Statistical characterization and optimization of integrated circuits based on singular value decomposition

One of the major objectives of statistical IC design is to reduce variabilities of circuit performances, resulting from process variations and environmental effects, such as temperature. The simplest method of calculating performance variabilities is based on the use of the Propagation of Variance (POV) formula. This requires computation of the circuit Jacobian matrix at every iteration, which makes the entire process expensive. A new methodology is proposed, based on statistical system characterization using the Singular Value Decomposition (SVD) of the scaled system Jacobian matrix. Several measures of the overall system performance variability are related to the sum of squares of the singular values of the scaled Jacobian matrix, and thus to its Frobenius norm. Since some of the singular values are often very small, a reduced-space characterization of the system variability is obtained, which is important for both better circuit understanding by the IC designers and for more efficient circuit optimization