High-Sensitive Parity-Time Symmetric Oscillator in Coupled Transmission Lines With Nonlinear Gain

Abstract

A scheme for generating oscillations based on an exceptional point of degeneracy (EPD) is proposed in two-coupled resonators made of two coupled transmission lines terminated on balanced gain and loss, exhibiting a double pole. The EPD is a point in the parameter space of the system at which two or more eigenmodes coalesce in both their eigenvalues (here, resonance frequencies) and eigenvectors. We show that a finite-length single transmission line terminated with gain and loss possesses no degeneracy point, whereas second-order EPDs are enabled in two finite-length coupled transmission lines (CTLs) terminated with balanced gain and loss. We demonstrate the conditions for EPDs to exist for three different termination configurations with balanced gain and loss, and show the eigenfrequency bifurcation at the EPD following the fractional power expansion series related to the Puiseux series. We study the oscillatory regime of operation assuming the gain element is nonlinear, and the extreme sensitivity of the degenerate self-oscillation frequency to perturbations and how it compares with the sensitivity of the linear-gain case. Finally, we show that the sensitivity of the EPD-CTL resonator is much higher than the one of a single-TL resonator. The very sensitive EPD based oscillator can be used as sensors when very small variations in a system shall be detected.

Keywords

• Coupled mode analysis
• microwave oscillators
• microwave sensors
• resonators
• sensitivity analysis