A robust method to perform time-domain analysis of PWL dynamic circuits

The most basic type of circuit simulation consists of solving the nonlinear state equations of a circuit as a function of time, starting at given initial conditions. But both chaotic and stiff circuits present solutions that involve numerical errors inevitably amplified during simulation. For this reason, in particular for circuits of moderate order with nonlinear characteristics approximated with a piecewise-linear (PWL) function, a new approach is preferable. It consists of subdivided the space of circuit variables into regions where the circuit coincides with a linear circuit. In each of these linear regions, the solution is calculated analytically, and then evaluated for a sequence of time values. Thus time-domain analysis is fast and accurate and numerical errors do not accumulate during simulation. This analysis must be preceded by a DC analysis of the circuit in the initial conditions.