Yong Yook-Kong, Patel Mihir, Vig John, Ballato Arthur
Department of Civil and Environmental Engineering, Rutgers University, Piscataway, NJ, USA.
IEEE Trans Ultrason Ferroelectr Freq Control. 2009 Feb;56(2):353-60. doi: 10.1109/TUFFC.2009.1044.
The quartz resonator Q with aluminum electrodes was studied with respect to its fundamental thickness shear mode frequency and its viscoelastic, viscopiezoelectric, and viscopiezoelectromagnetic behaviors. The governing equations for viscoelasticity, viscopiezoelectricity, and viscopiezoelectromagnetism were implemented for an AT-cut quartz resonator. To simulate the radiation conditions at infinity for the viscopiezoelectromagnetic model, perfectly matched layers over a surface enclosing the resonator were implemented to absorb all incident electromagnetic radiation. The shape of the radiation spectrum of a 5.6 MHz AT-cut quartz resonator was found to compare relatively well the measured results by Campbell and Weber. The mesa-plate resonator was studied for a frequency range of 1.4 GHz to 3.4 GHz. The resonator Q was determined to be influenced predominantly by the quartz viscoelasticity; however at frequencies greater than 2.3 GHz, the quartz electromagnetic radiation had an increasingly significant effect on the resonator Q. At 3.4 GHz, the electromagnetic radiation accounted for about 14% of the loss in resonator Q. At frequencies less than 2 GHz, the calculated resonator Q compared well with the intrinsic Q(x) provided by the formula Q(x) = 16 x 10(6)/f where f was in MHz. At frequencies higher than 2.3 GHz, the aluminum electrodes had significant effects on the resonator Q. At 3.4 GHz, the electromagnetic radiation loss in the electrodes was an order of magnitude greater than their viscoelastic loss; hence, the vibrating aluminum electrodes became an efficient emitter of electromagnetic waves. The effects of electrical resistance in both the electrodes and quartz were determined to be negligible.
对带有铝电极的石英谐振器Q进行了研究，涉及其基本厚度剪切模式频率以及粘弹性、粘压电性和粘压电磁行为。针对AT切割石英谐振器，实施了粘弹性、粘压电性和粘压电磁学的控制方程。为了模拟粘压电磁模型在无穷远处的辐射条件，在包围谐振器的表面上设置了完全匹配层，以吸收所有入射电磁辐射。发现5.6MHz的AT切割石英谐振器的辐射光谱形状与坎贝尔和韦伯的测量结果比较吻合。对台面平板谐振器在1.4GHz至3.4GHz的频率范围内进行了研究。确定谐振器Q主要受石英粘弹性的影响；然而，在频率大于2.3GHz时，石英电磁辐射对谐振器Q的影响越来越显著。在3.4GHz时，电磁辐射约占谐振器Q损耗的14%。在频率小于2GHz时，计算得到的谐振器Q与公式Q(x)=16×10(6)/f（其中f以MHz为单位）给出的固有Q(x)比较吻合。在频率高于2.3GHz时，铝电极对谐振器Q有显著影响。在3.4GHz时，电极中的电磁辐射损耗比其粘弹性损耗大一个数量级；因此，振动的铝电极成为了高效的电磁波发射器。确定电极和石英中的电阻影响可忽略不计。
