Modeling and measured verification of stored energy and loss in MEMS toroidal inductors

This paper presents the derivation and verification of a sinusoidal-steady-state equivalent-circuit model for microfabricated inductors developed for use in integrated power electronics. These inductors have a low profile, a toroidal air core, and a single-layer winding fabricated via high-aspect-ratio molding and electroplating. Such inductors inevitably have a significant gap between winding turns. This makes the equivalent resistance more difficult to model. The low profile increases the significance of energy stored in the winding which, together with the winding gap, makes the equivalent inductance more difficult to model as well. The models presented here account for these effects. Finally, the models are verified against results from 2D FEA, 3D FEA, direct measurement, and in-circuit experimentation. In all cases, the equivalent-circuit model is observed to be accurate to within several percent.