I. Introduction
Modern computer systems often include many voltage supplies. These are generated using dc–dc converters where buck converters are used to step-down the voltage from a main dc supply. Depending on the voltage conversion ratio, buck converters have a power efficiency in the range of 70%–90% [1]–[4]. The buck converters are also referred to as voltage regulator modules (VRMs). To improve both power efficiency and voltage regulation, the recent trend is to move toward fully integrated voltage regulators (FIVR) to supply both the core and I/O circuits for system-on-chip (SoC) applications [5]–[7]. One implementation of FIVR is to integrate the buck converter with SoC as a two-chip solution on a package with passives such as inductors and capacitors either surface mounted or embedded in the package [8].