Algebraic foundation of self adjusting Switched Capacitors Converters

An algebraic model that describes the operation of binary switched-capacitor converters (SCC) was developed and generalized to any radix case. The proposed approach reduces the power loss by increasing the number of target voltages. In the binary case, the flying capacitors are automatically kept charged to binary weighted voltages and consequently, the resolution of the possible target voltages is binary. The paper presents the underlining theory of the proposed SCC and two new control methods to regulate the output voltage. It is shown that the theoretical formulation of the new number systems can describe many SCC circuits on the market and can help design new SCC with a larger number of target voltages. The theoretical results were verified for the binary case by simulation and experimentally. Excellent agreement was found between the theory and experimental results. The down side of the proposed SCC schemes is the relatively large number of switches which makes the approach more suitable for low power applications.