Coupled vibrations and frequency shift of compound system consisting of quartz crystal resonator in thickness-shear motions and micro-beam array immersed in liquid

The dynamic characteristics of a quartz crystal resonator（QCR） in thicknessshear modes（TSM） with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction（surface shear force）, thus changing the system resonant frequency. The obtained results are useful in resonator design and applications.

The Characteristics of the Shear-Vibrating Quartz Crystal Resonator

<正>According to the piezoelectric equation and the vibration theory of the quartz crystal,the relations between the vibrating frequency and structural parameters under the thickness-shear-vibration of AT-cut quartz crystal have been studied. The frequency conditions under which quartz crystal resonator formed stationary wave inside the electrode district and the transmission characteristics of wave outside the electrode district have also been discussed.A quartz crystal resonator was developed based on this analysis.The experiment showed that the force-sensing characteristics were independent of the fixation of the crystal edge.The detecting distinguish ability was up to 0.001°,and the short-term frequency stability was up to 1.38×10~ (-10)/min.

Effect of strain-gradients of surface micro-beams on frequency-shift of a quartz crystal resonator under thickness-shear vibrations

With introduction of the first-order strain-gradient of surface micro-beams into the energy density function,we developed a two-dimensional dynamic model for a compound quartz crystal resonator（QCR） system,consisting of a QCR and surface micro-beam arrays.The frequency shift that was induced by micro-beams with consideration of strain-gradients is discussed in detail and some useful results are obtained,which have important significance in resonator design and applications.

Simultaneous Multimode Oscillation of Stress-Compensated Cut Quartz Resonator with Narrow-Band Wide Variable-Range Quartz Crystal Oscillator

A multimode-quartz-crystal oscillator was developed to excite stable dual-mode resonance at different frequencies: The oscillation of the 3rd harmonic resonance of the principle C-mode and an additional resonance B-mode of SC-cut crystal. Harmonic combinations of the 3rd and fundamental mode of B-mode with the 3rd harmonics of C-mode are demonstrated. The measurement of the temperature dependence of the oscillation frequency is demonstrated along with the stability determined by root Allan variance. Dependence on the open conductance of the active circuit and the dependence on the coupling capacitors are discussed.

Influence of surface micro-beams with large deflection on the resonance frequency of a quartz crystal resonator in thickness-shear mode vibrations

We study the dynamic behavior of a quartz crystal resonator （QCR） in thickness-shear vibrations with the upper surface covered by an array of micro-beams （MBs） under large deflection. Through taking into account the continuous conditions of shear force and bending moment at the interface of MBs/resonator, dependences of frequency shift of the compound QCR system versus material parameter and geometrical parameter are illustrated in detail for nonlinear and linear vibrations. It is found that the frequency shift produces a little right （left） translation for increasing elastic modulus （length/radius ratio） of MBs. Moreover, the frequency right （left） translation distance caused by nonlinear deformation becomes more serious in the second-order mode than in the first-order one,

Electric admittance analysis of quartz crystal resonator in thickness-shear mode induced by array of surface viscoelastic micro-beams

The electric admittance of a compound system composed of a thickness-shear mode （TSM） quartz crystal resonator （QCR） and an array of surface viscoelastic micro-beams （MBs） is studied. The governing equations of the MBs are derived from the Timoshenko-beam theory in consideration of shear deformation. The electrical admittance is described directly in terms of the physical properties of the surface epoxy resin （SU-8） MBs from an electrically forced vibration analysis. It is found that both the inertia effect and the constraint effect of the MBs produce competitive influence on the resonant frequency and admittance of the compound QCR system. By further comparing the numerical results calculated from the Timoshenko-beam model with those from the Euler-beam model, the shear deformation is found to lead to some deviation of an admittance spectrum. The deviations are revealed to be evident around the admittance peak（s） and reach the maximum when a natural frequency of the MBs is identical to the fundamental frequency of the QCR. Besides, a higher order vibration mode of the MBs corresponds to a larger deviation at the resonance.

Thickness shear mode quartz crystal resonators with optimized elliptical electrodes

Quartz crystal resonators （QCRs） with circular electrodes have been widely used for various liquid and gas sensing applications. In this work, quartz crystal resonators with elliptical electrodes were studied and tested for liquid property measurement. Mindlin＇s theory was used to optimize the dimension and geometry of the electrodes and a 5-MHz QCR with minimum series resistance and without any spurious modes was obtained. A series of AT-cut QCRs with elliptical electrodes of different sizes were fabricated and their sensing performances were compared to devices with circular electrodes. The experimental result shows that the device with elliptical electrodes can obtain lower resonance impedance and a higher Q factor, which results in a better loading capability. Even though the sensitivities of devices with elliptical and circular electrodes are found to be similar, the sensor with elliptical electrodes has much higher resolution due to a better frequency stability. The study indicates that the performance of QCRs with elliptical electrodes is superior to that of traditional QCRs with circular electrodes.

Start-Up Acceleration of Quartz Crystal Oscillator Using Active Inductance Double Resonance and Embedded Triggering Circuit

Low-frequency double-resonance quartz crystal oscillator was developed with active inductance circuit aiming the start-up of stable oscillation of tuning fork-type quartz crystal resonator at 32.768 kHz within 0.37 ms. The initial oscillation is triggered by a part of crystal oscillator forming a CR oscillator. The negative resistance ranges to 4 MΩ at gmf of 4.1 μA/V. In a limited frequency range, the circuit shows negative reactance Ccci = -3.4 pF equivalent to inductance Lcc = 9.8 H. The Allan standard deviation indicated 10-11 to 10-10, showing high stability comparable to general quartz crystal oscillator.

The Multi-field Coupled Vibration Analysis of AT-Cut Quartz Crystal Resonators with Parallelism Error

During the fabrication of quartz crystal resonators(QCRs),parallelism error is inevitably generated,which is rarely investigated.In order to reveal the influence of parallelism error on the working performance of QCRs,the coupled vibration of a non-parallel AT-cut quartz crystal plate with electrodes is systematically studied from the views of theoretical analysis and numerical simulations.The two-dimensional thermal incremental field equations are solved for the free vibration analysis via the coefficient-formed partial differential equation module of the COMSOL Multiphysics software,from which the frequency spectra,frequency–temperature curves,and mode shapes are discussed in detail.Additionally,the piezoelectric module is utilized to obtain the admittance response under different conditions.It is demonstrated that the parallelism error reduces the resonant frequency.Additionally,symmetry broken by the non-parallelism increases the probability of activity dip and is harmful to QCR’s thermal stability.However,if the top and bottom surfaces incline synchronously in the same direction,the influence of parallelism error is tiny.The conclusions achieved are helpful for the QCR design,and the methodology presented can also be applied to other wave devices.

三种石英晶体谐振器频率测试方法对比分析研究

测试石英晶体谐振器频率的传统方法有间接计算法、信号源起振法和网络分析仪法,三种方法各有大的缺陷。根据石英晶体谐振器频率的特点,提出三种新的测试方法:示波器测试法、频率计测试法和频谱仪测试法。这三种方法在基本测试原理、设备配置要求、测试精度和适用环境等方面存在差异。对三种方法的优缺点进行了详细比较,并针对不同应用条件提出了选用建议:如果只单纯测量石英晶体谐振器频率,选用频谱仪测试法;如果需要测量频率的同时还需要知道频率的特性等内容,宜选用频率计测试法;示波器测试法则可用在对石英晶体谐振器频率定性的粗测。此外,还根据各自的优势探讨了仪器协作测试的可能性。

FeGa膜/AT切石英晶片双面复合蝶形谐振磁场传感器

蝶形磁致伸缩膜由于磁汇聚,其中心区域的磁致伸缩应变增强,但是和矩形AT切石英晶片复合时,磁膜耦合至矩形晶片电极区的应变会向周围无磁膜区域扩散,降低应变对晶片厚度剪切振动的作用,降低磁场传感器灵敏度。提出AT切石英晶片和FeGa膜形状一样的蝶形谐振磁场传感器,蝶形晶片可以将蝶形磁膜增强的晶片应变汇聚至晶片电极区,以提高传感器灵敏度。仿真结果预测,在23.8~118.9 Oe的磁场范围内,蝶形结构的灵敏度为蝶形磁膜/矩形晶片结构的3.73倍。通过微机械加工,制作了蝶形器件,对实际器件测试的结果表明,在76.4~117 Oe的线性区间内,蝶形传感器的灵敏度可达-29.08 Hz/Oe。

基于Chip-on-TEC的高精度晶体振荡器研究

提高晶体振荡器频率稳定度的首要手段是保持温度的稳定。基于热电制冷器具有的恒温特性,采用Chip-on-TEC方法,给出了一种高精度的晶体振荡器的设计方案。利用多物理仿真软件,针对商用的音叉型石英晶体,首次建立了32.768 kHz石英晶片的完整的有限元多物理场仿真模型。仿真结果表明,晶体的谐振频率与商用产品完全相同;基于TEC的晶体振荡器设计方案可以使得晶片温度变化低至0.008℃,对应的频率稳定度5.4×10^(-9)。考虑到高精度切型晶片材料的非易得性,所给出的方案为采用低精度切型晶片设计高精度的晶体振荡器提供了思路。

ON THE INTERACTION BETWEEN A QUARTZ CRYSTAL RESONATOR AND AN ARRAY OF MICRO-BEAMS IN THICKNESS-SHEAR VIBRATIONS

We studied the coupled dynamic behavior of a quartz-crystal-resonator （QCR）/micro- beams system in the thickness-shear motions. Through taking into account the couple stress in the dynamic equations of the quartz plate, both continuous conditions of shear force and bending moment at the resonator/micro-beams interface are realized. Frequency shift of the compound QCR system induced by micro-beams is studied in detail. The obtained results are useful in device design and frequency-stability analysis of quartz crystal resonators.

高温环境下AT切石英谐振器振动特性分析

为了研究AT切型石英晶体谐振器在不同温度环境下的振动状态,利用有限元仿真软件COMSOL Multiphysics 6.0分析了石英晶体在不同温度下沿x方向振动位移分布情况,直观地观察了寄生模态的振动位移,计算了不同温度下电极区能量占比以及品质因数,并通过实验测量了不同温度下AT切型石英晶体品质因数及温频效应。仿真结果表明,随温度变化,AT切型石英晶体表面始终存在典型的能陷效应,未加剧模态间的耦合问题。实验结果表明,AT切型石英晶体频率随温度变化趋势与理论一致,实验数据与仿真计算的品质因数随温度改变均无明显变化。研究成果证明AT切型石英晶体具有良好的热稳定性,可以作为石英晶体微天平(Quartz Crystal Microbalance,QCM)传感器在高温环境下的敏感元件,对高温环境下敏感器件的选择具有指导意义。

ENERGY TRAPPING OF THICKNESS-SHEAR AND THICKNESS-TWIST MODES IN A PARTIALLY ELECTRODED AT-CUT QUARTZ RESONATOR

The thickness-shear and thickness-twist vibrations of a finite and partially elec- troded AT-cut quartz resonator are investigated. The equations of anisotropic elasticity are used with the omission of the small elastic constant c56. An analytical solution is obtained using Fourier series from which the free vibration resonant frequencies, mode shapes, and energy trapping are calculated and examined.

实现AT切石英晶体振荡器微处理器温度补偿的新方法

本文介绍实现AT切石英晶体振荡器微处理器温度补偿的新方法———双频温度自测法 .AT切石英谐振器各泛音次数的频率温度曲线不同 ,利用基频与 3次泛音除一阶温度系数不同外其他各阶温度系数相等的特性 ,基频的 3倍频与 3次泛音频率的差频输出与温度近似成线性关系 .同时激励并测量基频和 3次泛音频率 ,经过微处理器计算差频实现谐振器温度自测并进行晶体振荡器的微处理器温度补偿 .与使用分立温度传感器相比 ,消除了测温元件与石英谐振器温度时间常数不同以及温度场梯度造成的测温误差 ,提高了测温和补偿精度 .

切变振动型石英晶体谐振器的特点及其应用

根据石英晶体的压电方程和晶体振动理论,研究了AT-切石英晶体厚度切变振动模式下振动频率与结构参数间的关系,以及石英晶体谐振器在电极区形成稳衡驻波的频率条件及电极区外波的传播特性。试验表明,根据本文研究结果设计的石英晶体谐振器,其力敏特性基本与晶体边缘的固接方式无关,利用这种结构形式的石英谐振器作力敏元件用于姿态检测时,检测分辨率可达0.001°,短期频率稳定性达到1.38×10-10/min。

π网络法石英晶体谐振器测试技术研究

为了提高石英晶体谐振器参数的测量精度,对π网络法测量石英晶体谐振器参数的原理及π网络中分布参数对测量精度的影响进行了研究,在此基础上,设计并制作了π网络最大传输法石英晶体测量实验系统,实验系统在1～120MHz的测试范围内,石英晶体谐振器串联谐振频率的测试精度为±2ppm。测试方法符合国际标准,性能指标优于目前国内使用的阻抗计型测试仪器。

石英晶体板高频振动的三维有限元分析

通过建立石英晶体板的三维模型,运用有限元分析软件ANSYS获得了石英晶体板厚度剪切振动的振动频率和位移云图。验证了数值计算结果的收敛性并提出了避免振动模态强烈耦合的石英晶体板最佳长厚比的选取方法。模型分析过程中发现,六面体网格比四面体网格易观察到石英晶体板的厚度剪切振动。

石英谐振式力传感器及几个工程问题的研究

本文介绍了一种高准确度石英谐振式力传感器，针对其在工程化过程中遇到的一系列问题，从理论到实验进行了研究，解决了组合式结构石英传感器的蠕变问题，并研究了传感器的稳定性与谐振器厚度及支撑状况的关系。