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This paper presents an analysis on the effect of having different number of capacitors n in the first-stage switched-capacitor circuit of an improved hybrid switched-capacitor buck converter for high-voltage-gain conversion. Various aspects of the topology, operation, and efficiency are investigated. It is shown both analytically and experimentally that a higher n in the step-down capacitor stage does not necessarily lead to an overall improved power efficiency. A design and optimization method is thus proposed for the improved SC-buck converter.