Optimal Charging of Nonlinear Capacitors

Constant-current charging is the optimal solution for charging linear (fixed) capacitors. In this letter, we extend this principle to nonlinear capacitors using a variational method. We address the case where the capacitance depends only on the applied voltage. We show that a nonlinear capacitor stores energy electrostatically and by another mean, depending on the phenomena behind the variation of the capacitance. We compute the optimal charging voltage curves for a linearly increasing or decreasing capacitance with the bias voltage. We highlight that the efficiency of the charging is improved if the capacitance increases with the applied voltage, and vice versa. We finally apply our results to two types of nonlinear capacitors that are widely used in power electronics: Supercapacitors and class II ceramic capacitors. We demonstrate that the charging efficiency is higher for supercapacitors than for ceramic capacitors.