Simulation of piezoelectric excitation of guided waves using waveguide finite elements

A numerical method for computing the time response of infinite constant cross-section elastic waveguides excited by piezoelectric transducers was developed. The method combined waveguide finite elements (semi-analytical finite elements) for modeling the waveguide with conventional 3-D piezoelectric finite elements for modeling the transducer. The frequency response of the coupled system was computed and then used to simulate the time response to tone-burst electrical excitation. A technique for identifying and separating the propagating modes was devised, which enabled the computation of the response of a selected reduced number of modes. The method was applied to a rail excited by a piezoelectric patch transducer, and excellent agreement with measured responses was obtained. It was found that it is necessary to include damping in the waveguide model if the response near a "cut-on" frequency is to be simulated in the near-field.     

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     

Analysis of piezoelectric ultrasonic transducers attached to waveguides using waveguide finite elements

A finite-element modeling procedure for computing the frequency response of piezoelectric transducers attached to infinite constant cross-section waveguides, as encountered in guided wave ultrasonic inspection, is presented. Two-dimensional waveguide finite elements are used to model the waveguide. Conventional three-dimensional finite elements are used to model the piezoelectric transducer. The harmonic forced response of the waveguide is used to obtain a dynamic stiffness matrix (complex and frequency dependent), which represents the waveguide in the transducer model. The electrical and mechanical frequency response of the transducer, attached to the waveguide, can then be computed. The forces applied to the waveguide are calculated and are used to determine the amplitude of each mode excited in the waveguide. The method is highly efficient compared to time integration of a conventional finite-element model of a length of waveguide. In addition, the method provides information about each mode that is excited in the waveguide. The method is demonstrated by modeling a sandwich piezoelectric transducer exciting a waveguide of rectangular cross section, although it could be applied to more complex situations. It is expected that the modeling method will be useful during the optimization of piezoelectric transducers for exciting specific wave propagation modes in waveguides.     

Controlled-source analogous circuits and SPICE models forpiezoelectric transducers

Transmission line analogous circuits for piezoelectric transducers are developed which employ controlled sources rather than the traditional transformer to model the coupling between the electrical and the mechanical systems. A novel method is used to derive each model that consists of adding a term that is equal to zero to one of the device electromechanical equations. When this is done, it is shown that the equations can be cast into the form of the familiar telegraphist's equations for the voltage and current on an electrical transmission line. The circuits are derived for both the thickness-mode piezoelectric transducer and the side-electrode bar piezoelectric transducer. SPICE models of the analogous circuits are presented and an example simulation is given     

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.     

An Inductively Coupled Lamb Wave Transducer

Wafer-type piezoelectric transducers are effective transducers for the excitation and detection of ultrasonic Lamb waves in plate-like structures. Such transducers are, however, vulnerable to corrosion and physical damage when mounted in exposed locations. In this paper we describe an inductively coupled Lamb wave transducer that eliminates the need for direct electrical connections. Signals are coupled into and out of the transducer using two probe coils. In this paper we explore the operation of inductively coupled transducers both analytically and experimentally. Finite-element analysis is used to determine inductances and the coupling constant, and electrical circuit analysis to determine the transfer function and its dependence on the gap between the probe coils and the transducer. Experiments show that return signals of millivolt amplitude are obtained when the transducer is excited with 10-V amplitude pulses. These transducers are suitable for permanent mounting on structures to be monitored for cracks or flaws     

A system of two piezoelectric transducers and a storage circuit for wireless energy transmission through a thin metal wall

A system to wirelessly convey electric energy through a thin metal wall is proposed in the paper, where 2 piezoelectric transducers are used to realize energy transformation between electric and mechanical, and a rechargeable battery is employed to store the transmitted energy. To integrate them as a whole, an interface of a modulating circuit is applied between the transducer system and the storage battery. In addition, a synchronized switch harvesting on inductor in parallel with the transducer system is introduced to artificially extend the closed interval of the modulating circuit. The process of transmitting energy is computed, and the performance of the transducer system is optimized in detail for a prescribed external electric source. The results obtained are useful for understanding and designing wireless energy supply systems.     

SPICE model for lossy piezoceramic transducers

A transmission line equivalent circuit for piezoelectric transducers has been modified to provide modeling of lossy piezoceramic transducers. A lossy transmission line is used to model the mechanical losses. The equivalent circuit parameters are derived from analogies between electrical transmission lines and acoustic wave propagation. Implementation of the equivalent circuit model in SPICE is shown. Simulations and measurements in the time and frequency domain of a low-Q material and a multilayered ultrasonic sensor using a low-Q piezoceramic transducer are presented.     

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.     

基于系统相似方法的叠堆型压电驱动器非线性动力学建模及实验研究

根据机械系统与电气系统的相似方法,将叠堆型压电驱动器的非线性电-机械耦合模型完全转换到电气域内,建立了其非线性相似电路模型;给出了非线性相似电路模型中迟滞因子的辨识方法,并对某款商用叠堆型压电驱动器进行了迟滞因子的辨识试验;基于非线性相似电路模型和迟滞因子的辨识结果,对该款叠堆型压电驱动器的非线性特性进行了仿真分析,得到了其非线性位移迟滞回线;仿真结果与试验结果吻合,证明了该建模过程与辨识方法的正确性。该建模方法在电气域内对叠堆型压电驱动器电-机械耦合特性及非线性迟滞特性进行描述,建模过程物理意义清晰且简单实用,对于研究压电驱动器的动态特性及控制算法具有实际意义。     

基于机械品质因数的全波压电超声换能器设计

针对全波压电超声换能器常规设计方法存在的尺寸参数较多、计算较复杂等问题,研究了一种利用机械品质因数设计全波压电超声换能器的方法.基于压电超声理论推导了全波压电超声换能器的频率方程,利用电学理论推导了全波压电超声换能器各组成部分的等效电路,利用等效电路求取了在任意等效截面处的等效机械阻抗,进而推导出全波压电超声换能器各部...     

Transmitting electric energy through a metal wall by acoustic waves using piezoelectric transducers

The feasibility of transmitting electric energy through a metal wall by propagating acoustic waves using piezoelectric transducers is examined by studying the efficiency of power transmission and its dependence upon the relevant system parameters for a simplified system consisting of an elastic plate sandwiched by two piezoelectric layers. One of these layers models the driving transducer for generating acoustic wave, and the other layer models the receiving transducer for converting the acoustic energy into electric energy to power a load circuit. The output voltage, the output power, and the efficiency of this system are expressed as explicit functions of the system parameters. A numerical example is included to illustrate the dependence of the system performance upon the physical and geometrical parameters.     

Characterization of piezoceramic rectangular parallelepipeds by means of a two-dimensional model

The characterization of piezoelectric resonators is a field of intense scientific work; moreover, clear and accepted IEEE and IEC Standards have been published, showing the concepts and routes to perform the complete characterization of piezoelectric resonators. All of the accepted procedures define some resonator geometries, each of them related with a set of parameters, that can be obtained following resonance measurements at the corresponding resonance frequencies. The basis of the standards is the existence, for each geometry, of well-defined modes that have been analytically solved. The development of multi-dimensional models of the waves' propagation in piezoceramic materials opens the possibility of characterizing piezoelectric resonators with geometries different from those recommended in the standards. In this paper, a two-dimensional model, which takes into account the mechanical and dielectric losses, has been used to characterize piezoceramics with the shape of a regular parallelepiped. A set of elastic, dielectric, and piezoelectric parameters, which are useful for piezoelectric transducer design, can be obtained. For a given sample, the measured input electrical impedance is used to obtain the parameters by means of a fitting process with the corresponding model output. The results obtained with low and high loss materials show that the parameters found have values similar to those obtained following the procedures and geometries recommended by the standards. This procedure permits the characterization of materials when the manufacturing procedure does not allow the fabrication of the shapes recommended by the standards, making it a useful tool for transducer manufacturers and material scientists     

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.     

Theoretical modeling and equivalent electric circuit of a bimorph piezoelectric micromachined ultrasonic transducer

An electric circuit model for a circular bimorph piezoelectric micromachined ultrasonic transducer (PMUT) was developed for the first time. The model was made up of an electric mesh, which was coupled to a mechanical mesh via a transformer element. The bimorph PMUT consisted of two piezoelectric layers of the same material, having equal thicknesses, and sandwiched between three thin electrodes. The piezoelectric layers, having the same poling axis, were biased with electric potentials of the same magnitude but opposite polarity. The strain mismatches between the two layers created by the converse piezoelectric effect caused the membrane to vibrate and, hence, transmit a pressure wave. Upon receiving the echo of the acoustic wave, the membrane deformation led to the generation of electric charges as a result of the direct piezoelectric phenomenon. The membrane angular velocity and electric current were related to the applied electric field, the impinging acoustic pressure, and the moment at the edge of the membrane using two canonical equations. The transduction coefficients from the electrical to the mechanical domain and vice-versa were shown to be bilateral and the system was shown to be reversible. The circuit parameters of the derived model were extracted, including the transformer ratio, the clamped electric impedance, the spring-softening impedance, and the open-circuit mechanical impedance. The theoretical model was fully examined by generating the electrical input impedance and average plate displacement curves versus frequency under both air and water loading conditions. A PMUT composed of piezoelectric material with a lossy dielectric was also investigated and the maximum possible electroacoustical conversion efficiency was calculated.     

Optimization of composite transducer designing in high frequency applications

The main obstacle to constructing a wide bandwidth and high frequency composite transducer comes from its internal vibration field fluctuation, which is aggravated as frequency increases. We found an optimized structure of 2-2 composite in which the vibration field in both phases remains nearly uniform over a wide frequency range and the piezoelectric coupling coefficient reaches its maximum value simultaneously. This article also proposes a modified representation to calculate more precisely the effective piezoelectric coupling coefficient when the vibration fluctuation has been taken into account.     

Fundamental noise limit of piezoelectric accelerometer

Since significant progress is achieved in the development of piezoelectric (PE) accelerometers for small signal applications nowadays (for example, piezoelectric seismic vibration sensors), the question about the fundamental noise limit of these sensors becomes vital. The noise of the PE transducer is the fundamental noise limit of the PE accelerometer and should be taken into account if the noise of the electronics is small enough. The two noise sources of PE transducer, the mechanical-thermal noise of the damped mechanical harmonic oscillator and the electrical-thermal noise of the PE element's material, are analyzed in this paper. The equation of the total fundamental noise limit of the PE accelerometer is presented. This equation can be used for the calculation of the fundamental noise limit of PE accelerometers if their parameters are known or can be obtained by measurement.     

Development of a high voltage sensor using a piezoelectrictransducer and a strain gage

The authors describe the principle and design of an AC high-voltage sensor. When an electric stress is applied, this sensor accurately detects the mechanical strain of a piezoelectric transducer on which a foil strain gage is cemented. Two types of these sensors were designed, and a high-voltage measuring system using them was manufactured for trial. To confirm the frequency response of the trial sensors, an impedance of the trial piezoelectric transducer was performed using a YHP impedance analyzer, and the response-confirmation test of its vibration mode was carried out at the same time. Theoretical and experimental analyses are discussed in terms of the relation between the strain on the piezoelectric transducer and the applied sinusoidal AC voltage. It was ascertained that the strain was directly proportional to the voltage measured, and it was found that the measured percentage errors were less than ±2% for voltages up to 26000 V_p-p     

Mathematical Analysis of Piezoelectric Sandwich Torsion Transducers Based on the d36-Effect

In the present article, we analyze a d₃₆-effect piezoelectric torsion transducer following the Saint-Venant torsion theory taking the electrical field into account. A representation of the stress function, the electric potential, and the warping function are derived and solved with finite differences. Then, the one-dimensional governing equations at the structural beam level, including the constitutive relations as well as the balance equations for the dynamics of the transducer, are presented. The axial moment and the total charge are computed as functions of the rate of twist and the applied potential difference. As an example, a cantilevered transducer is studied.     

Consideration of impedance matching techniques for efficient piezoelectric energy harvesting

This study investigates multiple levels of impedance-matching methods for piezoelectric energy harvesting in order to enhance the conversion of mechanical to electrical energy. First, the transduction rate was improved by using a high piezoelectric voltage constant (g) ceramic material having a magnitude of g33 = 40 x 10(-3) V m/N. Second, a transducer structure, cymbal, was optimized and fabricated to match the mechanical impedance of vibration source to that of the piezoelectric transducer. The cymbal transducer was found to exhibit approximately 40 times higher effective strain coefficient than the piezoelectric ceramics. Third, the electrical impedance matching for the energy harvesting circuit was considered to allow the transfer of generated power to a storage media. It was found that, by using the 10-layer ceramics instead of the single layer, the output current can be increased by 10 times, and the output load can be reduced by 40 times. Furthermore, by using the multilayer ceramics the output power was found to increase by 100%. A direct current (DC)-DC buck converter was fabricated to transfer the accumulated electrical energy in a capacitor to a lower output load. The converter was optimized such that it required less than 5 mW for operation.