Emergence of current branches in a series array of negative differential resistance circuit elements

TL;DR

This paper investigates how heterogeneity in a series array of negative differential resistance elements causes multiple current branches and voltage distribution patterns, with analytical and numerical analysis of the effects of voltage ramping rate.

Contribution

It introduces an inhomogeneity parameter to quantify voltage deviation among elements and derives analytical expressions relating it to ramping rate.

Findings

Heterogeneity leads to multiple current branches.

The inhomogeneity parameter depends on voltage ramping rate.

Analytical expressions match numerical simulations.

Abstract

We study a series array of nonlinear electrical circuit elements that possess negative differential resistance and find that \emph{heterogeneity} in the element properties leads to the presence of multiple branches in current-voltage curves and a non-uniform distribution of voltages across the elements. An inhomogeneity parameter $r_{max}$ is introduced to characterize the extent to which the individual element voltages deviate from one another, and it is found to be strongly dependent on the rate of change of applied voltage. Analytical expressions are derived for the dependence of $r_{max}$ on voltage ramping rate in the limit of fast ramping and are confirmed by direct numerical simulation.