EFFICIENT PERFORMANCE-FUNCTION INTERPOLATION SCHEME AND ITS APPLICATION TO STATISTICAL CIRCUIT-DESIGN

A concept of 'maximally flat' polynomial interpolation of circuit responses (or performance functions) is proposed, developed and exploited. This kind of simple approximation of circuit behaviour proves extremely useful for Monte Carlo statistical yield estimation and optimization. Application of the resulting interpolating polynomials may substantially reduce the number of actual, time-consuming circuit analyses. Results of all available circuit analyses can be utilized to construct the interpolating polynomials, even if their number is not sufficient for a full unique quadratic or higher-order interpolation. This is accomplished by selecting the 'maximally flat' interpolation in which all higher-order-term coefficients are minimized in the least squares sense. More importantly, a low-cost updating of the interpolating polynomials is developed in order to accommodate the results of additional circuit simulations as they become available. Examples of this approximation of circuit responses as well as its application to yield estimation and optimization are shown.