Frequency stabilization in nonlinear micromechanical oscillators

Abstract

mechanical oscillators are present in almost every electronic device. They mainly consist of a resonating element providing an oscillating output with a specific frequency. Their ability to maintain a determined frequency in a specified period of time is the most important parameter limiting their implementation. Historically, quartz crystals have almost exclusively been used as the resonating element, but micromechanical resonators are increasingly being considered to replace them. These resonators are easier to miniaturize and allow for monolithic integration with electronics. However, as their dimensions shrink to the microscale, most mechanical resonators exhibit nonlinearities that considerably degrade the frequency stability of the oscillator. Here we demonstrate that, by coupling two different vibrational modes through an internal resonance, it is possible to stabilize the oscillation frequency of nonlinear self-sustaining micromechanical resonators. our findings provide a new strategy for engineering low-frequency noise oscillators capitalizing on the intrinsic nonlinear phenomena of micromechanical resonators.

Symmetry breaking in a mechanical resonator made from a carbon nanotube

“…Symmetry breaking also leads to mode mixing and to parametric resonance in response to additive driving. This holds promise for a number of applications, such as controlled mode mixing [35][36][37] and phase noise cancellation [38][39][40] .…”

Detection of weak stochastic forces in a parametrically stabilized micro-optomechanical system

“…[13] indeed keeps short (∼ms) measurement times. Therefore, even when willing to apply an efficient data analysis, as well as in several kinds of refined optomechanical experiments, stabilization and feedback techniques acting on the optomechanical system are crucial, and indeed this issue has been recently considered by a few groups [14,15].…”

Passive linearization of nonlinear resonances

“…Isochronicity for the first resonance can now be enforced through Eq. (13), and the result is the solid line in Fig. 6.…”

“…However, nonlinearity is a frequent occurrence in physical and engineering applications. For instance, in micro-and nanoresonators used for ultrasensitive force and mass sensing 1-3 , radio-frequency signal processing 4 , narrow band filtering 5,6 , time keeping 7-9 and nanoscale imaging 10,11 , nonlinear behaviors are already experienced at low amplitudes compared to the noise floor 12,13 . Nonlinearity may result in plethora of dynamic phenomena including amplitude-frequency dependence 14 , modal couplings [15][16][17] , mixed hardeningsoftening behaviors 12 and chaotic responses 18,19 .…”

“…Bistability and jump phenomena were used to enhance noise squeezing 24 , to enlarge the bandwidth of energy harvesters [25][26][27][28] , to improve mass detection 29 , to reduce the sensitivity of a resonator to the phase of the drive 7 and to develop new mechanical memory devices 30,31 . Superharmonic excitation and internal resonances were employed to improve stability properties of resonators 32 and time keeping devices 13 . Finally, the inherent frequency-energy dependence of nonlinear oscillations was exploited in broadband vibration absorbers 33 .…”