, which avoids the unaffordable computational cost of FEA software. Simulations and experimental measurements are carried out for seven toroidal power inductors, from 10 Hz up to 200 kHz. Three different well-known state-of-the-art analytical models are used for comparison purposes. The results obtained with the proposed model are in good agreement with those from FEA and the experiments. The proposed model shows a maximum deviation below 20% while the overestimation of the existing analytical methods reaches values from 93% to 226%.