A Parametric Study on Admittance Signatures of a PZT Transducer Under Free Vibration

Piezoelectric material is proven to be a versatile collocated sensor and actuator. Its specific application includes electromechanical impedance (EMI)-based structural health monitoring (SHM). To date, several EMI models are available in the literature but parametric studies are scarcely available. This study aims at providing a parametric study on selected models, considering a freely vibrating piezoelectric transducer. The effect of varying mechanical and electrical parameters of the transducer on the admittance signatures was investigated. The theoretical results were compared against the experiments. Accuracy of the model was successfully refined upon model updating.     

Design and fabrication of a 40-MHz annular array transducer

This paper investigates the feasibility of fabricating a five-ring, focused annular array transducer operating at 40 MHz. The active piezoelectric material of the transducer was a 9-microm thick polyvinylidene fluoride (PVDF) film. One side of the PVDF was metallized with gold and forms the ground plane of the transducer. The array pattern of the transducer and electrical traces to each annulus were formed on a copper-clad polyimide film. The PVDF and polyimide were bonded with a thin layer of epoxy, pressed into a spherically curved shape, then back filled with epoxy. A five-ring transducer with equal area elements and 100-microm kerfs between annuli was fabricated and tested. The transducer had a total aperture of 6 mm and a geometric focus of 12 mm. The pulse/echo response from a quartz plate located at the geometric focus, two-way insertion loss (IL), complex impedance, electrical crosstalk, and lateral beamwidth all were measured for each annulus. The complex impedance data from each element were used to perform electrical matching, and the measurements were repeated. After impedance matching; fc approximately equal to 36 MHz and -6-dB bandwidths ranged from 31 to 39%. The ILs for the matched annuli ranged from -28 to -38 dB.     

An analytical model of multilayer ultrasonic transducers with an inversion layer

Inversion layer ultrasonic transducers have been investigated recently as an interesting approach in wideband transducer design. In this paper we present an analytical model of multilayer ultrasonic transducers with an inversion layer. Our analysis of the wave propagation problem of an inversion layer transducer includes a functional decomposition of the electrical input impedance. It becomes clear from this decomposition that an inversion layer transducer can be modeled as three elements in series connection, i.e., a clamped capacitance, a classical motional impedance, and a coupled motional impedance. The first two elements make up the classical model of a single element transducer. The coupled motional impedance describes the coupled interaction between the regular and the inverted piezoelectric sublayers, and thus reflects the effect of an inversion layer. We present examples which show that inversion layer transducers are advantageous in achieving such useful features as dual-frequency operation mode as used in harmonic imaging or broadband performance desired in most ultrasonic applications.     

Lateral mode coupling to reduce the electrical impedance of small elements required for high power ultrasound therapy phased arrays

A method that uses lateral coupling to reduce the electrical impedance of small transducer elements in generating ultrasound waves was tested. Cylindrical, radially polled transducer elements were driven at their length resonance frequency. Computer simulation and experimental studies showed that the electrical impedance of the transducer element could be controlled by the cylinder wall thickness, while the operation frequency was determined by the cylinder length. Acoustic intensity (averaged over the cylinder diameter) over 10 W/cm² (a therapeutically relevant intensity) was measured from these elements.     

Input impedance matching of acoustic transducers operating at off-resonant frequencies

The input impedance matching technique of acoustic transducers at off-resonant frequencies is reported. It uses an inherent impedance property of transducers and thus does not need an external electric matching circuit or extra acoustic matching section. The input electrical equivalent circuit includes a radiation component and a dielectric capacitor. The radiation component consists of a radiation resistance and a radiation reactance. The total reactance is the sum of the radiation reactance and the dielectric capacitive reactance. This reactance becomes zero at two frequencies where the impedance is real. The transducer size can be properly chosen so that the impedance at one of the zero-crossing frequencies is close to 50 Ω, the output impedance of signal generators. At this off-resonant operating frequency, the reflection coefficient of the transducer is minimized without using any matching circuit. Other than the size, the impedance can also be fine tuned by adjusting the thickness of material that bonds the transducer plate to the substrates. The acoustic impedance of the substrate and that of the bonding material can also be used as design elements in the transducer structure to achieve better transducer matching. Lead titanate piezoelectric plates were bonded on Lucite, liquid crystal polymer (LCP), and bismuth (Bi) substrates to produce various transducer structures. Their input impedance was simulated using a transducer model and compared with measured values to illustrate the matching principle.     

Calculation of dissipation resistances in a single-element transducer

In this paper, a new formulation of the electrical input impedance of a single element transducer is presented. The resistive part of the electrical impedance that takes into account acoustic radiation in the front medium and losses in the transducer is split into a radiation resistance on one hand and into dissipation resistances related to each transducer component on the other hand. To confirm these theoretical results, characterization methods based on temperature measurements and pulse-echo response are presented. Measurements have been conducted on 1 MHz transducers, which consist of a piezoelectric ceramic glued on a backing. The results show a good agreement between experience and theory for dissipation resistance and radiation resistance values, which confirms the theoretical approach.     

Parametric linear modeling of circular cMUT membranes in vacuum

We present a lumped element parametric model for the clamped circular membrane of a capacitive micromachined ultrasonic transducer (cMUT). The model incorporates an electrical port and two sets of acoustic ports, through which the cMUT couples to the medium. The modeling approach is based on matching a lumped element model and the mechanical impedance of the cMUT membrane at the resonance frequencies in vacuum. Very good agreement between finite element simulation results and model impedance is obtained. Equivalent circuit model parameters can be found from material properties and membrane dimensions without a need for finite element simulation.     

A magnetoresistive transducer with superconducting control lines

The design and the static and dynamic response of a thin film magnetoresistive transducer with superconducting control lines cooled at 4.2 K are described. The transducer facilitates a linear transfer of electrical signals by transformation of the impedance level and by perfect electrical insulation between the input and output circuit. In addition, voltage and power amplifications at low frequencies are achieved.The device can be used to sense supercurrents or currents generated by sources of very low impedance, such as superconducting quantum interferometers (SQUID's).     

Piezoceramics for high-frequency (20 to 100 MHz) single-elementimaging transducers

The performance of transducers operating at high frequencies is greatly influenced by the properties of the piezoelectric materials used in their fabrication. Selection of an appropriate material for a transducer is based on many factors, including material properties, transducer area, and operating frequency. The properties of a number of piezoceramic materials have been experimentally determined by measuring the electrical impedance of air-loaded resonators whose thickness corresponds to resonance frequencies from 10 to 100 MHz. Materials measured include commercially available compositions of lead zirconate titanate (PZT) with relatively high dielectric constants and a modified lead titanate (PT) composition with a much lower dielectric constant. In addition, materials which have been designed or modified to result in improved properties at high frequencies are studied. Conclusions concerning the influence of the microstructure and composition on the frequency dependence of the material properties are made from the calculated properties and microstructural analysis of each material. Issues which affect transducer performance are discussed in relation to the properties. For transducers larger than about 1 mm in diameter, the use of a lower dielectric constant material is shown to result in a better electrical match between the transducer and a standard 50 Ω termination. For transducers whose impedance is close to that of the connecting cables and electrical termination, equivalent circuit model simulations show improved performance without the need for electrical matching networks. Measurements of fabricated transducers show close agreement with the simulations, validating the measurements and showing the performance benefits of electrically matched transducers     

Large improvement of the electrical impedance of imaging and high-intensity focused ultrasound (HIFU) phased arrays using multilayer piezoelectric ceramics coupled in lateral mode

With a change in phased-array configuration from one dimension to two, the electrical impedance of the array elements is substantially increased because of their decreased width (w)-to-thickness (t) ratio. The most common way to compensate for this impedance increase is to employ electrical matching circuits at a high cost of fabrication complexity and effort. In this paper, we introduce a multilayer lateral-mode coupling method for phased-array construction. The direct comparison showed that the electrical impedance of a single-layer transducer driven in thickness mode is 1/(n2(1/(w/t))2) times that of an n-layer lateral mode transducer. A large reduction of the electrical impedance showed the impact and benefit of the lateral-mode coupling method. A one-dimensional linear 32-element 770-kHz imaging array and a 42-element 1.45-MHz high-intensity focused ultrasound (HIFU) phased array were fabricated. The averaged electrical impedances of each element were measured to be 58 Ω at the maximum phase angle of -1.2° for the imaging array and 105 Ω at 0° for the HIFU array. The imaging array had a center frequency of 770 kHz with an averaged -6-dB bandwidth of approximately 52%. For the HIFU array, the averaged maximum surface acoustic intensity was measured to be 32.8 W/cm2 before failure.     

高静水压下换能器阻抗特性的测量方法研究

针对在小腔体中阻抗分析仪发射连续波无法准确测得换能器阻抗的问题,提出一种在高静水压下使用脉冲正弦信号激励换能器测量阻抗的方法。以采样电阻法为基础,根据腔体尺寸确定发射脉冲个数以及可测频率范围来有效避免腔体边界反射对测量造成的影响。通过设置不同的发射频率,分别采集换能器两端及采样电阻两端的电压波形信号,利用已知频率的三参数正弦曲线拟合法分别得到波形信号的幅值和初始相位角,计算得到换能器的导纳值。改变静水压力,利用脉冲法测得0~10 MPa静水压下换能器导纳特性。实验结果表明,采用脉冲正弦信号激励的方法可在有限空间内准确测量换能器的阻抗特性;且随着静水压力的升高换能器的谐振频率发生偏移,导纳圆直径减小。     

Piezoelectrically actuated flextensional micromachined ultrasound transducers--I: theory

This series of two papers considers piezoelectrically actuated flextensional micromachined ultrasound transducers (PAFMUTs) and consists of theory, fabrication, and experimental parts. The theory presented in this paper is developed for an ultrasound transducer application presented in the second part. In the absence of analytical expressions for the equivalent circuit parameters of a flextensional transducer, it is difficult to calculate its optimal parameters and dimensions and difficult to choose suitable materials. The influence of coupling between flexural and extensional deformation and that of coupling between the structure and the acoustic volume on the dynamic response of piezoelectrically actuated flextensional transducer are analyzed using two analytical methods: classical thin (Kirchhoff) plate theory and Mindlin plate theory. Classical thin plate theory and Mindlin plate theory are applied to derive two-dimensional plate equations for the transducer and to calculate the coupled electromechanical field variables such as mechanical displacement and electrical input impedance. In these methods, the variations across the thickness direction vanish by using the bending moments per unit length or stress resultants. Thus, two-dimensional plate equations for a step-wise laminated circular plate are obtained as well as two different solutions to the corresponding systems. An equivalent circuit of the transducer is also obtained from these solutions     

Modeling and optimization of high-frequency ultrasound transducers

Obtaining an accurate transducer model for a high-frequency transducer can be troublesome using traditional models, such as the KLM model, since it is often difficult to measure precisely the piezoelectric, dielectric, and mechanical properties of the transducer. This paper describes an alternative method of modeling transducers using network theory. The network theory model for a transducer is determined from a measurement of the transducer impedance in water and the pulse-echo response of the system for a given electrical source and load. A discussion of how this model can be used to optimize the design of an electrical matching circuit is given. This method is illustrated by designing a two-element transmission line matching circuit for a miniature 53 MHz transducer. Excellent agreement between the network model prediction and the experimental response is obtained     

Numerical simulation of the electro-acoustical response of a transducer excited by a time-varying electrical circuit

Existing methods for the modeling of piezoelectric transducer response are generally frequency domain-based. The major disadvantage of this type of model is that they cannot take into account the electrical elements present in the emitting or receiving circuit whose values vary with respect to time. The need for a method that accounts for time-varying elements arises, for example, when the circuit comprises active electrical elements, such as diodes, or when the transducer is excited by capacitive discharge via a switch. Indeed, in this last example, it is known that the output impedance of the generator depends on the state of the switch: if it is off, its value is high; if it is on, its value is low. A time-domain-based method is presented to compute the electro-acoustical response of a piezoelectric transducer and its electrical circuit, taking into account the presence of time-varying elements. An application to a current example makes it possible to show the influence of these elements on waveforms and the capacity of our model to account for them     

Ultrasonic Transducer Sensitivity and Model-Based Transducer Characterization

It is shown that the role that an ultrasonic piezoelectric transducer plays in both generating and receiving ultrasound in an ultrasonic nondestructive evaluation (NDE) measurement system can be completely described in terms of the transducer's electrical impedance and open-circuit, blocked force receiving sensitivity. Furthermore, it is shown that both of these quantities can be obtained experimentally via a model-based approach and purely electrical measurements. The measurement of sensitivity uses a method originally developed for lower-frequency acoustic transducers. However, it is shown that at the higher frequencies found in ultrasonic NDE applications electrical cabling effects play an important role and must be compensated for in determining the transducer sensitivity. Examples of experimental measurement results using these new approaches are given.     

Radiation impedance and equivalent circuit for piezoelectric ultrasonic composite transducers of vibrational mode-conversion

The piezoelectric ultrasonic composite transducer, which can be used in either gas or liquid media, is studied in this paper. The composite transducer is composed of a longitudinal sandwich piezoelectric transducer, a mechanical transformer, and a metal circular plate in flexural vibration. Acoustic radiation is produced by the flexural circular plate, which is excited by the longitudinal sandwich transducer and transformer. Based on the classic flexural theory of plates, the equivalent lumped parameters for a plate in axially symmetric flexural vibration with free boundary conditions are obtained. The radiation impedance of the plate is derived and the relationship between the radiation impedance and the frequency is analyzed. The equivalent circuits for the plate in flexural vibration and the composite transducer are given. The vibrational modes and the harmonic response of the composite piezoelectric transducer are simulated by the numerical method. Based on the theoretical and numerical analysis, two composite piezoelectric ultrasonic transducers are designed and manufactured, their admittance-frequency curves are measured, and the resonance frequency is obtained. The flexural vibrational displacement distribution of the transducer is measured with a laser scanning vibrometer. It is shown that the theoretical results are in good agreement with the measured resonance frequency and the displacement distribution.     

Ultrasonic Transducer Sensitivity and Model-Based Transducer Characterization

It is shown that the role that an ultrasonic piezoelectric transducer plays in both generating and receiving ultrasound in an ultrasonic nondestructive evaluation (NDE) measurement system can be completely described in terms of the transducer's electrical impedance and open-circuit, blocked force receiving sensitivity. Furthermore, it is shown that both of these quantities can be obtained experimentally via a model-based approach and purely electrical measurements. The measurement of sensitivity uses a method originally developed for lower-frequency acoustic transducers. However, it is shown that at the higher frequencies found in ultrasonic NDE applications electrical cabling effects play an important role and must be compensated for in determining the transducer sensitivity. Examples of experimental measurement results using these new approaches are given.     

Computer derivation of equivalent-circuit RLC values for an ultrasonic transducer from measured values of the transducer's driving-point impedance

An ultrasonic transducer is modelled as a circuit having three parallel branches. The RLC parameters for the equivalent circuit are computed from measured values of the complex driving-point impedance of the tranducer in the frequency range 0 to 6 MHz. The computed RLC values representing the acoustically active part of the crystal are highly reproducible under constant loading. Significantly, these values change substantially when the loading is changed from air to water or to metal. The impedance measurements and the RLC computations for a transducer are performed on-line in less than 1 min by a portable 16 bit microcomputer using a 512-point FFT algorithm.     

Determination of an ultrasonic transducer's sensitivity and impedance in a pulse-echo setup

The role that an ultrasonic piezoelectric transducer plays in an ultrasonic measurement system can be described in terms of the transducer's input electrical impedance and its sensitivity. Here, a new model-based approach is proposed to determine both the transducer impedance and sensitivity in a pulse-echo setup. This new method is much simpler to apply than previous "self-reciprocity" calibration methods for determining sensitivity and generalizes those methods. It is demonstrated that sensitivities obtained with this new method agree well with the sensitivities obtained by a three-transducer method commonly used in calibration studies. It is demonstrated that at the megahertz frequencies at which ultrasonic transducers operate it is important to compensate for cabling effects in these measurements. The influence of the pulser/receiver settings on the results obtained also will be discussed.     

声波测井压电换能器多频点阻抗匹配技术研究

针对声波测井压电换能器的多频点阻抗匹配技术展开研究,首先采用多模态等效电路精确描述了换能器的导纳特性;然后通过分析多模态阻抗匹配理论,设计电感-电容复合阻抗匹配网络,并结合换能器等效电路进行参数优化和电路仿真。实验表明,相比于换能器没有阻抗匹配的测试结果,该阻抗匹配技术可大幅提高换能器在谐振频率附近多个频率处的有功功率,频带内的有功功率平均提高了30倍,从而改善换能器的激励带宽和激励效率,提高测井仪器的适应性、探测深度和分辨率。