Dynamic Analysis of Two-Phase Switched-Capacitor DC-DC Converters

A method that aims at analyzing the dynamic behavior of some two-phase switched-capacitor charge pump circuits is proposed. A recurrence relation on the voltages across the charging capacitors of a given two-phase charge pump circuit is developed. The output voltage and the accumulated charge of a charge pump circuit after any clock cycle were found by solving some basic matrix equations, with a specific loading current and some required initial conditions. The validation of the proposed method was done by SPICE simulations based on a 8 × linear, Fibonacci, and an exponential charge pump. The analysis results were also verified with the simulation results obtained from some charge pump circuits designed with the 0.18 μm CMOS process. Results show that the proposed method can yield a close estimation on the dynamic behavior of a charge pump circuit in most of the designs. We further found that the rising times for the exponential and Fibonacci charge pumps are shorter, especially when the conversion ratio is high, than that of the linear one.