RC(L) interconnect sizing with second order considerations via posynomial programming

There has been substantial work on interconnect sizing algorithms for delay and area optimization in terms of the Elmore delay. Recently, however, signal integrity issues have become of equal or greater importance than delay and area for deep submicron designs. Modeling signal integrity requires more than the Elmore delay approximation, especially when interconnect inductance effects are considered. This paper studies a new interconnect sizing formula?tion with signal attenuation and transition time constraints that cap?tures the same global optimality as the Elmore delay based approaches. With the signal attenuation (or the signal transition time) modeled by the second order central moment of the circuit response, we formulate a provably posynomial optimization prob?lem for RC trees such that the well studied algorithms for geometric programming can be applied with guaranteed convergence to a glo?bal minima. For RCL cases we demonstrate that this formulation remains convex and posynomial under reasonable conditions. Suffi?cient conditions are given in terms of the technology parameters and termination conditions.