Rutgers University, Piscataway, NJ, USA.
IEEE Trans Ultrason Ferroelectr Freq Control. 2010 Aug;57(8):1831-9. doi: 10.1109/TUFFC.2010.1622.
A novel analytical/numerical method for calculating the resonator Q and its equivalent electrical parameters due to viscoelastic, conductivity, and mounting supports losses is presented. The method presented will be quite useful for designing new resonators and reducing the time and costs of prototyping. There was also a necessity for better and more realistic modeling of the resonators because of miniaturization and the rapid advances in the frequency ranges of telecommunication. We present new 3-D finite elements models of quartz resonators with viscoelasticity, conductivity, and mounting support losses. The losses at the mounting supports were modeled by perfectly matched layers (PMLs). A previously published theory for dissipative anisotropic piezoelectric solids was formulated in a weak form for finite element (FE) applications. PMLs were placed at the base of the mounting supports to simulate the energy losses to a semi-infinite base substrate. FE simulations were carried out for free vibrations and forced vibrations of quartz tuning fork and AT-cut resonators. Results for quartz tuning fork and thickness shear AT-cut resonators were presented and compared with experimental data. Results for the resonator Q and the equivalent electrical parameters were compared with their measured values. Good equivalences were found. Results for both low- and high-Q AT-cut quartz resonators compared well with their experimental values. A method for estimating the Q directly from the frequency spectrum obtained for free vibrations was also presented. An important determinant of the quality factor Q of a quartz resonator is the loss of energy from the electrode area to the base via the mountings. The acoustical characteristics of the plate resonator are changed when the plate is mounted onto a base substrate. The base affects the frequency spectra of the plate resonator. A resonator with a high Q may not have a similarly high Q when mounted on a base. Hence, the base is an energy sink and the Q will be affected by the shape and size of this base. A lower-bound Q will be obtained if the base is a semi-infinite base because it will absorb all acoustical energies radiated from the resonator.
提出了一种新的分析/数值方法，用于计算由于粘弹性、电导率和安装支撑损耗而导致的谐振器 Q 和等效电参数。所提出的方法对于设计新的谐振器以及减少原型制作的时间和成本将非常有用。由于小型化和电信频率范围的快速发展，也需要对谐振器进行更好和更现实的建模。我们提出了具有粘弹性、电导率和安装支撑损耗的石英谐振器的新的 3-D 有限元模型。安装支撑处的损耗通过完全匹配层（PML）建模。之前发表的耗散各向异性压电固体理论以弱形式表述，适用于有限元（FE）应用。在安装支撑的底部放置 PML 以模拟能量损耗到半无限基底。对石英音叉和 AT 切石英谐振器的自由振动和强迫振动进行了 FE 模拟。给出了石英音叉和厚度剪切 AT 切谐振器的结果，并与实验数据进行了比较。比较了谐振器 Q 和等效电参数的结果及其测量值。发现了很好的等价性。低 Q 和高 Q AT 切石英谐振器的结果与实验值都很好地吻合。还提出了一种从自由振动获得的频谱中直接估计 Q 的方法。石英谐振器的品质因数 Q 的一个重要决定因素是能量从电极区域通过安装件损失到基底。当板安装到基底上时，板谐振器的声学特性会发生变化。基底会影响板谐振器的频谱。当安装在基底上时，具有高 Q 的谐振器可能不会具有类似的高 Q。因此，基底是能量的汇，Q 将受到基底形状和尺寸的影响。如果基底是半无限基底，则会获得下限 Q，因为它将吸收从谐振器辐射的所有声能。
