An analytical formulation for phase noise in MEMS oscillators

Study of the Influence of Phase Noise on the MEMS Disk Resonator Gyroscope Interface Circuit

In this paper, a detailed analysis of the influence of phase noise on the micro-electro-mechanical system (MEMS) disk resonator gyroscope (DRG) is presented. Firstly, a new time-varying phase noise model for the gyroscope is established, which explains how the drive loop circuit noise converts into phase noise. Different from previous works, the time-varying phase noise model in this paper is established in mechanical domain, which gain more physical insight into the origin of the phase noise in gyroscope. Furthermore, the impact of phase noise on DRG is derived, which shows how the phase noise affects angular velocity measurement. The analysis shows that, in MEMS DRG, the phase noise, together with other non-ideal factors such as direct excitation of secondary resonator, may cause a low frequency noise in the output of the gyroscope system and affect the bias stability of the gyroscope. Finally, numerical simulations and experiment tests are designed to prove the theories above.

Resonance tracking in a micromechanical device using phononic frequency combs

Micro and nanomechanical resonators have been extensively researched in recent decades for applications to time and frequency references, as well as highly sensitive sensors. Conventionally, the operation of these resonant sensors is implemented using a feedback oscillator to dynamically track variations in the resonant frequency. However, this approach places limitations on the frequency stability of the output response, particularly owing to near-carrier noise shaping, limiting measurement stabilities at short-to-moderate integration times. Here, in this paper, utilizing the recent experimental demonstration of phononic frequency combs, we demonstrate an alternative resonance tracking approach with the potential to provide significant improvements in near-carrier phase noise and long-term stability. In addition, we also showcase comb dynamics mediated resonant frequency modulation which indirectly points to the possible control of inevitable noise processes including thermomechanical fluctuations. This resonant tracking approach may also have general applicability to a number of other physical oscillators.

Micromachined Resonators: A Review

This paper is a review of the remarkable progress that has been made during the past few decades in design, modeling, and fabrication of micromachined resonators. Although micro-resonators have come a long way since their early days of development, they are yet to fulfill the rightful vision of their pervasive use across a wide variety of applications. This is partially due to the complexities associated with the physics that limit their performance, the intricacies involved in the processes that are used in their manufacturing, and the trade-offs in using different transduction mechanisms for their implementation. This work is intended to offer a brief introduction to all such details with references to the most influential contributions in the field for those interested in a deeper understanding of the material.

Numerical Verification of an Analytical Model for Phase Noise in MEMS Oscillators

A new analytical formulation for phase noise in MEMS oscillators was recently presented encompassing the role of essential nonlinearities in the electrical and mechanical domains. In this paper, we validate the effectiveness of the proposed analytical formulation with respect to the unified theory developed by Demir et al. describing phase noise in oscillators. In particular, it is shown that, over a range of the second-order mechanical nonlinear stiffness of the MEMS resonator, both models exhibit an excellent match in the phase diffusion coefficient calculation for a square-wave MEMS oscillator.