On the effect of linear feedback and parametric pumping on a resonators frequency stability

TL;DR

This paper investigates how linear feedback and parametric pumping influence the frequency stability of resonators in M/NEMS sensors, revealing that noise sources determine the effectiveness of these techniques for enhancing sensor performance.

Contribution

The study provides analytical models of feedback and parametric pumping effects on resonator Q, including noise considerations, and identifies conditions where these techniques improve stability.

Findings

Parametric pumping increases amplitude Q but decreases phase Q.

Feedback enhances Q in both amplitude and phase.

Amplifier noise dominance allows Q enhancement benefits from parametric pumping.

Abstract

Resonant sensors based on Micro- and Nano-Electro Mechanical Systems (M/NEMS) are ubiquitous in many sensing applications due to their outstanding performance capabilities, which are directly proportional to the quality factor (Q) of the devices. We address here a recurrent question in the field: do dynamical techniques that modify the effective Q (namely parametric pumping and direct drive velocity feedback) affect the performance of said sensors? We develop analytical models of both cases, while remaining in the linear regime, and introduce noise in the system from two separate sources: thermomechanical and amplifier (read-out) noise. We observe that parametric pumping enhances the quality factor in the amplitude response, but worsens it in the phase response on the resonator. In the case of feedback, we find that Q is enhanced in both cases. Then, we establish a solution for the noisy problem with direct drive and parametric pumping simultaneously. We also find that, in the case when thermomechanical noise dominates, no benefit can be obtained from neither artificial Q-enhancement technique. However, in the case when amplifier noise dominates, we surprisingly observe that a significant advantage can only be achieved using parametric pumping in the squeezing region.