Accurate Analysis and Design of Integrated Single Input Schmitt Trigger Circuits

Abstract

Schmitt trigger (ST) circuits are widely used integrated circuit (IC) blocks with hysteretic input/output (I/O) characteristics. Like the I/O characteristics of a living neuron, STs reject noise and provide stability to systems that they are deployed in. Indeed, single-input/single-output (SISO) STs are likely candidates to be the core unit element in artificial neural networks (ANNs) due not only to their similar I/O characteristics but also to their low power consumption and small silicon footprints. This paper presents an accurate and detailed analysis and design of six widely used complementary metal-oxide-semiconductor (CMOS) SISO ST circuits. The hysteresis characteristics of these ST circuits were derived for hand calculations and compared to original design equations and simulation results. Simulations were carried out in a well-established, 0.35 μm/3.3 V, analog/mixed-signal CMOS process. Additionally, simulations were performed using a wide range of supplies and process variations, but only 3.3 V supply results are presented. Most of the new design equations provide better accuracy and insights, as broad assumptions of original derivations were avoided.

Weak Inversion Model of an Inverting CMOS Schmitt Trigger

“…Under these assumptions, 𝑀 3 is off, while 𝑀 1,4,5 are conducting. 𝑉 𝐻𝐿 can be then determined by finding the switching voltage of the inverter composed of 𝑀 1,2 , with finite voltage 𝑉 𝑚,𝑛 across 𝑀 6 [7]. Assuming all transistors in saturation, the equation relating transistors 𝑀 1 and 𝑀 2 is given by: 𝐼 0,𝑝1 ⋅ 𝑒 𝑉 𝑑𝑑 −𝑉 𝐻𝐿 𝑛 𝑝 ⋅ϕ = 𝐼 0,𝑛2 ⋅ 𝑒 𝑉 𝐻𝐿 −𝑛 𝑛 ⋅𝑉 𝑚,𝑛 𝑛 𝑛 ⋅ϕ (5) where 𝑉 𝑑𝑑 is the supply voltage.…”

“…Now that an expression for 𝑉 𝑚,𝑛 is determined, we can substitute (7) in (5), and solve for 𝑉 𝐻𝐿 . The final result is shown in (8).…”

“…1(b). STs are implemented in comparators, oscillators, converters and many others circuits [7]. Due to the voltage supply scaling trend, many researchers are modeling and employing Schmitt trigger circuits in weak inversion [8]- [14].…”

“…This circuit has not been yet modeled in weak inversion. We have chosen to model the subthreshold characteristics of this circuit because is a low power Schmitt trigger circuit [7]. In this article we derive simple expressions for the high-to-low (𝑉 𝐻𝐿 ) and lowto-high (𝑉 𝐿𝐻 ) transition voltages, which define the hysteresis of the ST, as can be observed in Fig.…”

Simulation-Based Approaches for Comprehensive Schmitt-Trigger Analyses

“…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.…”