Accurate delay computation for noisy waveform shapes

We present a new gate delay model for accurate modeling of difficult waveform shapes, such as those resulting from coupling capacitance noise, inductive ringing and resistive shielding. Our modeling approach uses a process of time shifting and time stretching of a set of so-called base-waveforms. These base-waveforms are selected from a large set of noisy waveform shapes that occur in interconnect structures with coupling and other types of noise, such that the delay error across all considered waveforms is minimized. Depending on the desired accuracy one or more base-waveforms can be used. This method is also used to model the gate output waveforms allowing for closure, in terms of the used base-waveforms across a circuit library. We show that the determination of the optimal set of base-waveforms under such input-to-output closure is exponential in complexity. We, therefore, propose an heuristic approach that maps the problem to the unate covering problem for which efficient solution methods are available. The new delay model can be applied in a timing analysis program with minor changes. We present results that demonstrate the accuracy of the new delay model for waveforms perturbed with noise for a large set of waveform shapes.