A substitution algorithm for solving nonlinear circuits with multi-frequency components

In this paper, we present an efficient algorithm for calculating the steady-state response of nonlinear circuits such as forced circuits driven by multi-frequency-component signals, forced oscillators, and coupled oscillators. We call the technique a substitution method because the variation at each step is calculated by solving an associated time-invariant sensitivity circuit at each frequency component of the residual error, whose circuit is derived from a relaxation method. the algorithm is very simple and efficient, and it can be applied to a wide variety of nonlinear circuits.