Exceptional Points in Gyrator-Based Circuit and Nonlinear High-Sensitivity Oscillator

TL;DR

This paper introduces a gyrator-based circuit exploiting exceptional points of degeneracy to create highly sensitive oscillators capable of detecting minute circuit perturbations, with potential applications in advanced sensing technologies.

Contribution

The study demonstrates a novel circuit design using exceptional points for high sensitivity, including experimental validation and analysis of nonlinear effects and stability considerations.

Findings

Eigenfrequency bifurcation described by Puiseux series near EPD

Experimental stable self-oscillations with 10 Hz linewidth

Sensitivity surpasses comparable linear resonators and is robust to perturbation polarity

Abstract

We present a scheme for high-sensitive oscillators based on an exceptional point of degeneracy (EPD) in a circuit made of two LC resonators coupled by a gyrator. The frequency of oscillation is very sensitive to perturbations of a circuit element, like a capacitor. We show conditions that lead to an EPD, assuming one of the two resonators is composed of an inductor and a capacitor of negative values. The EPD occurrence and sensitivity to perturbations in the linear case are demonstrated by showing that the eigenfrequency bifurcation around the EPD is described by the relevant Puiseux (fractional power) series expansion. We also investigate the effect of small losses in the system and show that they lead to instability. We fabricate the circuit, and exploit its instability and nonlinearity, observing experimentally stable self-oscillations under the saturated regime. We measure the circuit's sensitivity to a small capacitor perturbation. A shift in frequency of oscillation after saturation is well detectable with very distinct spectral peaks with 10 Hz linewidth, clean until -70 dB from the peak value. The sensitivity is (i) higher than the one of a comparable simple LC linear resonator, (ii) comparable or better than other published EPD circuits, and (iii) applicable to both negative and positive values of the capacitance perturbation, contrary to what happens in PT-symmetric circuits. The proposed scheme can pave the way for a new generation of high-sensitive sensors to measure slight variations in physical, chemical or biological quantities.