Highly Sensitive Coupled Oscillator Based on an Exceptional Point of Degeneracy and Nonlinearity

We propose a scheme to obtain highly sensitive oscillators in a coupled-resonator system with an exceptional point of degeneracy (EPD) and a small instability. The oscillator with the exceptional degeneracy is realized by using two coupled resonators with an almost balanced small-signal gain and loss, that saturates due to nonlinear effects of the active component, resulting in an oscillation frequency that is very sensitive to a perturbation of the circuit. Two cases are investigated, with two parallel $LC$ resonators with balanced small-signal gain and loss that are either coupled wirelessly by mutual inductance or coupled wired by a capacitor. This paper demonstrates theoretically and experimentally the conditions to obtain a second-order EPD oscillator and analyzes the ultrasensitivity of the oscillation frequency to components' perturbation, including the case of asymmetric perturbation that breaks $PT$ symmetry. We discuss the effects of nonlinearity on the performance of the oscillator and how the proposed scheme improves the sensing's sensitivity of perturbations. In contrast to previous methods, our proposed degenerate oscillator can sense either positive or negative changes of a circuit component. The degenerate oscillator circuit may find applications in various areas, such as ultrasensitive sensors, tunable oscillators, and modulators.