The Metastable Behavior of a Schmitt-Trigger

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 nondigital) 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.

Efficient Metastability Characterization for Schmitt-Triggers

“…As a consequence, the S/T must be susceptible to metastability. This intuitive argument has been more formally supported by Marino [1] already, and more recently Steininger et al [2] have detailed several practically relevant scenarios where metastability may occur and where it may not. While there exist analytic solutions to calculate certain properties such as the threshold voltages [3], none have been presented so far regarding metastability.…”

“…For this purpose we replace the load capacitance by a voltage source and actually measure the current through the latter (visible in the second code line). In comparison to the approach from [2], where the authors performed transient analysis and picked V out , this is considerably faster but serves the same purpose, albeit we get I out as a result instead. To compare the results of static and transient simulation (see Section III-B) in Fig.…”

“…These data are of interest when investigating more advanced features such as the overall probability to enter metastability or how quickly it is resolved. More specifically, we • derive a more fine grained map (compared to [2]) of the output derivative V out over the V in −V out plane, which we use as basis for more accurate estimations and analyses about the general behavior.…”

Does Cascading Schmitt-Trigger Stages Improve the Metastable Behavior?

“…To avoid oscillating behavior for inputs close to the reference, Schmitt-Trigger (S/T) stages [4] are employed instead whose hysteresis behavior makes them ignore irrelevant voltage fluctuations. However, it has been shown that for certain input traces a S/T can become metastable as well [5], [6]. Following the lessons learned from synchronizers, one may ask whether the cascading of S/Ts is again effective in reducing the risk of metastable upsets.…”

“…4) until V m reaches V L,2 (V in = V 1 ) the second S/T will start to switch and can be driven into metastability in the same way as the first one. While keeping both S/Ts in metastability, which is either possible with very precise or very fast control of V in (for a more detailed explanation see [6]), the output values between LO and HI shown in Fig. 7 are reachable.…”