Modeling and Measured Verification of Stored Energy and Loss in MEMS Toroidal Inductors

Abstract

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 the energy that is stored in the winding, which together with the winding gap makes the equivalent inductance more difficult to model. The models presented here account for these effects. Finally, the models are verified against results from 2-D and 3-D finiteelement analysis (2-D FEA and 3-D FEA) direct measurement, and from in-circuit experimentation. In all cases, the equivalent-circuit model is observed to be accurate to within several percentage.

A Technology Overview of the PowerChip Development Program

“…Such an approach has also been used successfully to analyze electrical machines [61]. The magnetic field in the toroid can be found directly from the minimized energy functional, and from this field, the inductance and surface currents, and thus loss on the inside of the windings, follow directly [62]. Fig.…”

“…In the latter case, a lumped capacitance is placed from each turn to the substrate or core. All turns are assumed to couple to a common magnetic flux, and hence are treated as a multiwinding transformer [62].…”

“…To calculate the electrically driven losses for a toroid, we solve Maxwell's equations in 2-D polar coordinates. To calculate the magnetically driven losses, we assume axial symmetry and solve Maxwell's equations in 1-D [62].…”

A toroidal power inductor using radial-anisotropy thin-film magnetic material based on a hybrid fabrication process

“…The model proposed in [22] accounts for all the effects discussed here and is a good alternative whereas the others are more approximate. An air-core toroidal inductor with a single-layer foil winding is shown in Fig.…”

“…The current in the toroidal winding can be decomposed into a radial and a circumferential component [22]. The radial current component (called the poloidal current in [22]) induces the main field inside the toroid, and flows on the interior surface of the winding with high-frequency excitations.…”