Optimal wire and transistor sizing for circuits with non-tree topology

Conventional methods for optimal sizing of wires and transistors use linear RC circuit models and the Elmore delay as a measure of signal delay. If the RC circuit has a tree topology, the sizing problem reduces to a convex optimization problem which can be solved using geometric programming. The tree topology restriction precludes the use of these methods in several sizing problems of significant importance to high-performance deep submicron design including, for example, circuits with loops of resistors, e.g. clock distribution meshes, and circuits with coupling capacitors, e.g. buses with crosstalk between the lines. The paper proposes a new optimization method which can be used to address these problems. The method uses the dominant time constant as a measure of signal propagation delay in an RC circuit, instead of Elmore delay. Using this measure, sizing of any RC circuit can be cast as a convex optimization problem which can be solved using the recently-developed efficient interior-point methods for semidefinite programming. The method is applied to two important sizing problems-the sizing of clock meshes and the sizing of buses in the presence of crosstalk.