MEMS和压电谐振器中Q与TCF的关联研究
Connecting Q to TCF for MEMS and piezoelectric resonators
AI总结：
本研究通过唯象非简谐振子模型揭示MEMS谐振器的品质因数Q与频率温度系数TCF的关联，发现产生TCF的非线性项为Q设定上限，推导了相关损耗公式并验证其适用性，可推广至各类非零TCF谐振系统。
摘要：
微机电系统（MEMS）谐振器的两个关键特性是品质因数（$Q$）和频率温度系数（$TCF$）。本文通过唯象非简谐振子模型揭示了$Q$与$TCF$之间的关联。具体而言，研究表明导致$TCF$的同一非线性项为谐振器的$Q$设定了上限。本文推导了一个估算该损耗的简洁公式，且证实该公式与描述Akhiezer阻尼的Woodruff公式密切相关。通过将模型拓展至一类重要的MEMS器件——压电谐振器，本文展示了该公式的应用方式。最后，研究将该模型应用于已发表的AlN-on-diamond压电谐振器的实验数据。本文聚焦于MEMS谐振器，但该方法应可广泛适用于任何具有非零$TCF$的谐振系统。
英文摘要：
Two critical characteristics for any MEMS resonator are the quality factor ($Q$) and the temperature coefficient of frequency ($TCF$). The connection between $Q$ and $TCF$ is demonstrated here with a phenomenological anharmonic oscillator model. Specifically, it is shown that the same nonlinear terms responsible for the $TCF$ set an upper limit on the resonator's $Q$. A concise formula is found to estimate this loss and is shown to be closely related to Woodruff's formula for Akhiezer damping. The use of this formula is illustrated by extending the model to an important class of MEMS; piezoelectric resonators. Finally, the model is applied to published data for an AlN-on-diamond piezoelectric resonator. The focus here is on MEMS resonators, but the method should apply broadly to any resonance with non-zero $TCF$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
