Statistical design of integrated circuits using maximum likelihood estimation of the covariance matrix

A new formulation is proposed for statistical design of integrated circuits with correlated input parameters. The method uses a polyhedral approximation of the feasible region and finds the maximum volume ellipsoid contained in that polyhedron. The orientation of the ellipsoid is fixed by a maximum likelihood estimate (MLE) of the correlation matrix. The ellipsoid center is a nominal design with the maximum yield. The covariance estimation is formulated as a semidefinite program which uses the sampling observations as input data. The design centering problem is presented as a second-order cone programming and solved by a special interior-point optimization algorithm. The optimal design of a switched-capacitor filter is presented.