Dissipativity analysis of negative resistance circuits

TL;DR

This paper extends classical passivity theory to analyze nonlinear circuits with negative resistance elements, enabling better understanding of circuits that switch and oscillate.

Contribution

It introduces a generalized dissipativity framework using signed storage functions and supply rates for circuits with negative resistance components.

Findings

Provides a new theoretical tool for analyzing active nonlinear circuits.

Enables stability and behavior analysis of circuits with negative resistance.

Bridges passive and active circuit analysis through signed dissipativity.

Abstract

This paper deals with the analysis of nonlinear circuits that interconnect passive elements (capacitors, inductors, and resistors) with nonlinear resistors exhibiting a range of $\it{negative}$ resistance. Such active elements are necessary to design circuits that switch and oscillate. We generalize the classical passivity theory of circuit analysis to account for such non-equilibrium behaviors. The approach closely mimics the classical methodology of (incremental) dissipativity theory, but with dissipation inequalities that combine $\it{signed}$ storage functions and $\it{signed}$ supply rates to account for the mixture of passive and active elements.