Multilayer piezoelectric resonators for medical ultrasoundtransducers

Multilayer piezoelectric resonators were fabricated and the dependence of the electrical impedance and the coupling coefficient were measured as a function of the number of layers, for N=1, ···, 20 layers. The magnitude of the electrical impedance followed the theoretical predicted 1/N² relation, and the coupling coefficient, K_t, remained relatively constant out to N=15 layers. These cofired resonators are suitable for medical ultrasound transducers     

Resonant spectrum method to characterize piezoelectric films in composite resonators

In this paper, we present a direct method to characterize a piezoelectric film that is sandwiched with two electrodes and deposited on a substrate to form a four-layer thickness extension mode composite resonator (also known as over-moded resonator). Based on the parallel and series resonant frequency spectra of a composite resonator, the electromechanical coupling factor, the density and the elastic constant of the piezoelectric film can be evaluated directly. Experimental results on samples consisting of ZnO films on fused quartz substrates with different thickness are presented. They show good agreement with theoretical prediction. The mechanical effect of the electrode on the method is investigated, and numerical simulation shows that the effect of the electrodes can be properly corrected by the modified formulae presented in this paper. The effect of mechanical loss in piezoelectric film and in substrate on this method also has been investigated. It is proven that the method is insensitive to the losses.     

Analysis of aging of piezoelectric crystal resonators

Aging of piezoelectric (quartz crystal) resonator has been identified as one of the most important quality control problems of quartz crystal products. Aging is defined as frequency change with time. Aging in quartz resonators can be due to several sources: mass transfer due to contamination inside the resonator enclosure, stress-strain in the resonator blank, quartz defect, etc. In this study, the stress-strain effect, which has been believed as a dominant factor contributing to aging, is studied. The stress-strain effect is caused mainly by the long-term viscoelastic properties of bonding adhesive that attach quartz crystal plate to the ceramic base package. With the available accelerating testing method under elevated temperatures, the stress-strain induced aging in the quartz crystal resonators can be investigated. Because of the miniaturized size of the resonator, a digital image analysis method called image intensity matching technique (IIMT) is applied to obtain deformation patterns in the quartz blank due to thermal load. Our preliminary results showed that the unsymmetric thermal deformations may be a dominant contributing factor to aging. For simulation purposes, finite-element analysis is used to investigate the deformation patterns (i.e., stress-strain distributions) and corresponding natural frequency shift in the piezoelectric resonators. The viscoelastic behavior of mounting adhesives is incorporated into the analysis to show the dominant effect of long-term behavior of stress-strain developed in the crystal resonators. Also, some geometrical aspects-such as uneven mounting supports due to distances, volumes and heights of the adhesives-are simulated in the model.     

Analysis of nonlinear transient responses of piezoelectric resonators

The electric transient response method is an effective technique to evaluate material constants of piezoelectric ceramics under high-power driving. In this study, we tried to incorporate nonlinear piezoelectric behaviors in the analysis of transient responses. As a base for handling the nonlinear piezoelectric responses, we proposed an assumption that the electric displacement is proportional to the strain without phase lag, which could be described by a real and constant piezoelectric e-coefficient. Piezoelectric constitutive equations including nonlinear responses were proposed to calculate transient responses of a piezoelectric resonator. The envelopes and waveforms of current and vibration velocity in transient responses observed in some piezoelectric ceramics could be fitted with the calculation including nonlinear responses. The procedure for calculation of mechanical quality factor Q(m) for piezoelectric resonators with nonlinear behaviors was also proposed.     

Mode excitation efficiency for contour vibrations of piezoelectric resonators

This paper addresses a theoretical procedure for control of the contour mode excitation efficiency in thin piezoelectric arbitrarily-shaped resonators by adjusting the surface electrode configuration to the mechanical stress distribution. The procedure allows accurate determination of at least five efficiently excited modes for various electrode configurations. This is validated by experimentally measured data for rectangular resonators. For the first time, electrode configurations are suggested that provide high values of the dynamic electromechanical coupling factor for the longitudinal edge mode in a rectangular resonator, while the excitation of spurious modes is suppressed.     

Accurate determination of complex materials coefficients of piezoelectric resonators

This paper presents a method of accurately determining the complex piezoelectric and elastic coefficients of piezoelectric ceramic resonators from the measurement of the normalized electric admittance, Y~, which is electric admittance Y of piezoelectric resonator normalized by the angular frequency /spl omega/. The coefficients are derived from the measurements near three special frequency points that correspond to the maximum and the minimum normalized susceptance (B~) and the maximum normalized conductance (G~). The complex elastic coefficient is determined from the frequencies at these points, and the real and imaginary parts of the piezoelectric coefficient are related to the derivative of the susceptance with respect to the frequency and the asymmetry of the conductance, respectively, near the maximum conductance point. The measurements for some lead zirconate titanate (PZT) based ceramics are used as examples to demonstrate the calculation and experimental procedures and the comparisons with the standard methods.     

计及压电效应时矩形振子的三维振动研究

在计及压电效应的情况下，本文利用解析方法对有限尺寸压电陶瓷矩形振子的三维振动进行了研究，推出了振子耦合振动的频率方程，并对振子的振动模式进行了分析。理论研究表明，利用本文中的解析法研究振子的耦合振动，计算简单、物理意义明显。与传统的一维理论分析方法及数值方法相比，由于本研究考虑了振子的压电效应以及不同振动模式不同的相互耦合，因此，振子的理论计算频率与测量值更加符合。     

Finite element modelling of nanostructured piezoelectric resonators (NAPIERs)

A new modification to the traditional piezoelectric thin film bulk acoustic wave resonator (FBAR) and solidly mounted acoustic wave resonator (SMR) is proven to significantly improve their performances. The proposed design involves the surface micro/nano structuring of planar piezoelectric thin films to realize an array of a large number of rod-like structures. In contrast to the plate-like thickness extensional resonance in traditional FBAR and SMR devices, the rod-like structures can be excited in their length extensional resonance, yielding a higher electromechanical coupling factor and effectively eliminating the spurious resonances from lateral modes of vibration. The designs have been investigated by two and three-dimensional finite element analyses and one-dimensional transmissionline modelling. The results show that significant increases in the electromechanical coupling factor of ca. 40% can be achieved by using the rod-like length extensional resonances as compared with the plate-like thickness extensional resonances in traditional devices. Simulations show that rod width-to-thickness aspect ratios of less than 0.5 could result in an electromechanical coupling factor (k2eff) of over 10% for a zinc oxide device, compared with approximately 7% for a conventional design.     

Frequency-temperature compensation of piezoelectric resonators by electric DC bias field

Electromechanical resonators have been widely used in signal processing and frequency control applications. It has been found that the resonant frequency of most resonator devices is highly temperature dependent, as temperature variation leads to materials properties change as well as resonator dimension change, which result in the undesirable shift of the resonance frequency. In this paper, we present a new frequency tuning method in which direct current (DC) bias field is used to control the resonance frequency of the piezoelectric resonator that is subjected to ambient temperature variations. It has been found that, depending on the polarity, the application of a DC bias field can reduce or increase the resonance frequency of the resonator. The experimental results demonstrate that the DC bias field tuning can achieve fairly good temperature compensation within a certain temperature range, and that the mechanical Q factor of the resonator is quite stable under different DC bias fields.     

Optimal electrode shape and size of lateral-field-excited piezoelectric crystal resonators

We determine optimal electrode shape and size of lateral-field-excited (LFE) thickness-shear resonators. The determined electrodes are optimal in that they satisfy the criterion for Bechmann's number in every direction. Numerical and graphical results are provided for AT-cut quartz, (yxl)- 45°langasite, and (yxl)-16.5°LiTaO(3) LFE resonators. The optimal electrodes of AT-cut quartz LFE resonators are also compared with those of AT-cut quartz thickness-field-excited (TFE) resonators.     

Pure-mode loci in piezoelectric plate resonators: application to materials evaluation in class 4 mm

The accuracy of piezoelectric material evaluations can be enhanced by the use of pure-mode orientations, provided that exact analytic expressions for the pure-mode eigenvalues are known. The accuracy is enhanced by eliminating the need to extract constants from the differences in sums and products of measured quantities. It is necessary to adopt an approach for determining pure-mode loci in piezoelectric crystals which yields simple analytic expressions for the stiffness eigenvalues and provides a convenient engineering methodology for pure-mode sample set selection. The theory of simple thickness modes in piezoelectric plate vibrators is reviewed. The determination of pure-mode loci and its application to pure-mode sample set selection for dilithium tetraborate are presented. Thickness- and lateral-field excitation considerations are discussed.     

Theory and design of piezoelectric resonators immune to acceleration: present state of the art

A typical low noise oscillator uses a crystal resonator as the frequency-determining element. An understanding of the fundamental nature of acceleration sensitivity in crystal oscillators resides primarily in understanding the behavior of the crystal resonator. The driving factor behind the acceleration-induced frequency shift is shown to be deformation of the resonator. The deformation drives two effects: an essentially linear change in the frequency-determining dimensions of the resonator and an essentially nonlinear effect of changing the velocity of the propagating wave. In this paper, the fundamental nature of acceleration sensitivity is reviewed and clarified, and attendant design guidance is developed for piezoelectric resonators. The basic properties of acceleration sensitivity and general design guidance are developed through the simple examples of “bulk acoustic wave (BAW) in a box” and “surface transverse wave (STW) in a box.” These examples serve to clarify a number of concepts, including the role of mode shape and the basic difference between the BAW and STW cases. The design equations clarify the functional dependencies of the acceleration sensitivities on the full range of crystal resonator design and fabrication parameters     

Preparation of chemically etched piezoelectric resonators for density meters and viscometers

Photolithography and chemical etching were investigated as a potential means of fabricating miniature piezoelectric devices. Among the acids studied, concentrated HCl demonstrated the fastest etching of PZT disks over a wide temperature range. HCl also proved to be compatible with some commercially available photoresists and so could be incorporated into a simple processing procedure for delineating and etching patterns in the ceramic.Using this technique, flexural mode resonators similar to tuning forks were generated with fundamental resonances between 10 and 115 kHz. These devices were then used to provide simultaneous measurements of the density and viscosity of liquids by monitoring the position of the resonance frequency and the width of the resonant peak, respectively.     

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.     

Characterization of electromechanical coupling coefficients of piezoelectric films using composite resonators

By analyzing the resonance frequency spectrum of a composite resonator consisting of a piezoelectric ceramic film deposited on a substrate plate, the thickness extensional mode electromechanical coupling coefficient of the film, k(t)(2), can be directly calculated from the effective coupling factor values, k(eff )(2), for two special modes of the resonator. The effects of the mechanical loss in the piezoelectric films on the measurement are investigated by numerical simulation, and some guidelines for improving the accuracy of the k(t)(2) measurement are reported.     

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.     

Study on electromechanical characterization of piezoelectric polymer PVDF in low-frequency band

Polyvinylidene fluoride (PVDF), a piezoelectric polymer material, is well known as one of the best smart materials to be used for tactile sensors in robots for its good performance. It has been used in many applications including sensors, actuators and surface acoustic wave (SAW) devices. This paper presents an experimental setup and experimental procedures for studying the electromechanical characterization of piezoelectric polymer films, by which the electromechanical characterization of the PVDF films under quasi-static loads and dynamic loads in a wide range of frequency can be researched. Through quasi-static tests, the stress–strain relationships of PVDF films in different directions were obtained. Furthermore, the viscoelastic and piezoelectric properties of PVDF films were analyzed based on the measurement results of dynamic tests under low frequency from 5 Hz to 200 Hz, and some suggestions of the applications of PVDF piezoelectric films in robot tactile sensor are presented.