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.

中文翻译：

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线性反馈和参量泵浦对谐振器频率稳定性的影响

基于微纳机电系统 (M/NEMS) 的谐振传感器因其出色的性能而在许多传感应用中无处不在，这些性能与设备的品质因数 (Q) 成正比。我们在这里解决该领域的一个反复出现的问题：修改有效 Q 的动态技术（即参数泵送和直接驱动速度反馈）是否会影响所述传感器的性能？我们开发了两种情况的分析模型，同时保持线性状态，并从两个不同的来源在系统中引入噪声：热机械和放大器（读出）噪声。我们观察到参数泵浦增强了幅度响应中的品质因数，但会使谐振器的相位响应中的品质因数变差。在反馈的情况下，我们发现 Q 在两种情况下都得到了增强。然后，我们建立了同时使用直接驱动和参数泵送的噪声问题的解决方案。我们还发现，在热机械噪声占主导地位的情况下，这两种人工 Q 增强技术都无法获得任何好处。然而，在放大器噪声占主导地位的情况下，我们惊讶地观察到只有在压缩区域使用参数泵浦才能获得显着优势。