Efficient Metastability Characterization for Schmitt-Triggers

Abstract

Despite their attractiveness as metastability filters, Schmitt-Triggers can suffer from metastability themselves. Therefore, in the selection or construction of a suitable Schmitt-Trigger implementation, it is a necessity to accurately determine the metastable behavior. Only then one is able to compare different designs and thus guide proper optimizations, and only then one can assess the potential for residual metastable upsets. However, while the state of the art provides a lot of research and practical characterization approaches for flip-flops, comparatively little is known about Schmitt-Trigger characterization. Unlike the flip-flop with its single metastable point, the Schmitt-Trigger exhibits a whole range of metastable points depending on the input voltage. Thus the task of characterization gets much more challenging.In this paper we present different approaches to determine the metastable behavior of Schmitt-Triggers using novel methods and mechanisms. We compare their accuracy and runtime by applying them to three common circuit implementations. The achieved results are then used to reason about the metastable behavior of the chosen designs which turns out to be problematic in some cases. Overall the approaches proposed in this paper are generic and can be extended beyond the Schmitt-Trigger, i.e., to efficiently characterize metastable states in other circuits as well.

Simulation-Based Approaches for Comprehensive Schmitt-Trigger Analyses

“…The design goals for the closed-loop system are a short rise time t r to reduce transient simulation times in HSPICE and low overshoot for fast regulation of the setpoint I out,d . However, since these two aspects contradict one another according to (10) and (11), a compromise value of o = 10% is chosen. Solving (11) for ξ yields the damping ξ ≈ 0.5912.…”

“…While latches exhibit only a single metastable state, the input of S/Ts remains connected all the time, which gives rise for a whole range of metastable voltages V M (V in ). Previous works investigated the metastable states and dynamics of S/Ts based on analytical models [6]- [9], detailed SPICE simulations [1], [10] and experimental measurements [11], [12]. However, efficient methods that facilitate a quantification of the metastability behavior in practice, have, to the best of the authors' knowledge, not been published.…”