I. Introduction
Fully integrated voltage regulators (FIVRs) can improve the performance and reduce the power consumption of a system-on-chip (SoC) by providing point-of-load voltage regulation with dynamic voltage scaling capability [1]–[3]. The desirable attributes of FIVRs include high power efficiency, high power density, and fast transient response. FIVRs can be linear or switching. A linear regulator can have high power density and fast transient response, but its power efficiency is inherently limited by the voltage conversion ratio (VCR), i.e., the ratio of the output voltage to the input voltage, [1]. Thus, linear regulators are not suitable for applications where the VCR is small or dynamically changes over a wide range. In contrast, switching regulators can be designed with high power efficiency across a wide range of output voltages, but they suffer from performance degradation when being fully integrated due to the on-chip area constraint and parasitic effects [7]. Specifically, low-quality and low-density on-chip passive components, i.e., inductors and capacitors, are currently the main performance-limiting factors of switching FIVRs.