Bistable Circuit Behaviour as a 2 level (stable/metastable) potential energy system

TL;DR

This paper presents a new energy-based model for analyzing Schmitt trigger circuits as two-level systems with stable and metastable states, providing insights into their dynamics and design parameters.

Contribution

The paper introduces a novel energy model for Schmitt triggers that incorporates nonlinear MOS behavior and cross coupling, offering physical insights and simulation validation.

Findings

Simulation confirms the existence of stable and metastable states.

The model aligns with nonlinear dynamic system approaches.

Design parameters influence energy characteristics and system stability.

Abstract

A novel model of analyzing Schmitt trigger as 2 level (metastable/stable) energy system is presented. The energy of the 2 level system is identified. In an MOS implementation, this arises from the electrostatic potential energy of the electrons on the gate to source capacitance of the cross coupled MOS transistors. The electrostatic energy, upon co-ordinate transformation, (incorporating the nonlinear MOS device behaviour and cross coupling), yields an expression for the 2 level system energy. The 2 level system, described under the transformed co-ordinate, is simulated. Simulation on the dynamics of the system shows a metastsable state and two stable states, corresponding to the a maximum(metastable) energy and a minimum(stable) energy, as predicted by the energy expression in the model. This result agrees with earlier attempt based on nonlinear dynamic system approach, whereby the potential is interpreted from the point of view of the gradient of vector field. In addition, the model gives physical design insight on how the change in circuit parameters (such as gm, R), affects the energy characteristics, hence leads to effective design of such 2 level system.