Ecole Centrale de Paris
Laboratoire de Lasers et Photonique Industriels
Grande Voie des Vignes, Châtenay-Malabry, FRANCE

Designing circuits in the face of statistical uncertainty is a current problem.
Statistical variations in components values are due to manufacturing tolerances. The effect of these variations is that the circuit response also exhibits variations from one sample to another. In this case the manufacturing yield, which is the proportion of manufactured circuits which meet the performance specifications, is of considerable interest for the designer. Achieving an acceptable manufacturing yield is one of the main goals for a designer of electronic circuits.
There are two complementary aspects in the consideration of component tolerances and their effect on circuit performances. The first one, tolerance analysis, helps to answer the question : what effect will have component tolerances on performances ? The other one, tolerance design, tries to answer the complementary question : what can we do to reduce unwanted effects of component tolerances ?
The Monte-Carlo method is used to simulate component variations in order to estimate the yield because it exhibits generality and weak dependence to the number of stochastic variables.
For the tolerance design problems, the solution of increasing the yield can involve a change in nominal component values with the tolerances held fixed ('design centering'), or a change in tolerances component values with the nominal values held fixed ('tolerance assignment'), or a combination of two approaches. Design centering is important in that it involves no increase in component manufacturing cost.
We adapted the gravity centers method to maximaze the manufacturing yield, estimated through the Monte-Carlo method ; the tolerance design problem is expressed as an optimization problem, of which objective function is the manufacturing yield. The gravity centers method is simple and robust but it can be trapped into local optima of the yield. To overcome this problem, we present an approach for the manufacturing yield optimization of circuits, in which the simulated annealing and the gravity centers methods are combined to improve the computational efficiency.
We have implemented our tolerance design package, using the SPICE-PAC simulator, which has two major avantages. The first one is that a large number of circuit simulations can be performed selectively by SPICE-PAC. The second one is that the access to parameters, in order to modify their values, is very easy.
Finally, as an illustration of the statistical analysis and design module efficiency, severalexamples of circuit analysis are presented.