An exact solution to the transistor sizing problem for CMOS circuits using convex optimization

Abstract

A general sequential circuit consists of a number of combinational stages that lie between latches. For the circuit to meet a given clocking specification. it is necessary for combinational stage to satisfy a certain delay requirement. Roughly speaking, increasing the sizes of some transistors in a stage reduces the delay, with the penalty of increased area. The problem of transistor sizing is to minimize the area of a combinational stage, subject to its delay being less than a given specification. Although this problem has been recognized is a convex programming problem, most existing approaches do not take full advantage of this fact, and often give nonoptimal results. An efficient convex optimization algorithm has been used here. This algorithm is guaranteed to find the exact solution to the convex programming problem. We have also improved upon existing methods for computing the circuit delay as an Elmore time constant, to achieve higher accuracy. CMOS circuit examples, including a combinational circuit with 832 transistors are presented to demonstrate the efficacy of the new algorithm.