Double-resonance quartz crystal oscillator and excitation of a resonator immersed in liquid media

In this work we propose a novel circuit design: a double-resonance oscillator. Its oscillation shows two oscillation modes: frequency locking to the quartz crystal resonance and LC resonance oscillation. Transition of the oscillation mode and the strength of oscillation are analyzed and reviewed for the fundamental mode in comparison with a Colpitts oscillator. The experimental results support the estimates of negative resistance for the double-resonance oscillator compared with the LC oscillator.     

Isolated electrodeless high-frequency quartz crystal microbalance for immunosensors

This paper presents a contactless technique to measure shear bulk wave resonance frequencies of an isolated quartz crystal in a flow cell. The line antenna placed outside the cell generates and detects the resonance frequencies in a wireless-electrodeless manner. It is revealed that this mechanism relies on the quasistatic electric field. A 0.3-mm-thick AT-cut quartz was used, and its overtone resonance frequencies up to 80 MHz were measured in liquids. Exact vibrational analysis was carried out for a triple-layered resonator system consisting of the adsorbed material layer, the electrode film, and the quartz plate. It predicts higher frequency sensitivity to the adsorbed material at higher modes when the electrode layer is removed. The 13th overtone (72-MHz resonance frequency) was used to detect human immunoglobulin G with concentrations between 0.1 and 20 microg/mL captured by protein A immobilized on one side of the crystal. The real-time measurement of the frequency response yielded the equilibrium constant KA=5.21 x 10(7) M(-1).     

An experimental study of frequency jumps during the aging of quartzoscillators

The cause of abrupt frequency jumps observed during the aging of high-stability quartz oscillators is investigated. For this purpose a precise method of measuring the resonant frequency versus drive current is used, and this method is applied to AT-cut crystal resonators used in oven controlled crystal oscillators (OCXOs). Experimental results show that there are some cases where the resonance frequency jumps when crystal current is changed; this phenomenon originates with spurious resonances near the fundamental mode, and the current that causes coupling between the spurious and fundamental modes shifts according to crystal driving time. Furthermore, we show that the abrupt jumping in long-term frequency observation is caused by a “shift” of the current that causes the couplings     

Voltage-controlled narrowband and wide, variable-range four-segment quartz crystal oscillator

In this work, our goal is to develop a voltage-controlled variable-frequency quartz crystal oscillator with narrowband response, wide, variable frequency range and the capacity to oscillate across the series resonance frequency using a four-segment configuration of a quartz crystal oscillator. In conventional quartz oscillators, the quartz resonator is inserted in the feedback loop between the input and the output of the active circuit, providing sufficient gain and the phase relation. In the oscillator developed here, the quartz crystal resonator is inserted between the loop circuit and the ground potential. The performance of the voltage-controlled variable-frequency oscillator is demonstrated across the series resonance frequency.     

Temperature dependence of piezoelectric properties for textured SBN ceramics

Temperature dependences of piezoelectric properties were studied for h001i textured ceramics of bismuth layer-structured ferroelectrics, SrBi(2)Nb(2)O(9) (SBN). The textured ceramics with varied orientation degrees were fabricated by templated, grain-growth method, and the temperature dependences of resonance frequency were estimated. Excellent temperature stability of resonance frequency was obtained for the 76% textured ceramics. The resonance frequency of the 76% textured specimens varied almost linearly over a wide temperature range. Therefore, the variation was slight, even in a high temperature region above 150 degrees C. Temperature stability of a quartz crystal oscillator is generally higher than that of a ceramic resonator around room temperature. The variation of resonance frequency for the 76% textured SrBi(2)Nb(2)O(9) was larger than that of oscillation frequency for a typical quartz oscillator below 150 degrees C also in this study. However, the variation of the textured SrBi(2)Nb(2)O(9) was smaller than that of the quartz oscillator over a wide temperature range from -50 to 250 degrees C. Therefore, textured SrBi(2)Nb(2)O(9) ceramics is a major candidate material for the resonators used within a wide temperature range.     

Influence of interchannel spacing on the dynamical properties of multichannel quartz crystal microbalance

For a multichannel quartz crystal microbalance (MQCM) device, the key problem in design is to minimize the frequency interference between adjacent channels. In this paper, the effects of interchannel separation on the resonance frequencies and frequency interference of the device are studied. The results show that, for the channels with the same size, the resonant modes will appear alternatively, and the frequency interference keeps oscillating in a very small scope in the cases of large interchannel separations. Based on the studies, the considerations for MQCM design also are discussed.     

Monitoring cell adhesion by piezoresonators: impact of increasing oscillation amplitudes

In recent years, the quartz crystal microbalance (QCM) has been established as a sensitive analytical tool to monitor the attachment and spreading of mammalian cells to in vitro surfaces. Due to its superior time resolution, the device is capable of reading even subtle differences in cell adhesion kinetics. However, thickness shear mode piezoresonators, which are the core component of the QCM approach, can be used not only as a sensor but also as an actuator when the oscillation amplitude of the crystal is increased so that molecular recognition at the solid-liquid interface is disturbed. In this study, we have addressed the impact of elevated lateral oscillation amplitudes on the adhesion kinetics of three mammalian cell lines. We used AT-cut piezoresonators with a fundamental resonance frequency of 5 MHz, and the analytical readout was performed by impedance analysis. Formation of stable cell-substrate contacts is retarded or entirely blocked when the lateral oscillation amplitude (in the center of the resonator) exceeds values higher than 20 nm. Shear oscillations of similar amplitude were, however, not sufficient to displace attached cells from the surface. Moreover, the experimental data prove that the normal QCM readout with oscillation amplitudes smaller than 1 nm is, indeed, non-invasive with respect to mammalian cells.     

A dual-frequency QCM-D setup operating at elevated oscillation amplitudes

An often raised, but rarely addressed, question with respect to applications of the quartz crystal microbalance technique is whether the shear oscillation of the sensor surface influences the adsorption kinetics or binding events being studied. Motivated by this uncertainty, as well as by the possibility of using elevated amplitudes to influence and steer specific biomolecular interactions, we have further developed the quartz crystal microbalance with dissipation monitoring (QCM-D) technique to operate in dual-frequency mode. One mode (one harmonic) is utilized for continuous excitation of the QCM-D sensor at resonance, at variable driving amplitudes, while the other mode (another harmonic) is used for combined frequency and energy dissipation (damping) measurements. To evaluate this experimental approach, we investigated the following: (i) the well-established process by which intact lipid vesicles adsorb and decompose into a planar supported lipid bilayer on SiO2, recently shown to be very sensitive to external perturbations, and (ii) specific streptavidin binding to biotin-modified surfaces. In the former case, we observed a clear influence of elevated oscillation amplitudes on the bilayer formation kinetics, while in the latter case, no influence was observed for protein monomers. However, binding was inhibited when the biotin-binding protein was coupled to colloidal particles (o.d. approximately 200 nm).     

A corrected modal representation of thickness vibrations in quartz plates and its influence on the transversely varying case

A modal representation of the thickness vibrations of rotated Y-cut quartz plates, which was used in the treatment of driven transversely varying thickness modes, is shown to be defective in certain respects. The differential equations and edge conditions for transversely varying thickness modes have been used in the accurate treatment of trapped energy resonators, monolithic crystal filters, and contoured quartz resonators, even though those defects were present. In this work those defects in the thickness solution are corrected along with the influence on the differential equations and edge conditions in the transversely varying case. The corrected modal representation shows that, because in practical applications to the above mentioned devices, the driving frequency is always near a thickness resonant frequency, essentially the same results will be obtained with the corrected representation as were obtained with the defective one, which explains why the results obtained with the defective equations were so accurate.     

An analysis of nonlinear vibrations of coupled thickness-shear and flexural modes of quartz crystal plates with the homotopy analysis method

We investigated the nonlinear vibrations of the coupled thickness-shear and flexural modes of quartz crystal plates with the nonlinear Mindlin plate equations, taking into consideration the kinematic and material nonlinearities. The nonlinear Mindlin plate equations for strongly coupled thickness- shear and flexural modes have been established by following Mindlin with the nonlinear constitutive relations and approximation procedures. Based on the long thickness-shear wave approximation and aided by corresponding linear solutions, the nonlinear equation of thickness-shear vibrations of quartz crystal plate has been solved by the combination of the Galerkin and homotopy analysis methods. The amplitude frequency relation we obtained showed that the nonlinear frequency of thickness-shear vibrations depends on the vibration amplitude, thickness, and length of plate, which is significantly different from the linear case. Numerical results from this study also indicated that neither kinematic nor material nonlinearities are the main factors in frequency shifts and performance fluctuation of the quartz crystal resonators we have observed. These efforts will result in applicable solution techniques for further studies of nonlinear effects of quartz plates under bias fields for the precise analysis and design of quartz crystal resonators.     

Influence of diquat on growth and death of HepG2 cells using quartz crystal and micro CCD camera

Diquat is widely used agent which produces toxicity in human and implicated as an environmental toxicity. HepG2 cell was cultured onto an indium tin oxide (ITO) surface of quartz crystal modified a collagen film. In this paper, we investigated the physical properties and the morphological change of the HepG2 cells cultured onto the ITO electrode of the quartz crystal sensor with micro CCD camera. The resonance responses of the quartz crystal and the morphological change were directly monitored. After seeding the cells and diquat injection into the chamber, the resonance frequency and the resonance resistance were obtained with real time morphologies. From the resonance characteristics and the series of morphologies, we could know the diquat to be death and weakening of the cells.     

On the accuracy of Mindlin plate predictions for the frequency-temperature behavior of resonant modes in AT- and SC-cut quartz plates

The frequency spectra of resonant modes in AT- and SC-cut quartz plates and their frequency-temperature behavior were studied using Mindlin first- and third-order plate equations. Both straight-crested wave solutions and two-dimensional plate solutions were studied. The first-order Mindlin plate theory with shear correction factors was previously found to yield inaccurate frequency spectra of the modes in the vicinity of the fundamental thickness-shear frequency. The third-order Mindlin plate equations without correction factors, on the other hand, predict well the frequency spectrum in the same vicinity. In general, the frequency-temperature curves of the fundamental thickness-shear obtained from the first-order Mindlin plate theory are sufficiently different from those of the third-order Mindlin plate theory that they raise concerns. The least accurately predicted mode of vibration is the flexure mode, which results in discrepancies in its frequency-temperature behavior. The accuracy of other modes of vibrations depends on the degree of couplings with the flexure mode. Mindlin first-order plate theory with only the shear correction factors is not sufficiently accurate for high frequency crystal vibrations at the fundamental thickness-shear frequency. Comparison with measured resonant frequencies and frequency-temperature results on an AT-cut quartz plate shows that the third-order plate theory is more accurate than the first-order plate theory; this is especially true for the technically important fundamental thickness shear mode in the AT-cut quartz plate.     

Resonant frequency function of thickness-shear vibrations of rectangular crystal plates

The resonant frequencies of thickness-shear vibrations of quartz crystal plates in rectangular and circular shapes are always required in the design and manufacturing of quartz crystal resonators. As the size of quartz crystal resonators shrinks, for rectangular plates we must consider effects of both length and width for the precise calculation of resonant frequency. Starting from the three-dimensional equations of wave propagation in finite crystal plates and the general expression of vibration modes, we obtained the relations between frequency and wavenumbers. By satisfying the major boundary conditions of the dominant thickness-shear mode, three wavenumber solutions are obtained and the frequency equation is constructed. It is shown the resonant frequency of thickness-shear mode is a second-order polynomial of aspect ratios. This conforms to known results in the simplest form and is applicable to further analytical and experimental studies of the frequency equation of quartz crystal resonators.     

Identification of eigenmodes of volume piezoelectric resonators in resonant ultrasound spectroscopy

Eigenmodes of volume piezoelectric resonators used in resonant ultrasound spectroscopy (RUS) are considered. A novel method for the identification of these modes is proposed, which is based on the measurement of a temperature shift of the resonance frequency. A good coincidence of the measured and calculated eigenmode spectra is demonstrated for a quartz crystal. In comparison to the other methods of identification, the proposed approach is simple to implement and provides reliable results in solving RUS problems.     

Analysis of piezoelectric bulk-acoustic-wave resonators as detectors in viscous conductive liquids

An analytical solution for the resonance condition of a piezoelectric quartz resonator with one surface in contact with a viscous conductive liquid is presented. The characteristic equation that describes the resonance condition and accounts for all interactions including acoustoelectric interactions with ions and dipoles in the solution is obtained in terms of the crystal and liquid parameters. A simple expression for the change in the resonance frequency is obtained. For viscous nonconductive solutions, the frequency change is reduced to a relationship in terms of the liquid density and viscosity. For dilute conductive liquid, the change in frequency is derived in terms of the solution conductivity and dielectric constant. The boundary conditions for the problem are defined with and without the electrical effects of electrodes. Experiments were conducted with various viscous and conductive chemical liquids using a fabricated miniature liquid flow cell containing an AT-cut quartz crystal resonator. The results, which show good agreement with the theory, on the use of quartz crystal resonators as conductivity and/or viscosity sensors are reported.     

Application of the photo-elastic method to measurement of dynamicstress distribution for NS-GT cut quartz crystal resonators

NS-GT cut quartz crystal resonators are widely used as a frequency standard element in consumer products and communication equipment. The vibration mode of the resonators was analyzed by the finite element method (FEM) because they have a complicated shape. As a result, an asymmetrical vibration mode at the main resonant frequency has been obtained by the FEM simulation. But, it is necessary to confirm the asymmetrical vibration mode experimentally because it is just a simulation. In this paper, stress distributions of the NS-GT cut quartz crystal resonators are measured experimentally by using a dynamic photo-elastic method when the resonators are vibrating in the resonant frequency; thereafter, vibration modes of the NS-GT cut resonators are estimated with the experimental data of the stress distributions. This experiment for the NS-GT cut quartz crystal resonators exposes the existence of a twisted asymmetrical vibration mode at the main resonant frequency, with the magnitude of the twisted vibration in proportion to thickness of the resonators     

Quartz Crystal Parameters Measurement System

A device for measurement of quartz crystal resonator parameters is presented. This device is using a synthesizer, the frequency of which is swept step by step to find the resonance of the crystal. With a phase loop, which controls the synthesizer's interpolator, the resonance frequency and the bandwidth of the crystal can be measured. A low-cost computer gives the values of the resistance and the Q factor. The time constants of the crystal and of the phase loop are studied to determine the best measurement speed of this automatic device.     

Quartz resonator instabilities under cryogenic conditions

The phase noise of a quartz crystal resonator working at liquid helium temperatures is studied. Measurement methods and the device environment are explained. The phase noise is measured for different resonance modes, excitation levels, amount of operating time, device orientations in relation to the cryocooler vibration axis, and temperatures. Stability limits of a frequency source based on such devices are evaluated in the present measurement conditions. The sources of phase flicker and white noises are identified. Finally, the results are compared with previous works.     

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。     

Optical feedback laser with a quartz crystal plate in the external cavity

We studied the optical feedback characteristics of a single-mode He-Ne laser with a quartz crystal plate in the external cavity. The fringe frequency of the laser system can be doubled when the quartz crystal plate is positioned at a certain angle between the crystalline axis and the beam in the crystal plate. Theoretical analysis shows that the birefringent effect of the quartz crystal plate and the laser beam's second pass through the external cavity result in this phenomenon. The experimental results are in good agreement with the theoretical analysis. A quartz crystal plate can double the resolution of a self-mixing sensing system.