Limits to On-Chip Power Conversion With Thin Film Inductors

Successful implementation of on-chip power conversion using ferromagnetic inductors requires both high power efficiency and high power density. The theoretical limits to power density and efficiency possible with thin film ferromagnetic inductors in a buck converter topology with and without coupling are explored. Power density can be related to energy density of the inductor, while efficiency can be related to Q and the DC resistance loss of the inductor. To achieve 100
${\rm A/cm}^{2}$
for a 100 MHz 2:1 V converter witha 90% inductor efficiency, a peak Q of more than 8 is required with an energy storage of more than 5
${\rm nJ/mm}^{2}$
. Using coupling, the power density can be further increased, but is ultimately limited by DC resistance loss in the coils. Figures of merit (FOM) for comparing inductors of various designs are also discussed.