Stability of characteristic curves of nonlinear resistive circuits

In this paper, we discuss the stability of the characteristic curves for nonlinear resistive circuits including parasitic elements. Although the dc solution is determined by analyzing the nonlinear resistive circuit, its equilibrium point will be stable or unstable because every resistive element has a small parasitic component in practice. We consider here two parasitic elements: a capacitor between every resistor node and ground and an inductor in series with each resistor. Of course, the stability can be decided by solving the variational equation at each equilibrium point obtained by the dc analysis; however, this is very time consuming. We show here that the stability is mainly changed at the boundary of the presence of negative differential resistance (NDR) and the bifurcation points, such as turning and pitchfork points on the dc characteristic curves. The instability regions of the solution curve are easily found by both the locations of bifurcation points and NDR regions of the nonlinear resistors.