Analysis and Optimization of Multi-Winding Toroidal Inductors for Use in Multilayered Technologies

The aim of this paper is to compare the performance of planar toroidal inductors and circular spiral inductors in multilayered technologies, in terms of achievable inductance density. New multi-winding toroidal inductor geometry is proposed to cover as much of the integration area as possible with the component footprint. The optimization of planar multi-winding toroidal inductors in multilayered substrates is investigated theoretically, and closed formulae are derived for their inductances as a function of geometrical parameters for any given value of the number of windings in the coil. The model obtained is validated experimentally and through electromagnetic simulation. Comparing the inductance of multi-winding toroidal inductors and compact spiral inductors allows us to update previously reported selection rules for the most suitable topology that leads to the most compact design.