Generic statistical circuit design based on the unscented transformation and its application to capacitive sensor instrumentation

A generic approach for statistical circuit design that combines performance optimization and yield maximization is proposed. The inherent trade-off between peak performance and device robustness can be freely adjusted in a wide range. The method makes use of the unscented transformation for the estimation of statistical parameters. It allows to estimate the mean and covariance of nonlinearly transformed random variables from discrete samples. The beneficial properties of this transformation, namely the small number of required function evaluations, the conservation of differentiability and good estimation accuracy, are thus incorporated in our statistical design approach. As a consequence, the method can be used with arbitrary optimization algorithms and circuit simulators. A case study on the design of capacitive sensor electronics is used to demonstrate the validity of the proposed approach and to emphasize the advantages over worst case and nominal design