Maximum Reduction in Peak Voltage Using Stepped Currents to Deliver Charge to $RC$ Circuits

This brief analyzes the performance achievable by regularly sampled piecewise constant current waveforms in reducing the peak voltage across the driving terminals of an RC circuit when delivering a given charge over a given time duration into the terminals, as compared with using a fixed current. It is shown analytically for two and three current steps and numerically for more steps that the biggest achievable peak voltage reduction obtained with a simple series RC circuit cannot be exceeded with a more complicated RC circuit. Then the biggest peak voltage reduction that can be obtained is approximately 22.98% using either an infinite number of current steps of infinitesimal duration or a constant voltage drive. These are new basic results on RC circuits and have application to the design of neurostimulators.