An estimate on the second-order normal acceleration sensitivity of a quartz resonator

An estimate is given for a second-order effect in the normal acceleration sensitivity of a perfectly symmetric Y-cut quartz resonator whose first-order normal acceleration sensitivity is zero. The order of the second-order frequency shift is 10-11 per g.     

STW in-line acoustically coupled resonator filter on quartz

The scattering-matrix method was used for design of a surface transverse wave (STW) in-line acoustically coupled resonator filter on quartz. In this filter, two one-port STW resonators were coupled by means of a center reflector, grating phase shifters were placed between interdigital transducers and reflectors, and the pass band of the filter was located near the center frequency of the reflectors. At a frequency of about 509 MHz, insertion loss of about 5 dB and a 3 dB bandwidth of about 0.23 MHz was obtained. Differences between the measured and calculated amplitude responses are explained and design guidelines are presented. High STW velocity, low insertion loss, and very weak transverse mode make this filter attractive for high-frequency applications.     

SAW synchronous multimode resonator with gold electrodes on quartz

A surface acoustic wave synchronous multimode resonator with gold electrodes on ST-cut quartz was designed, fabricated, and measured. At a frequency of about 194.3 MHz, an insertion loss of about 14 dB, and loaded and unloaded quality factors of 11,500 and 14,500, respectively, were obtained.     

Survey of quartz bulk resonator sensor technologies

The term ;bulk resonator' is used to include a variety of vibrational modes. The survey is broken down by type of resonant mode, namely thickness shear, single-ended flexural, double-ended flexural, and torsional. Where appropriate, the discussion of each type of resonant mode includes items related to the frequency-control applications of the particular mode to emphasize the cross fertilization occurring between frequency control and sensor work.     

Influence of electrodes arrangement on the quartz resonator equivalent circuit

The strip electrodes deposited on the main surfaces of the rotated Y-cut quartz plate in the Z' direction and overlapping only in the central part of the plate excite a non-negligible electric field parallel to the surface of the plate. The influence of this field on the parameters of the electrical equivalent circuit and frequency-temperature characteristic of the AT-cut quartz plates is examined. The influence of this electric field parallel to the surface depends on the orientation of electrodes in the rectangular coordinate system of quartz.     

Growth sector boundaries and their influence on quartz resonator performance

Journal of Materials Science -     

First-order sensitivity analysis of quartz crystal resonator model parameters

A first-order measurement sensitivity analysis of a single mode, quartz resonator device model was conducted. This analysis predicts the variations in the motional arm resistance versus the resonance S-parameter as a function of measurement errors. The accuracy of this first-order sensitivity analysis is verified by computer simulation and experimentally. The model parameters were extracted following the recommended EIA-512 standard. The theoretical first-order sensitivity analysis, the computer simulation results, and the experimental measurements are found to be in good agreement.     

Force-frequency coefficient of symmetrical incomplete circular quartz crystal resonator

The changes in the resonance frequencies of the thickness-shear vibration of symmetrical incomplete circular AT-cut quartz crystal resonators (QXRs), which are used as sensing elements in digital force sensors or pressure transducers, by the application of diametrical forces are discussed by considering the piezoelectric effect and the anistropic characteristics of crystal plates. Two-dimensional motion equations for predicting the frequency changes are derived from three-dimensional piezoelectricity equations, and equations deduced by Janiaud for solving the stress distribution in crystal plates are used to calculate the force-frequency coefficients of incomplete circular resonators. The results show that the piezoelectric effect of crystal plates decreases the force-frequency coefficient of the azimuth angle 0 degrees by 7% as compared with no piezoelectricity assumption. The incomplete circular shape can be applied to a larger load than the circular disc because the flat regions of the incomplete shape provide a distributed load application without the problems of stress concentration of a point force inherent to a circular disc. The incomplete shape gives an increased force sensitivity when compared with the complete disc near azimuth angle 0 degrees. The theoretical curves agree well with Ratajski's experimental results.     

Measured resonance characteristics of a 2-ghz-fundamental quartz resonator

I fabricated an inverted-mesa AT-cut quartz resonator in which the thickness of the vibrating area was adjusted to 0.6 /spl mu/m by wet etching, and I demonstrated the excitation of a fundamental thickness vibration of 2.074 GHz. This main mode was inductive, and Q was 1037. However, all inharmonic modes were capacitive.     

Strained surface layers of quartz plates produced by lapping and polishing and their influence on quartz resonator performance

The strained surface layers of AT-cut quartz plates produced by lapping and polishing have been studied using the X-ray double crystal method. In addition, the influence of surface strain on the characteristics of quartz resonators has been investigated. Experimental results from X-ray double crystal measurements indicate that a residual stress layer in the lapped and polished surface is created and that the quartz resonator performance is also affected.     

Effect of transverse force on the performance of quartz resonator force sensors

This paper discusses the effect of transverse force on the performance of quartz crystal resonator (QXR) force sensors that use symmetrical incomplete circular QXRs as sensing elements. Based on Lee's vibration theory and the transverse force-induced stress distribution, frequency changes are derived. This result and finite element method (FEM) are applied to investigate the performance of two metal-quartz combined sensors under the action of transverse force. Analytical and experimental results show that transverse force affects the sensitivity and linearity of QXR force sensors.     

A thickness-shear quartz resonator force sensor with dual-mode temperature compensation

An AT-cut thickness-shear quartz crystal resonator (QXR) has been used as a force sensing and self-temperature-sensing (STS) element to develop a digital output force sensor. The QXR is fixed in a two-line mounting configuration in a cylindrical metal shell by double diaphragms, through which a diametric force proportional to the unknown force is applied to the QXR. The double diaphragms improve the reliability and the mechanical stability of the sensor significantly. In order to increase the measurement range and the sensitivity, the energy trapping-based QXR is cut to a symmetrical, incomplete circular shape to decrease stress concentration. Because operating the QXR in dual-mode excitation allows the separation of force change effects from temperature change effects, force measurement and STS are accomplished simultaneously with the same QXR. The structure and the configuration are optimized with theoretical analysis and FEM. The dual-mode STS and temperature compensation are described in detail, as well as a trimming method to reduce activity dips of AT-cut QXRs.     

Thickness-shear and thickness-twist vibrations of an AT-cut quartz mesa resonator

We study thickness-shear and thickness-twist vibrations of an AT-cut quartz plate mesa resonator with stepped thickness. The equations of anisotropic elasticity are used with the omission of the small elastic constant c(56). An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and energy trapping are calculated and examined. The solution shows that a mesa resonator exhibits strong energy trapping of thickness-shear and thickness-twist modes, and that the trapping is sensitive to some of the structural parameters of the resonator.     

A theoretical analysis of mechanical dissipation of an electroded quartz resonator

In this paper, the dissipation effects of an electroded AT-cut quartz resonator due to the intrinsic damping of the quartz plate and the surface damping of the coated electrodes are discussed. The results obtained provide a theoretical understanding of the energy losses by these effects.     

Observations of vibration shape of AT-cut quartz resonator including electric twins

Quartz crystal resonators, including electric twins, are investigated. Electric twins are artificially formed in the usual AT-cut quartz crystal resonantor before the deposition of electrodes. We have directly observed that vibrations generated at electrodes propagate into the outside region isotropically, but cannot propagate into the region of electric twin.     

Thickness-shear vibration of an AT-cut quartz resonator with a hyperbolic contour

A theoretical analysis is performed on thicknessshear vibrations of a contoured AT-cut quartz resonator with a hyperbolic thickness variation using the Legendre equation and hypergeometric function. Based on the solution, resonant frequencies and modes are calculated. Strong energy trapping of the modes is observed. The effects of the parameters of the hyperbolic contour on resonant frequencies and modes are examined. A comparison with the conventional contoured resonator in the literature with a quadratic thickness variation is made. The behaviors of the two types of resonators are qualitatively similar, with small but significant quantitative differences.     

Design analysis of miniature quartz resonator using two-dimensional finite element model

This study focused on 2-D miniature quartz plates. By assigning appropriate boundary condition using finite element modeling (FEM), the vibration of a quartz plate was analyzed for converse piezoelectric effect. The quality and stability of the resonance of a quartz plate was determined by examining changes on the response curve of resonant frequency when the length of plate was decreased or increased. A graphical user interface (GUI) was adopted to assist the finite element software to calculate the frequency responses with different length of a large number of quartz plates, and to conclude a detailed curve of resonant frequency versus size. With this diagram, changes of the resonant mode for quartz plates caused by length variation can be easily observed. An optimum size of the quartz plate is obtained from the curve. Moreover, analyses were also conducted on the electrode coverage of a quartz plate and the mass-loading effect of metallic electrodes for this study, to discuss the influence on the resonant frequencies of quartz plates.     

Fast three-step method for shear moduli calculation from quartz crystal resonator measurements

Quartz crystal resonator measurements can be used for polymer material characterization. The non-gravimetric regime of these resonators is exploited: the electrical response of polymer-coated quartz resonators depends on the polymer shear modulus. Previously reported methods employ an electrical admittance analysis together with difficult and time-consuming data fitting procedures to calculate the film shear modulus. This contribution presents a fast and accurate three-step method for the calculation of complex shear moduli of polymer films from quartz crystal resonator measurements. In the first step, the acoustic load impedance is calculated from the electrical admittance of the quartz crystal. The key point of this method is the application of a family of approximations for the calculation of the shear modulus from the acoustic load impedance in the second step. In the third step, the best approximation is improved further in an iterative procedure.