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.     

高频长缆水声换能器的匹配技术研究

高频换能器接长电缆后谐振频率会发生偏移,导致与工作频率相差甚远,工作点的导纳值与不接长电缆时偏差较大。这使得换能器与发射机和接收机之间的阻抗严重失配。文章对高频长缆水声换能器匹配技术进行研究,通过建立换能器等效电路模型,利用传输线理论,进行四端口匹配网络的设计和仿真,并制作一块匹配电路板。实验结果表明,系统匹配性测试与仿真计算相吻合,提高了系统机电转换效率,证明了该匹配方法的可行性和工程实用性。     

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。     

高频宽带换能器多匹配层研究

在水声应用中,高频换能器往往需要较宽的工作带宽,以获得更多的目标信息。文章首先建立了等效电路模型,利用粒子群算法对匹配层材料和厚度进行初步选定,使得换能器具有最宽的工作频带;其次,通过有限元方法对匹配层换能器的导纳和发射电压响应进行分析计算;最后,在理论分析的基础上成功制得三匹配层高频宽带换能器,其工作频段约为150～430 kHz,相对带宽为93%,带内发送电压响应起伏为-6 dB。实验结果表明,三匹配层设计方案可以有效拓宽高频换能器的工作频段。     

Fabrication and characterization of transducer elements in two-dimensional arrays for medical ultrasound imaging

Some of the problems of developing a two-dimensional (2-D) transducer array for medical imaging are examined. The fabrication of a 2-D array material consisting of lead zirconate titanate (PZT) elements separated by epoxy is discussed. Ultrasound pulses and transmitted radiation patterns from individual elements in the arrays are measured. A diffraction theory for the continuous wave pressure field of a 2-D array element is generalized to include both electrical and acoustical cross-coupling between elements. This theory can be fit to model the measured radiation patterns of 2-D array elements, giving an indication of the level of cross-coupling in the array, and the velocity of the acoustic cross-coupling wave. Improvements in bandwidth and cross-coupling resulting from the inclusion of a front acoustic matching layer are demonstrated, and the effects of including a lossy backing material on the array are discussed. A broadband electrical matching network is described, and pulse-echo waveforms and insertion loss from a 2-D array element are measured.     

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     

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     

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.     

PSpice modelling of ultrasound transducers: comparison of software models to experiment

This paper presents a complete PSpice model of an ultrasound single-element transducer, including electrical and mechanical matching as well as the focusing lens. By using this model, it is possible to obtain a relation between the electrical driving source and the acoustic velocity on the transducer surface. This boundary condition then allows the acoustic field to be calculated by numerical methods. Experimental data obtained with two different transducers are in good agreement with results predicted by the related models.     

高频宽带换能器研究

主要研究高频换能器的匹配层技术,通过匹配层技术拓宽换能器的频带,首先利用等效电路法分析高频匹配层换能器,其次通过Matlab仿真分析匹配层材料的密度、声速、厚度变化对换能器电声参数性能的影响,进而对其电声性能进行优化设计,最终制作出一高频宽带换能器。通过实验测得结果与仿真结果基本一致,实验测得换能器的最大发送电压响应为178dB,工作频带为260～370kHz,带内发送电压响应起伏为-3dB,300kHz时换能器指向性-3dB开角为6．5°。     

Ultrasound transducer modeling--general theory and applications to ultrasound reciprocal systems

A tutorial presentation on the theory of reciprocal ultrasound systems is given, and a complete set of modeling equations for one-dimensional multi-layer ultrasound transducers is derived from first principles. The model includes dielectric losses and mechanical losses in the transducer material layers as well as sound absorption in the transmission medium. First, the so-called constitutive relations of a piezoelectric body are derived based on general thermodynamic considerations, assuming that transducer operation takes place under almost isentropic conditions. Second, full attention is given to transducers oscillating in the thickness mode, discarding all other vibration modes. Dynamic transducer equations are determined using Newton's Second Law, Poisson's equation, and the definition of strain applied to a piezoelectric transducer with one or more non-piezoelectric layers on the front surface (multilayer transducer). Boundary conditions include continuity of normal velocity and stress across material interfaces as well as a subsidiary electrical condition over the piezoceramic electrodes. Sound transmission is assumed to take place in a water bath such that the Rayleigh equation can be used to obtain the incoming pressure at the receiver aperture from the acceleration of the opposing transmitter. This allows, e.g., a detailed treatment of receiver signal variations as the receiver moves from the near-field zone to the far-field zone of the transmitter. In the remaining part of the paper, receiver voltage and current signals are obtained by solving the full set of dynamic equations numerically. Special attention is given to transducers consisting of a) a pure piezoceramic layer only, b) a piezoceramic layer and a quarter-wavelength matching layer of polyphenylensulphide (PPS), c) a piezoceramic layer and a half-wavelength matching layer of stainless steel, and d) a piezoceramic layer and a half-wavelength matching layer of stainless steel tuned to resonance by a parallel inductance. Results are also given for receiver incoming pressure and receiver voltage signals when sound reception takes place in the near-field and far-field zones of the transmitter.     

Optimization of the gain-bandwidth product of capacitive micromachined ultrasonic transducers

Capacitive micromachined ultrasonic transducers (cMUT) have large bandwidths, but they typically have low conversion efficiencies. This paper defines a performance measure in the form of a gain-bandwidth product and investigates the conditions in which this performance measure is maximized. A Mason model corrected with finite-element simulations is used for the purpose of optimizing parameters. There are different performance measures for transducers operating in transmit, receive, or pulse-echo modes. Basic parameters of the transducer are optimized for those operating modes. Optimized values for a cMUT with silicon nitride membrane and immersed in water are given. The effect of including an electrical matching network is considered. In particular, the effect of a shunt inductor in the gain-bandwidth product is investigated. Design tools are introduced, which are used to determine optimal dimensions of cMUTs with the specified frequency or gain response.     

Design of a platinum resistance thermometer temperature measuring transducer and improved accuracy of linearizing the output voltage

An improved method is presented for designing a temperature measuring transducer, the electrical circuit of which comprises an unbalanced bridge, in one arm of which is a platinum resistance thermometer, and containing a differential amplifier with feedback. Values are given for the coefficients, the minimum linearization error is determined, and an example is also given of the practical design of the transducer, using the given coefficients. A determination is made of the limiting achievable accuracy in linearizing the output voltage of the measuring transducer, as a function of the range of measured temperature.Translated from Izmeritel'naya Tekhnika, No. 1, pp. 48–50, January, 1995.     

Ultrasonic transducers as a black-box: equivalent circuit synthesis and matching network design

A new modeling technique for ultrasonic transducers is developed in order to build an analytical model in the Laplace s-domain. The model is intended for use in analog circuit CAD system for the front-end electronic design and to visualize the acoustic pulse modifications under different excitation conditions. The transducer is characterized by two analytical functions representing the driving point impedance and the electroacoustic transfer function. The transfer function is obtained as the ratio of the transducer axial response and the excitation voltage. The reference responses of the impedance and transfer function are derived by the Fourier transform of the measured signals. The model is derived by the measurements of the driving point current and voltage, and the field axial response is sensed by a hydrophone. The procedure for the model identification is described. The results of testing 5-MHz transducer for medical applications are presented. An approach for the design of broadband matching networks using a constant resistance network is reported.     

一种使用矢量网络分析仪的阻抗测量改进方法

基于反射法理论提出了一种使用矢量网络分析仪测量集总参数元件阻抗的方法,引入阻抗匹配电路,拓宽了矢量网络分析仪的阻抗测量范围.通过对匹配电路二端口网络模型中参量A的分析,给出相应的被测元件的阻抗计算式,消除了夹具对测量结果的影响.采用矢量网络分析仪直接测量法和该阻抗测量法分别测量了5种不同阻值的金属膜电阻,结果表明,该阻抗测量方法的测量精度高于矢量网络分析仪直接测量的精度,可在30 kHz～100 MHz频率范围内实现几欧至千欧阻抗的精确测量.     

压电水声换能器宽带匹配特性研究

采用等效电路变换和多物理场有限元仿真计算进行压电水声换能器宽带匹配特性研究,得出不同匹配电路下的换能器电声性能的变化规律,合理选择电感电容值和串并联方式进行调谐匹配实现双峰谐振,一方面提高换能器的工作带宽,另一方面提高工作频率范围内的发送电压响应值并减小工作频带内响应值的起伏,依照仿真数据设计制作了一款球形换能器,采用串联电感进行调谐匹配,并测试调谐匹配前后的水中电声性能,对比匹配前后换能器性能的差异。结果表明,测试结果和仿真计算吻合,运用多物理场仿真计算手段对于预测分析水声换能器电声性能具有较好的指导意义。     

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.     

A circuit simulation compatible surface acoustic wave interdigital transducer macro-model

In the present work, a surface acoustic wave (SAW) interdigital transducer (IDT) has been modeled as a resistance-inductance-capacitance (RLC) network. The model includes the effects of metal shorting and energy storage at metal discontinuities, as well as an arbitrary polarity sequence of fingers. A C++ program generates the equivalent electrical circuit, which is directly simulated by Simulation Program with Integrated Circuit Emphasis (SPICE), a popular electrical circuit simulator. Simulations compare well with reported experimental results, validating the proposed model.     

A circuit simulation compatible surface acoustic wave interdigital tranducer macro-model

In the present work, a surface acoustic wave (SAW) interdigital transducer (IDT) has been modeled as a resistance-inductance-capacitance (RLC) network. The model includes the effects of metal shorting and energy storage at metal discontinuities, as well as an arbitrary polarity sequence of fingers. A C++ program generates the equivalent electrical circuit, which is directly simulated by Simulation Program with Integrated Circuit Emphasis (SPICE), a popular electrical circuit simulator. Simulations compare well with reported experimental results, validating the proposed model.     

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