A new method for continuous monitoring of series resonance frequency and simple determination of motional impedance parameters for loaded quartz-crystal resonators

A new electronic design for continuous motional series resonant frequency monitoring of loaded quartz crystal resonators is presented. Using this circuit, a low-cost method for a simple determination of equivalent circuit parameters of quartz crystal resonators is described. Measurements made with the proposed system on typical AT cut quartz crystals are in good agreement with those of an Impedance Analyzer.     

QCM Operation in Liquids: An Explanation of Measured Variations in Frequency and Q Factor with Liquid Conductivity

Recently, several reports have shown that when one side of a quartz crystal microbalance (QCM) is exposed to a liquid, the parallel (but not the series) resonant frequency is influenced by the conductivity and dielectric constant of the liquid. The effect is still controversial and constitutes a serious complication in many applications of the QCM in liquid environments. One suggestion has been that acoustically induced surface charges couple to charged species in the conducting liquid. To explore this effect, we have measured the parallel and the series mode resonance frequencies, and the corresponding Q factors, for a QCM with one side facing a liquid. These four quantities have all been measured versus liquid conductivity, using a recently developed experimental setup. It allows the simultaneous measurement of the resonant frequency and the Q factor of an oscillating quartz crystal, intermittently disconnected from the driving circuit. Based on these results, a simple model together with an equivalent circuit for a quartz crystal exposed to a liquid is presented. The analysis shows that it is not necessary to infer the existence of surface charges (or other microscopic phenomena such as electrical double layers) to account for the influence of the liquid's electrical properties on the resonant frequency. Our results show that the contacting conductive liquid, in effect, enlarges the electrode area on the liquid side and thereby changes the parallel resonant frequency. By proper design of the QCM measurement, perturbing effects due to the liquid's electrical properties can be circumvented.     

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     

Improving the accuracy and operating range of quartz microbalancesensors by a purposely designed oscillator circuit

A method is presented to measure accurately the resonant frequency and to increase the functioning range of quartz microbalance sensors subject to heavy acoustic loading, such as encountered in in-liquid operation and with viscoelastic coating films. The method is based on an electronic circuit for the active cancellation of the crystal electrical capacitance, inserted in a phaselocked loop oscillator, which enables the tracking of the quartz series resonance with virtually zero error irrespective of the load. The principle is discussed, and experimental results confirming its successful application are presented     

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.     

基于锁相环的音叉式原子力显微镜测头电路系统研究

石英音又具有谐振频率稳定、品质因素高等优点,适合用于制作原子力显微镜探针.通过对原子力显微镜中使用的石英音叉探针驱动电路及对影响电路系统性能的器件参数进行分析,实现对石英音叉共振频率的检测及自动补偿调整,并对锁相环电路进行仿真及试验验证,试验结果表明电路系统满足原子力显微镜工作需求.     

Design and evaluation of an antiparallel coupled resonator for chemical sensor applications

In this paper, a new type of quartz crystal resonator in which the electrodes are located on one side has been developed for chemical sensing. The resonator has two electrodes for exciting thickness shear mode (TSM) vibrations on one side of the crystal and a conductive layer on the other side. These electrodes are capacitively coupled with the electric fields in opposite directions, forming an antiparallel coupled resonator (ACR). The resonant characteristics of the ACR were evaluated as a function of gap width between the two electrodes used to excite the TSM. The conductance value was observed to increase with decreasing gap width. We also discovered that the gap should be parallel with the crystallographic x-axis to obtain the highest sensitivity. The frequency response to a viscous loading was almost same as that of a standard quartz crystal microbalance (QCM). The ACR sensor is an attractive alternative to a QCM chemical sensor because it can be easily integrated into packaging and film coatings.     

Low Frequency Noise Quartz Crystal Oscillator

For years, engineers and scientists have been plagued by an extremely undesirable property of the quartz crystal unit-its significant frequency shift as a function of drive level for drive levels in excess of 10 to 100 ?W. This fact was reported by Hammond [1]. As a result, all precision and moderate precision quartz oscillators have been operated at low drive in an effort to avoid the phenomena. The author has discovered, however, that this unique property of the quartz resonator can be effectively utilized in the design of the quartz oscillator with the result of substantial improvement in oscillator short-term frequency stability. Futhermore, since the crystal frequency-drive characteristic is repeatable, maintenance of moderately high crystal drive in the oscillator circuit will not result in long-term frequency instability in excess of that required for the majority of radar and communication systems [2].     

Development of circuit for measuring both Q variation and resonant frequency shift of quartz crystal microbalance

Although frequency shift is often used for QCM (Quartz Crystal Microbalance) measurement, Q of a resonator also varies when viscous loading occurs. However, it is difficult to measure Q variation in real time in comparison with resonant frequency shift. Furthermore, oscillation frequency shift deviates from real resonant one in case of large viscous loading. Here, the authors have developed the circuit based upon motional admittance method for measuring both Q variation and real resonant frequency shift. It was applied to a quartz resonator gas sensor, and its Q variation was measured by this circuit. Moreover, it was compared with a conventional oscillation circuit and the frequency shift of the former was remarkably different from that of the latter in case of large Q variation. When a quartz resonator coated with PEG20M (PolyEthylene Glycol 20M) membrane was exposed to water vapor, its Q decreased from 38700 to 3650 and a frequency shift of the oscillation circuit was only about one sixth of this circuit.     

Predicting phase noise in crystal oscillators

In order to predict the phase noise in crystal oscillators an enhanced phase-noise model has been built. With this model, the power spectral densities of phase fluctuations can be computed in different points of the oscillator loop. They are calculated from their correlation functions. The resonator-caused noise as well as the amplifier-caused noise are taken into account and distinguished. To validate this enhanced model, the behavior of a batch of 10 MHz quartz crystal oscillators is observed and analyzed. The tested batch has been chosen in a facility production. Their associated resonators have been selected according to the value of their resonant frequency and their motional resistance. Open-loop and closed-loop measurements are given. The phase noise of the overall oscillator working in closed loop is provided by the usual active method. Theoretical and experimental results are compared and discussed.     

Contributions of amplitude measurement in QCM sensors

The characteristics of the amplifier and the feedback loop of a quartz crystal series oscillating circuit are investigated. The fact that the change of the vibration amplitude of the quartz crystal is proportional to the change of its motional resistance is derived. The concept of a characteristic damping coefficient is introduced and the behavior of a quartz crystal vibrating in liquids is analyzed. The experiment shows that the effect of mass loading can be distinguished from that of the liquid damping of a quartz crystal microbalance (QCM) sensor in liquids by simultaneously measuring the amplitude and the frequency change     

An instrument for simultaneous EQCM impedance and SECM measurements

A novel combination of an electrochemical quartz crystal microbalance (EQCM) and a scanning electrochemical microscope (SECM) has been built. Unlike conventional EQCMs, the instrument described here allows rapid in situ measurement of the modulus of the quartz crystal's transfer function. Data analysis in the complex plane for the Butterworth-Van Dyke (BVD) equivalent circuit yields the real and the imaginary components R (damping resistance) and XL (reactive inductance) of the crystal's electroacoustic impedance around its resonant frequency of 10 MHz. The influence of different tip shapes of an approaching microelectrode on the electroacoustic impedance of the quartz crystal was studied and found to be minimal for certain geometries. The capability of the EQCM/SECM instrument was tested in cyclic voltammetric plating/stripping experiments using a copper(I) chloride solution of high concentration in 1 M HCl. Four parameters, XL, R, the substrate, and the tip current, can be recorded simultaneously. Depletion layer effects were observed and could be corrected for to yield accurate current efficiencies for potentiodynamic and potentiostatic copper plating. The amperometric response of the SECM tip positioned closely to the substrate reflects the concentration changes of electroactive ions in the diffusion layer of the substrate electrode.     

一种谐振式露点测量方法

针对大气湿度测量问题,提出一种基于谐振式的露点测量方法,并设计了一套独立的露点传感装置.利用QCM原理将石英晶体谐振器作为湿敏元件,用半导体制冷器对其进行制冷,使其表面出现结露现象,导致石英晶体谐振器的谐振频率出现突变,以此达到对露点的识别,同时测取结露时刻石英晶体表面的温度,从而获得当前环境下的露点温度.通过实验验证了此方法的可行性与准确性,并将获取的实验数据与实际提供的环境数据进行对比分析,相对湿度误差达到±1.37%RH,此方法具有精度和灵敏度双高的优点,并且成本低、可操作性强.     

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.     

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.     

石英晶体微天平质量检测量研究

基于石英晶体微天平质量检测原理,通过分析石英谐振器表面的振动位移,得出决定其电极表面每一点处质量灵敏度的物理量为该点处的振动加速度。在此基础上,基于石英谐振器的巴特沃斯-范·戴克等效电路模型提出一种计算石英晶体谐振器表面振荡幅度的方法,最终得到石英晶体微天平在整个检测过程中能检测到的平均质量。用10MHz的石英晶体微天平进行了数值验证,计算值与其理论上能达到的pg级检测限基本相吻合。     

Thickness-shear vibrations of rotated Y-cut quartz plates with imperfectly bonded surface mass layers

A solution is obtained from the three-dimensional equations of linear piezoelectricity for the pure thickness-shear vibration of rotated Y-cut quartz or langasite plates with imperfectly bonded surface mass layers. The solution includes a few results in the literature as special cases. It is shown that the mass layers lower the resonant frequencies when they are relatively perfectly bonded to the crystal surface, and that loosely bonded mass layers may raise the frequencies. The results are useful in the analysis of frequency stability of quartz resonators and acoustic wave sensors.     

A New Type of Q Meter Using Variable-Width Pulse Excitation

There are several well-known methods of measuring the Q of a resonant circuit, each with its limitations. Errors are introduced into measurements of high-Q values due to loading effects and radiation losses. A theoretical basis for the development of a Q meter which will not load a high-Q resonant circuit has been established. This new type of Q meter will use variable-width pulse excitation in lieu of sinusoidal excitation and will use elapsed-time Q-measurement techniques. It is seen that if the width of the exciting pulse is known, the resonant frequency of the resonant circuit can be directly determined. A Q meter using this approach will actually yield more information about a resonant circuit than can be determined using presently standard-type Q meters and will yield this information well beyond the Q and frequency capabilities of today's Q meters.     

Voltage-controlled double-resonance quartz oscillator using variable-capacitance diode

In this work, we present a variable-frequency quartz crystal oscillator that is able to oscillate at LC resonance under frequency locking of a quartz crystal resonance, with the frequency tuning realized by variable-capacitance diodes. This circuit shows a steep transition between LC oscillation modes to quartz crystal double-resonance, which shows a characteristic change in the oscillation frequency. Control voltage of this diode is precisely adjusted from the low side to higher values and conversely in the vicinity of the oscillation mode transition. The transition of the oscillation modes is experimentally demonstrated and compared with an algebraic analysis.