We present a scheme for high-sensitivity 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 finding 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 demonstrate its instability and nonlinearity, experimentally observing stable self-oscillations in the saturated regime. We measure the circuit’s sensitivity to a small capacitor perturbation. A shift in oscillation frequency after saturation in the order of 1 kHz is well detectable with very distinct spectral peaks with only 10-Hz linewidth, and with a clean spectrum down to $-70$ 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 an alternative generation of high-sensitive sensors to measure slight variations in physical, chemical, or biological quantities.

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• Metrology
• Coupled oscillators
• Devices
• Exceptional points
• Metamaterials
• Chaos & nonlinear dynamics
• Noise measurements
• Perturbation theory