Wire-sizing for delay minimization and ringing control using transmission line model

In this paper, we consider continuous wire-sizing optimization for delay minimization and ringing control. The optimization is based on a fast and accurate delay estimation method under a finite ramp input, where an analytical expression is also derived to estimate overshoot/undershoot voltage. In this paper we specify the wire shape to be of the form f(x)=ae^-bx, since previous studies under the Elmore delay model suggest that exponential wire shape is effective for delay minimization. The relevant transmission line equations are solved by using the Picard-Carson method. The transient response in the time domain is derived as a function of a and b. The coefficients a and b are then determined such that either the actual delay (50% delay) is minimized, or the wiring area is minimized subject to a delay bound. At the same time, the overshoot/undershoot voltage is bounded to prevent false switching. Our method for delay estimation is very efficient. In all the experiments we performed, it is far more accurate than the Elmore delay model and the estimated delay values are very close to SPICE's results. We also find that in determining the optimal shape which minimizes delay, the Elmore delay model performs as good as our method in terms of the minimum actual delay it achieves, i.e. the Elmore delay model has high fidelity. However, in determining the optimal shape which minimizes area subject to a delay bound the Elmore delay model performs much worse than our method. We also find that the constraint for overshoot/undershoot control does affect optimization results for both delay and area minimization objectives.