Modeling and Analysis of Switched-Capacitor Converters With Finite Terminal Capacitances

In pre-existing analytical models of switched-capacitor (SC) converters, the input and output capacitances ($C_{\text{in}}$ and $C_{\text{out}}$) have long been assumed to be infinitely large so that the input and output can be modeled as ideal voltage sources. However, in practice, the terminal capacitances can be insufficient to ensure ideal input and output behaviors due to space and cost constraints. This article reveals that finite terminal capacitances can have considerable effects on the output impedance ($R_{\text{out}}$) and overall efficiency of SC converters. A general modeling and analysis methodology is proposed for SC converters to characterize the effects of finite terminal capacitances quantitatively. A 2-to-1 SC converter prototype is specially designed to verify the proposed general output impedance model. The relative error between the modeling results and the experimental measurements is less than 8%, which demonstrates the excellent accuracy of the proposed model. It is revealed that the insufficiency in $C_{\text{in}}$ can lead to a considerably higher $R_{\text{out}}$ and harm the overall efficiency. On the contrary, decreasing $C_{\text{out}}$ can counter-intuitively help reduce $R_{\text{out}}$, which contributes to both higher efficiency and higher power density, although this benefit comes at the cost of a larger output voltage ripple. In addition, $C_{\text{out}}$ has a stronger effect on $R_{\text{out}}$ in the slow switching region, while $C_{\text{in}}$ is more influential in the fast switching region, especially around the knee of the output impedance curve, which is the typical operating point of SC converters. Several design guidelines are provided based on these findings. Further discussions are provided to explain how to apply the proposed general output impedance model to arbitrary SC topologies.