Differentially passive circuits that switch and oscillate

TL;DR

This paper introduces a differential passivity framework for analyzing and designing switching and oscillating circuits using interconnection theory and dissipativity principles, extending classical linear methods to nonlinear systems.

Contribution

It develops a novel differential passivity approach that applies dissipativity theory to nonlinear circuits with op-amps, enabling quantitative analysis of switching and oscillations.

Findings

Demonstrates the application of dissipativity theory to nonlinear circuit architectures.

Shows how to analyze and design oscillating circuits using the proposed framework.

Extends classical passivity concepts to a differential setting for nonlinear systems.

Abstract

The concept of passivity is central to analyze circuits as interconnections of passive components. We illustrate that when used differentially, the same concept leads to an interconnection theory for electrical circuits that switch and oscillate as interconnections of passive components with operational amplifiers (op-amps). The approach builds on recent results on dominance and p-passivity aimed at generalizing dissipativity theory to the analysis of non-equilibrium nonlinear systems. Our paper shows how those results apply to basic and well-known nonlinear circuit architectures. They illustrate the potential of dissipativity theory to design and analyze switching and oscillating circuits quantitatively, very much like their linear counterparts.