Flying capacitor converters (FCCs) are recently attracting considerable interest because of their inherent natural voltage balancing property. We develop a sampled-data model for a single-phase single-leg three-level FCC. This provides a closed-form expression for the system dynamic behavior after each switching cycle. Analysis of this model provides considerable insight on the FCC and its natural balancing property. In particular, we prove that the natural balancing property indeed holds whenever the switching frequency is sufficiently high. We also rigorously analyze dynamic properties such as the capacitor time constant and relate them to the parameter values of the load, carrier frequency and duty ratio. These results shed light on the intricate relationship between the FCC parameters and its short- and long-term dynamic behavior. Copyright (c) 2011 John Wiley & Sons, Ltd.