Statistical Circuit Design: Nonlinear Circuits and Statistical Design

To date, most tolerance analysis of circuits has been in the frequency domain, as this series of articles indicates. The need for nonlinear analysis arises not only for large signal circuits but also for small signal ac circuits where device model parameters vary with bias. Recent advances in the speed of digital computers and numerical algorithms have made possible the analysis of circuits with nonlinear behavior. Large signal, or time domain analysis of nonlinear circuits, however, is still such a comparatively slow process that Monte Carlo methods are out of the question. Enough algorithmic innovations have been achieved in the static analysis of nonlinear circuits that Monte Carlo methods can be applied to a wide class of nonlinear problems. DC in the sense used in this paper implies that the dynamic behavior of the nonlinear devices is fast in relation to the response of the rest of the circuit. There are, in general, three types of circuits that fall into this class. (i) Circuits that are essentially dc, such as operational amplifiers, power supplies, and those circuits used as examples in this paper. 1173