Charging and Discharging of Non-Ideal Capacitors

Analytical expressions are given, it is believed for the first time, for the Laplace transforms of the time-dependent currents and voltages associated with step-function charging and discharging of lossy, i.e. dispersive capacitors through a series impedance. The capacitors are described by their characteristic response functions f(t) in the time domain. The expressions obtained provide the basis for carrying out inverse transformations into the time domain, which in general have to be obtained numerically, although analytical solutions are given for some limiting cases.