Performance Limits of Switched-capacitor Dc-dc Converters

Theoretical performance limits of twophase switched-capacitor (SC) dc-dc converters are discussed in this paper. For a given number of capacitors k, the complete set of attainable dc conversion ratios is found. The maximum step-up or stepdown ratio is given by the k t h Fibonacci number, while the bound on the number of switches required in any SC circuit is 3k 2. Practical implications, illustrated by several SC converter examples, include savings in the number of components required for a given application, and the ability to construct SC converters that can maintain the output voltage regulation and high conversion efficiency over a wide range of input voltage variations. Limits found for the output resistance and efflciency can be used for selection and comparison of SC converters.