# High-Efficiency Self-Adjusting Switched Capacitor DC-DC Converter with Binary Resolution - Mathematics > Number Theory

Abstract: Switched-Capacitor Converters SCC suffer from a fundamental power lossdeficiency which make their use in some applications prohibitive. The powerloss is due to the inherent energy dissipation when SCC operate between oroutside their output target voltages. This drawback was alleviated in this workby developing two new classes of SCC providing binary and arbitrary resolutionof closely spaced target voltages. Special attention is paid to SCC topologiesof binary resolution. Namely, SCC systems that can be configured to have ano-load output to input voltage ratio that is equal to any binary fraction fora given number of bits. To this end, we define a new number system and developrules to translate these numbers into SCC hardware that follows the algebraicbehavior. According to this approach, the flying capacitors are automaticallykept charged to binary weighted voltages and consequently the resolution of thetarget voltages follows a binary number representation and can be made higherby increasing the number of capacitors bits. The ability to increase thenumber of target voltages reduces the spacing between them and, consequently,increases the efficiency when the input varies over a large voltage range. Thethesis presents the underlining theory of the binary SCC and its extension tothe general radix case. Although the major application is in step-down SCC, asimple method to utilize these SCC for step-up conversion is also described, aswell as a method to reduce the output voltage ripple. In addition, the genericand unified model is strictly applied to derive the SCC equivalent resistor,which is a measure of the power loss. The theoretical predictions are verifiedby simulation and experimental results.

Author: Alexander Kushnerov

Source: https://arxiv.org/