State space modeling and performance analysis of a multilevel modular switched-capacitor converter using pulse dropping switching technique

Multilevel modular capacitor clamped dc-to-dc converter (MMCCC) is a two-phase modular switched capacitor converter. The conversion ratio of an ideal MMCCC is an integer and depends on the number of active modules. An MMCCC circuit can achieve fractional conversion ratios by varying the operating frequency or using the pulse dropping technique (PDT). Using PDT, the converter remains at the same state for longer time duration depending on the required conversion ratio needed. Therefore, PDT adds an additional degree of freedom to achieve variable conversion ratio at a constant frequency. Practical performance of switched-capacitor voltage regulator circuits are generally analyzed by measuring the equivalent output resistance of the converter at different frequencies. State space modeling technique has been used in this paper for measuring the equivalent output resistance when pulse dropping technique has been applied to MMCCC circuit. This analysis will define the boundaries of the PDT operation needed to achieve continuous conversion ratio, and the constraints on the output load resistance needed to achieve the required dynamic range of conversion ratio has been discussed as well. Detail of the state space modeling has been provided in this paper. Finally, the equivalent output resistance derived using the presented model has been validated using simulation and experimental results.