Moment-driven coupling-aware routing methodology

An underdamped signal response with a number of overshoots and undershoots may lead to false switching and increased settling time delay. This 'ringing' effect adversely affects the signal quality at the output and becomes a source of major concern at multi-GHz frequencies, as the self and mutual inductance of interconnects start playing a crucial role in the performance of a circuit. Reduction in wire length or minimization of coupling capacitance, the stronghold in many earlier routing techniques, may produce a routing solution suitable only at sub-GHz frequencies. In this paper, we propose a routing methodology that accounts for inductive and capacitive parasitics (self and mutual) of the interconnects in its cost function through a combination of second and third order central moments. A trade-off between signal delay and amount of ringing, quantified by second and third order central moments respectively, has been made, which generates a routing solution with the best compromise between ringing and delay for each net under a monotone signal response.