Differential Algebraic Equations and Averaged Models for Switched Capacitor Converters with State Jumps

Switched capacitor converters with ideal switches exhibit discontinuities in the electrical variables, i.e., state jumps at the switching time instants. This feature introduces some difficulties for the determination of compact dynamic models for these power converters. In this paper, we tackle the issue by considering a switched model where the dynamics of the modes are represented through differential algebraic equations. For this class of systems the classical averaged model fails. By including a suitable jump mode that approximates the state discontinuities, a generalized frequency-dependent averaged model is proposed. The effectiveness of the switched and averaged models is numerically and experimentally verified by analyzing the ladder, series-parallel, Fibonacci, and Dickson topologies, and by considering different switching frequencies, voltage sources, and circuits parameters.