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We demonstrate that a circuit comprising two unstable LC resonators coupledvia a gyrator supports an exceptional point of degeneracy (EPD) with purelyreal eigenfrequency. Each of the two resonators includes either a capacitor oran inductor with a negative value, showing purely imaginary resonance frequencywhen not coupled to the other via the gyrator. With external perturbationimposed on the system, we show analytically that the resonance frequencyresponse of the circuit follows the square-root dependence on perturbation,leading to possible sensor applications. Furthermore, the effect of smalllosses in the resonators is investigated, and we show that losses lead toinstability. In addition, the EPD occurrence and sensitivity are demonstratedby showing that the relevant Puiseux fractional power series expansiondescribes the eigenfrequency bifurcation near the EPD. The EPD has the greatpotential to enhance the sensitivity of a sensing system by orders ofmagnitude. Making use of the EPD in the gyrator-based circuit, our results pavethe way to realize a new generation of high-sensitive sensors to measure smallphysical or chemical perturbations.

Enhanced Sensitivity of Degenerate System Made of Two Unstable Resonators Coupled by Gyrator Operating at an Exceptional Point