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.
