Variability reduction: statistically based algorithms for reduction of performance variability of electrical circuits

A number of algorithms are presented for the reduction of circuit-response variability arising from component tolerances. A Monte Carlo analysis is carried out in the tolerance region and the responses F and differential response sensitivities ¿F/¿pi with respect to circuit parameters p calculated at each sample point. This enables both the variance of the responses and the circuit yield over the tolerance region to be estimated. At a given iteration, a descent direction for variance is determined by one of a number of different methods, and a suitable step length for the movement of the nominal point calculated. These two operations make extensive use of linear approximations to the response for the estimation of variance and yield for known displacements in the circuit parameters. As a consequence, the method is very efficient (¿F/¿pi are inexpensive to compute), since the number of fresh circuit analyses is kept to a minimum.