Optimal charging of nonlinear capacitors in RC and LRC circuits with bypass resistor

Abstract

The optimal-charging problem of nonlinear capacitors in RC and LRC circuits with bypass resistor is investigated by utilizing finite-time thermodynamics. Under condition that both charging time and total energy stored in capacitors are given, the optimal time-paths of source-voltage and capacitor-voltage for the minimum Joule heat dissipation of circuits are determined by applying optimal-control theory. Analytical solutions for linear capacitor case are derived based on universal optimal results, and optimal strategies are also compared with linear and constant source-voltage operation charging strategies. While for the nonlinear capacitor cases, numerical solutions are obtained, and effects of various parameters on optimal results are analyzed.