The Metastable Behavior of a Schmitt-Trigger

TL;DR

This paper analyzes the metastable behavior of Schmitt-Trigger circuits, providing a mathematical model and simulations to understand how different input signals affect their stability and output states.

Contribution

It offers a detailed analysis of Schmitt-Trigger metastability, extending existing results with a mathematical model and SPICE simulations for modern CMOS circuits.

Findings

Monotonic signals cause late transitions but no non-digital output.

Non-monotonic signals can pin the output to any voltage level.

The output can follow any waveform within the system's dynamic limits.

Abstract

Schmitt-Trigger circuits are the method of choice for converting general signal shapes into clean, well-behaved digital ones. In this context these circuits are often used for metastability handling, as well. However, like any other positive feedback circuit, a Schmitt-Trigger can become metastable itself. Therefore, its own metastable behavior must be well understood; in particular the conditions that may cause its metastability. In this paper we will build on existing results from Marino to show that (a) a monotonic input signal can cause late transitions but never leads to a non-digital voltage at the Schmitt-Trigger output, and (b) a non-monotonic input can pin the Schmitt-Trigger output to a constant voltage at any desired (also non-digital) level for an arbitrary duration. In fact, the output can even be driven to any waveform within the dynamic limits of the system. We will base our analysis on a mathematical model of a Schmitt-Trigger's dynamic behavior and perform SPICE simulations to support our theory and confirm its validity for modern CMOS implementations. Furthermore, we will discuss several use cases of a Schmitt-Trigger in the light of our results.