Perturbations of circuit evolution matrices with Jordan blocks

TL;DR

This paper develops a perturbation theory for simple LC-loop circuits with Jordan blocks near exceptional points of degeneracy, enabling enhanced sensitivity applications and stable operation analysis.

Contribution

It introduces a comprehensive perturbation framework for circuits with Jordan blocks near EPDs and proposes methods for detecting proximity to Jordan blocks.

Findings

Perturbation theory for circuits near EPDs

Methods to detect proximity to Jordan blocks

Strategies for stable operation near degeneracies

Abstract

In our prior studies we synthesized special circuits possessing evolution matrices that involve nontrivial Jordan blocks and the corresponding degenerate eigenfrequencies. The degeneracy of this type is sometimes referred to as exceptional point of degeneracy (EPD). The simplest of these circuits are composed just of two LC-loops coupled by a gyrator and they are of our primary interest here. These simple circuits when near an EPD state can be used for enhanced sensitivity applications. With that in mind we develop here a comprehensive perturbation theory for these simple circuits near an EPD as well way to assure their stable operation. As to broader problem of numerical treatment of Jordan blocks and their perturbation we propose a few approaches allowing to detect the proximity to Jordan blocks.