Design centering for analog‐integrated circuits using spherical surface random numbers

This paper considers the semiconductor integrated circuit, and proposes a solution to the decision problem for the optimum design, where circuit-element values are determined so that the yield is maximized. The spherical surface random number is employed in the calculation of the yield. Although various nonlinear programming methods can be applied to the optimization problem, this paper applies Newton's algorithm to the optimization algorithm. It is shown that the first- and the second-order derivatives of the yield to the design value, which are needed in the calculation of the search vector in Newton's method, can also be derived using the spherical surface random numbers. I is also shown that the center of the element value determined by the design specification can be calculated using the spherical surface random numbers, and the optimization can be performed efficiently using the center as the initial point for the optimization. Applying the proposed method to the 5th-order leapfrog-type switched-capacitor filter, the processing time is reduced to approximately onefourth compared with the case of the Monte-Carlo method.