Does Cascading Schmitt-Trigger Stages Improve the Metastable Behavior?

TL;DR

This paper investigates whether cascading Schmitt-Trigger stages can reduce metastability, combining theoretical analysis with HSPICE simulations, and finds partial improvements but also potential drawbacks in certain cases.

Contribution

It provides a theoretical and simulation-based analysis of cascading Schmitt-Trigger stages, revealing both benefits and limitations in metastability reduction.

Findings

Metastability is reduced from first to second stage in cascades.

Cascading can introduce acausal transitions in some cases.

Complete elimination of metastability through cascading is not achievable.

Abstract

Schmitt-Trigger stages are the method of choice for robust discretization of input voltages with excessive transition times or significant noise. However, they may suffer from metastability. Based on the experience that the cascading of flip-flop stages yields a dramatic improvement of their overall metastability hardness, in this paper we elaborate on the question whether the cascading of Schmitt-Trigger stages can obtain a similar gain. We perform a theoretic analysis that is backed up by an existing metastability model for a single Schmitt-Trigger stage and elaborate some claims about the behavior of a Schmitt-Trigger cascade. These claims suggest that the occurrence of metastability is indeed reduced from the first stage to the second which suggests an improvement. On the downside, however, it becomes clear that metastability can still not be completely ruled out, and in some cases the behavior of the cascade may be less beneficial for a given application, e.g. by introducing seemingly acausal transitions. We validate our findings by extensive HSPICE simulations in which we directly cover our most important claims.