A Simple Hybrid Model for Accurate Delay Modeling of a Multi-Input Gate

TL;DR

This paper introduces a simple hybrid delay model for multi-input gates that accurately captures small delay variations caused by input switchings, outperforming existing models and closely matching SPICE simulations.

Contribution

The paper presents a novel hybrid model using first-order ODEs for delay prediction in multi-input gates, improving accuracy over previous models.

Findings

Model accurately captures the Charlie effect in delay modeling.

Significant improvement over existing delay models.

Close agreement with SPICE simulation results.

Abstract

Faithfully representing small gate delay variations caused by input switchings on different inputs in close temporal proximity is a very challenging task for digital delay models. In this paper, we use the example of a 2-input NOR gate to show that a simple hybrid model leads to a surprisingly accurate digital delay model. Our model utilizes simple first-order ordinary differential equations (ODEs) in all modes, resulting from considering transistors as ideal switches in a simple RC model of the gate. By analytically solving the resulting ODEs, we derive expressions for the gate delays, as well as formulas that facilitate model parametrization. It turns out that our model almost faithfully captures the Charlie effect, except in just one specific situation. In addition, we experimentally compare our model's predictions both to SPICE simulations, using some 15 nm technology, and to some existing delay models. Our results show a significant improvement of the achievable modeling accuracy.