Abstract-The fundamental constraints for fast-response buck converters for applications such as microprocessor power delivery are analyzed, with an emphasis on the role of the inductor. Optimum values of ripple ratio, and thus inductor value, are calculated. Based on this analysis, microfabricated inductor designs are analyzed, and an inductor design is proposed with predicted performance including power density of 158 W/cm ¾ and 95% efficiency for an 8 MHz, 3.6 V to 1.1 V converter.