From MEMS to NEMS: Closed-loop actuation of resonant beams beyond the critical Duffing amplitude

Because of its moderate cost in terms of electronics, resonant sensing has become commonplace in the context of MEMS and NEMS devices. It is usual to drive such resonators below the critical open-loop Duffing amplitude, above which the oscillations become unstable. However, when scaling sensors down to NEMS, nonlinearities may occur at very low amplitudes, making oscillations very difficult to detect. This paper describes a very general way to compute the critical amplitude in open-loop operation for beam resonators, before it focuses on closed-loop Duffing-type resonators. The major contribution of this paper is the use of describing function analysis validated by numerical simulations to show that it is possible to obtain stable oscillations with amplitudes much larger than the critical Duffing amplitude. As a practical consequence, the measured currents are significantly increased and the constraints on the sensing electronics can be relaxed.