Achievable peak electrode voltage reduction by neurostimulators using descending staircase currents to deliver charge

This paper considers the achievable reduction in peak voltage across two driving terminals of an RC circuit when delivering charge using a stepped current waveform, comprising a chosen number of steps of equal duration, compared with using a constant current over the total duration. This work has application to the design of neurostimulators giving reduced peak electrode voltage when delivering a given electric charge over a given time duration. Exact solutions for the greatest possible peak voltage reduction using two and three steps are given. Furthermore, it is shown that the achievable peak voltage reduction, for any given number of steps is identical for simple series RC circuits and parallel RC circuits, for appropriate different values of RC. It is conjectured that the maximum peak voltage reduction cannot be improved using a more complicated RC circuit.