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Quality factor (Q) is an important property of micro- and nano-electromechanical (MEM/NEM) resonators that underlie timing references, frequency sources, atomic force microscopes, gyroscopes, and mass sensors. Various methods have been utilized to tune the effective quality factor of MEM/NEM resonators, including external proportional feedback control, optical pumping, mechanical pumping, thermal-piezoresistive pumping, and parametric pumping. This work reviews these mechanisms and compares the effective Q tuning using a position-proportional and a velocity-proportional force expression. We further clarify the relationship between the mechanical Q, the effective Q, and the thermomechanical noise of a resonator. We finally show that parametric pumping and thermal-piezoresistive pumping enhance the effective Q of a micromechanical resonator by experimentally studying the thermomechanical noise spectrum of a device subjected to both techniques.
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On the effect of linear feedback and parametric pumping on a resonator’s frequency stability
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 effectiveQ(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 thatQis 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 either artificialQ-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.
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- Award ID(s):
- 1662464
- PAR ID:
- 10303666
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- New Journal of Physics
- Volume:
- 22
- Issue:
- 9
- ISSN:
- 1367-2630
- Page Range / eLocation ID:
- Article No. 093049
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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