An efficient sequential quadratic programming formulation of optimal wire spacing for cross-talk noise avoidance routing

Abstract

In this paper we propose a new, and e ective, approach to cross-talk noise avoidance routing. In our new approach we attack the cross-talk noise problem immediately following topological routing, which is the point in the routing process that gives the best trade o between the ability t o detect cross-talk noise problems and the ability to correct the problems. We formulate the heart of this new approach as a convex, nonlinear, mathematical programming problem which determines an optimal set of wire spacings under cross-talk noise constraints. This new mathematical programming formulation is based on a detailed knowledge of the underlying cross-talk noise mechanisms and accounts for coupling capacitance, interconnect resistance, and aggressor net signal rise time on nets with arbitrarily complex tree topologies. Finally, b y slightly restricting this programming problem we formulate it as a linearly constrained, convex, nonlinear, mathematical program which can be quickly and e ciently solved using sequential quadratic programming.