Electromechanical Equivalent Circuit Research Articles

Fast and Reliable Modeling of Piezoelectric Transducers for Energy Harvesting Applications

This paper presents a fast and reliable model identification technique for piezoelectric transducers based on an equivalent electromechanical circuit easily implementable on SPICE-like simulation tools. Model parameter extraction is simple and requires just standard and inexpensive laboratory equipment. The equivalent circuits of four cantilevered Q220-A4-303YB transducers from Piezo Systems with different tip masses were identified and several simulations were performed with different electric loading conditions; measurement results agree with model response predictions in all the experiments. Indeed, the equivalent circuit representation permits the evaluation of the response of a real harvester system, where the electronic load is a synchronized switching converter which usually causes a significant feedback on the mechanical part of the system during energy extraction. Both simulation and measurements show that the damping effect is particularly important near resonance, where the adopted model is able to fit the experimental data and provides a more realistic description of the behavior of the system.

A multiscale model for array of capacitive micromachined ultrasonic transducers

A model is developed for studying the acoustic behavior of a cMUT array. This model is based on separate calculations of the terms describing the behavior of a single cMUT on one hand, and those corresponding to acoustic mutual coupling on the other hand. The terms are combined into an equivalent circuit with matrix terms which displays only one degree of freedom per cell. This approach allows the simulation of several dozen cMUTs considered individually with a very short computer time. A Finite Difference model is used for the simulation of an isolated cell radiating acoustic energy and the determination of its equivalent electromechanical circuit. It is shown for various mutual coupling situations that the coupling between cells can be correctly approximated using a very simple mutual impedance term. The model is compared with experimental results, using a set of different cMUT configurations. Experimental results were obtained with electrical impedancemetry and laser interferometry techniques performed in fluid immersion.

A new type of high power composite ultrasonic transducer

A new type of high power composite ultrasonic transducer was proposed and studied. The composite transducer consists of a sandwich longitudinal piezoelectric transducer, an isotropic metal hollow cylinder with large radial dimension, and the front and back metal radiation mass. By means of its special structure and Poisson’s effect, the composite transducer can produce vibrations both in its longitudinal and radial directions, and therefore, it can radiate sound waves in three-dimensional space. The electro-mechanical equivalent circuit of the composite transducer was derived and the resonance frequency equation was obtained analytically. Numerical methods were used to simulate the vibration of the composite transducer, and the vibrational displacement distribution, the resonance frequency and the radiation sound field are given. Some composite transducers are designed and manufactured; their resonance frequencies and the radiation acoustic field are measured and compared with the analytical and numerical results. It can be seen that the measured frequencies and acoustic field contour are in good agreement with the analytical and numerical results. It is expected that this kind of composite ultrasonic transducer can be used in more and more power ultrasonic applications, such as ultrasonic cleaning, ultrasonic extraction, ultrasonic sonochemistry and other ultrasonic liquid processing, where high ultrasonic power and large ultrasonic processing space are needed increasingly.

An improved cymbal transducer with combined piezoelectric ceramic ring and metal ring

An improved cymbal transducer with a combined piezoelectric ceramic ring and metal ring is presented and analyzed. The cymbal transducer is composed of metal caps in flexural vibration, a piezoelectric ceramic ring and a metal ring in radial vibration. The radial vibration of the radial combination of a piezoelectric ring and a metal ring is analyzed and its electro-mechanical equivalent circuit is obtained. By means of numerical method, the relationship between the resonance/anti-resonance frequency, the effective electro-mechanical coupling coefficient and the geometrical dimensions is studied. The vibrational modes of the cymbal transducer are analyzed; the admittance–frequency curve and vibrational displacement distribution are given. Two cymbal transducers are designed and manufactured, and their frequency characteristics are measured. It is shown that the simulated resonance/anti-resonance frequencies and the admittance curve of the cymbal transducer are in good agreement with the measured results. The improved cymbal transducer is expected to be used in high power underwater sound projector and ultrasonic radiators in air and liquid.

Diamond in Surface Acoustic Wave Sensors

The application of diamond in surface acoustic wave sensors is considered. The new method of the complete analyses of diamond-based gas chemical sensors is presented. It is based on the electromechanical equivalent circuit of the surface acoustic wave sensor. The method is very efficient and can be used for the optimal design of gas sensors. Since the diamond can be easily merged into solid state and biological systems, the development of smart biological sensors is possible. The advantages over silicon based sensors are also shown.

Transducer loading effect on the performance of PZT-based SHM systems

In the last years, the piezoelectric transducers of lead zirconate titanate (PZT) have been widely used in structural health monitoring (SHM) systems based on the electromechanical (E/M) impedance technique. Although many studies indicate the successful use of PZT in damage detection, some practical considerations still have to be considered in real applications. In this work, the effect of the transducer loading caused by mechanical impedance of the host structure is analyzed using an equivalent electromechanical circuit. Tests were performed on structures with various sizes and the results show that the transducer loading significantly reduces the sensitivity of the system for detecting structural damages.

The analysis of the electro-mechanical model of the cylindrical radial composite piezoelectric ceramic transducer

The cylindrical radial composite piezoelectric ceramic transducer is presented and studied. The transducer consists of an inner radially polarized piezoelectric ceramic thin-walled circular tube and an outer metal thin-walled cylindrical shell which are composed in the radial direction. The radial vibrations of a metal thin-walled cylindrical shell and a piezoelectric ceramic thin-walled circular tube are analyzed. Their radial electro-mechanical equivalent circuits are obtained. Based on the equivalent circuits and the radial boundary conditions, the composite electro-mechanical equivalent circuit of a cylindrical radial composite piezoelectric ceramic transducer is obtained, the resonance frequency and anti-resonance frequency equations of the cylindrical radial composite piezoelectric transducer are derived. Then the relationship between the resonance frequency, the anti-resonance frequency, the effective electro-mechanical coupling coefficient and the geometrical dimensions of the cylindrical radial composite piezoelectric ceramic transducer is analyzed. It is illustrated that the resonance frequencies and the anti-resonance frequencies from the frequency equations are in a good agreement with that of the experimental results.

Coupled vibration analysis of the thin-walled cylindrical piezoelectric ceramic transducers

Analysis of electromechanical transducers employing axially symmetric vibrations of piezoelectric ceramic thin-walled tubes of arbitrary aspect ratio is presented based on application of the energy method [B. S. Aronov, J. Acoust. Soc. Am. 117, 210-220 (2005)]. The suggestion made by Giebe and Blechshmidt [Ann. Physik, Ser. 5 18, 417-485 (1933)] regarding representation of a tube vibration as a coupled vibration of two partial systems is used to choose the assumed modes of the piezoceramic tube vibration, and the energy of the flexural deformations accompanying the extensional vibration of a tube is also taken into consideration. The Lagrange type equations describing the transducer vibrations are derived, and the equivalent electromechanical circuit is introduced that conveniently represents the solution. The resonance frequencies, effective coupling coefficients, and velocity distributions for differently poled piezoceramic tubes as functions of their height-to-diameter aspect ratio are calculated. The validity of the equivalent circuit is extended to the case that a piezoceramic tube is mechanically and acoustically loaded on the ends and acoustically loaded on its outer surface. The results of calculations are in good agreement with the results of experimental investigations.

Vibration of annular plate concentrators with conical cross-section

In this paper, the torsional vibration and radial vibration of isotropic metal thin annular plates with conical cross-section are deduced by using Bessel functions; and according to electro-mechanical analogy, the electro-mechanical equivalent circuits are obtained. Based on the electro-mechanical equivalent circuits, the resonance frequency equations and the expressions of angular and radial displacement amplitude magnifications are derived, and the resonance frequencies and magnifications are solved by analytical method. The relationships between torsional and radial resonance frequencies and geometrical dimensions are discussed; and the relationships between angular and radial displacement amplitude magnifications and the ratio of outer radius over inner radius are analyzed. Modal shapes are analyzed by finite element method (ANSYS). It is shown that the values calculated by using the theory of this paper are in good agreement with the results simulated by ANSYS. The method can serve as benchmark values for researchers to validate other variable thickness thin annular plates.

Study on the sandwich piezoelectric ceramic ultrasonic transducer in thickness vibration

A sandwich piezoelectric ceramic ultrasonic transducer in thickness vibration isstudied. The transducer consists of front and back metal masses, and coaxiallysegmented, thickness polarized piezoelectric ceramic thin rings. For this kindof sandwich piezoelectric transducers in thickness vibration, it is required thatthe lateral dimension of the transducer is sufficiently large compared with itslongitudinal dimension so that no lateral displacements in the transducer can occur(laterally clamped). In this paper, the thickness vibration of the piezoelectricceramic stack consisting of a number of identical piezoelectric ceramic thin rings isanalysed and its electro-mechanical equivalent circuit is obtained. The resonancefrequency equation for the sandwich piezoelectric ceramic ultrasonic transducer inthickness vibration is derived. Based on the frequency equation, two sandwichpiezoelectric ceramic ultrasonic transducers are designed and manufactured, and theirresonance frequencies are measured. It is shown that the measured resonancefrequencies are in good agreement with the theoretical results. This kind of sandwichpiezoelectric ultrasonic transducer is expected to be used in megasonic ultrasoniccleaning and sonochemistry where high power and high frequency ultrasound isneeded.

The radial composite piezoelectric ceramic transducer

The radial composite piezoelectric ceramic transducer is presented and analyzed. The transducer consists of two metal thin circular rings and a thickness polarized piezoelectric thin ring which is sandwiched between the two metal rings in the radial direction. The radial vibrations of a metal thin ring and a piezoelectric ceramic thin ring are analyzed. Their electro-mechanical equivalent circuits are obtained. Based on the electro-mechanical equivalent circuits and the radial boundary conditions, the composite electro-mechanical equivalent circuit of a radial composite piezoelectric transducer is obtained and the resonance and the anti-resonance frequency equations are derived. The relationship between the resonance frequency, the anti-resonance frequency, and the effective electro-mechanical coupling coefficient and the geometrical dimensions of the radial composite transducer is analyzed. It is illustrated that the resonance frequencies and the anti-resonance frequencies from the frequency equations are in a good agreement with experimental results.

Study on the radial vibration of a new type of composite piezoelectric transducer

In this paper, a new type of composite piezoelectric ceramic transducers is studied. The transducer consists of a piezoelectric ceramic thin ring polarized in the thickness direction and a metal thin circular ring. The radial vibration of the transducer is analyzed and its radial electro-mechanical equivalent circuit is obtained. Based on the electro-mechanical equivalent circuit, the resonance and anti-resonance frequency equations are obtained. The relationship between the resonance frequency, the anti-resonance frequency, and the effective electro-mechanical coupling coefficient and the geometrical dimensions is analyzed. Some radial composite piezoelectric transducers are designed and manufactured. The resonance frequencies and anti-resonance frequencies are measured and the effective electro-mechanical coupling coefficient is calculated. It is illustrated that the measured radial resonance frequencies are in good agreement with the theoretical results from the resonance frequency equation. The finite element method is also used to find the resonance frequency and the radial displacement distribution. It is shown that the resonance and anti-resonance frequencies from the finite element method are also in good agreement with those from the analytical method in this paper.

Radial vibration of the composite ultrasonic transducer of piezoelectric and metal rings

The radial composite ultrasonic transducer of a piezoelectric ceramic ring and a metal ring is studied. The radial vibrations of a piezoelectric ceramic ring polarized in the thickness direction and a metal ring are analyzed and their electromechanical equivalent circuits are obtained. On the basis of the electromechanical equivalent circuits of the piezoelectric and the metal ring and the radial boundary conditions, the total electromechanical equivalent circuit for the composite ultrasonic transducer is also obtained. The resonance frequency and anti-resonance frequency equations of the composite ultrasonic transducer are given. Some radial composite ultrasonic transducers are designed and manufactured and their resonance and anti-resonance frequencies are measured. Experiments show that the measured resonance frequencies are in a good agreement with the theoretical results.

Radial vibration of the combination of a piezoelectric ceramic disk and a circular metalring

The radial vibration of the combination of a thin piezoelectric ceramic disk and a thincircular metal ring that are clamped together in the radial direction is analyzed. This typeof combination of a piezoelectric ceramic disk and a circular metal ring can be used as theactive elements in moonie and cymbal transducers and actuators. In this paper, the radialvibrations of a thin piezoelectric ceramic disk and a thin circular metal ring are analyzed,and their radial electro-mechanical equivalent circuits are obtained, respectively. Based onelectro-mechanical equivalent circuits and using the radial boundary conditions, theelectro-mechanical equivalent circuit of the combination of a piezoelectric ceramic disk anda circular metal ring is given and its radial frequency equation is obtained. Therelationships between the resonance frequency, the anti-resonance frequency, and theeffective electro-mechanical coupling coefficient and the geometrical dimensions areanalyzed. The radial vibrational velocity ratio or the radial vibrational velocitymagnification is studied. It is illustrated that the theoretical radial resonance andanti-resonance frequencies from the frequency equation are in good agreement with themeasured results.

Study on the radial composite piezoelectric ceramic transducer in radial vibration

A new type of radial composite piezoelectric transducer in radial vibration is developed and analyzed. The radial composite transducer consists of a piezoelectric ceramic thin ring polarized in the thickness direction and a metal thin circular ring. They are connected together and excited to vibrate in the radial direction. The radial vibrations of a piezoelectric ceramic thin ring and a metal thin circular ring are analyzed, respectively. Their radial electro-mechanical equivalent circuits are obtained. Based on the electro-mechanical equivalent circuits and using the boundary conditions between the piezoelectric ceramic thin ring and the metal thin circular ring in the radial direction, the electro-mechanical equivalent circuit of the radial composite piezoelectric transducer is derived out and the resonance frequency equation is obtained. The relationship between the resonance frequency and the geometrical dimensions of the transducer is analyzed. Some radial composite piezoelectric transducers are designed and manufactured. The resonance frequencies and the anti-resonance frequencies, the electro-mechanical equivalent circuit parameters are measured. The effective electro-mechanical coupling coefficient and the mechanical quality factor are calculated. It is illustrated that the measured radial resonance frequencies are in good agreement with the theoretical results from the resonance frequency equation.

Study on the radial vibration of a piezoelectric ceramic thin ring with an inner metal disc

In this paper, a piezoelectric ceramic thin ring with an inner metal disc is studied. The radial vibrations of a metal thin disc and a piezoelectric ceramic thin ring are analysed. Their electro-mechanical equivalent circuits in radial vibration are obtained. Based on the electro-mechanical equivalent circuits and the radial boundary conditions, the composite electro-mechanical equivalent circuit of the combination of a piezoelectric ceramic thin ring and a metal disc is obtained and the resonance and anti-resonance frequency equations are derived. The relationship between the resonance frequency, the anti-resonance frequency, the effective electro-mechanical coupling coefficient and the geometrical dimensions is analysed. The resonance and anti-resonance frequencies are measured using the Agilent Precision Impedance Analyzer. It is illustrated that the measured radial resonance and anti-resonance frequencies are in good agreement with the theoretical results.

Study on a new type of radial composite piezoelectric ultrasonic transducers in radial vibration

In this paper, a new type of radial composite ultrasonic transducers in radial vibration is presented and studied. The radial composite ultrasonic transducer consists of a solid piezoelectric ceramic thin disk and a hollow metal thin, circular ring in radial vibration; and they are connected together in the radial direction. The radial vibrations of a piezoelectric ceramic thin disk and a hollow, metal, thin, circular ring are analyzed, respectively. Their radial electromechanical equivalent circuits are obtained. Based on the electromechanical equivalent circuits and using the boundary conditions between the piezoelectric ceramic thin disk and the hollow, metal, thin ring, the electromechanical equivalent circuit of the radial composite ultrasonic transducer is derived and the resonance frequency equation is obtained. The theoretical results from the resonance frequency equation are in good agreement with the measured radial resonance frequencies, and they also are in a good agreement with the results from the numerical method.

Electro-mechanical equivalent circuit of a piezoelectric ceramic thin circular ring in radial vibration

The radial vibration of a piezoelectric ceramic thin circular ring polarized in the thickness direction is studied. Its electro-mechanical equivalent circuit is derived, the resonance and anti-resonance frequency equations are obtained, and the relationship between the resonance frequencies and the material parameters and the geometrical dimensions is analyzed. It is illustrated that the first radial resonance frequency of a solid piezoelectric thin plate is larger than that of a hollow piezoelectric thin ring with the same outer radius. When the radius ratio is increased, the first radial resonance frequency is decreased. The relationship between the second radial resonance frequency and the radius ratio is complex. When the radius ratio is smaller than the definite value, the second radial resonance frequency is decreased as the radius ratio is increased; while when the radius ratio is larger than this value, the second radial resonance frequency is increased as the radius ratio is increased. When the radius ratio is larger than a definite value, the second radial resonance frequency is larger than that of a solid plate with the same outer radius. When the radius ratio limits one, the second radial resonance frequency limits infinity.

Model based analysis of piezoelectric transformers

Piezoelectric transformers are increasingly getting popular in the electrical devices owing to several advantages such as small size, high efficiency, no electromagnetic noise and non-flammable. In addition to the conventional applications such as ballast for back light inverter in notebook computers, camera flash, and fuel ignition several new applications have emerged such as AC/DC converter, battery charger and automobile lighting. These new applications demand high power density and wide range of voltage gain. Currently, the transformer power density is limited to 40 W/cm 3 obtained at low voltage gain. The purpose of this study was to investigate a transformer design that has the potential of providing higher power density and wider range of voltage gain. The new transformer design utilizes radial mode both at the input and output port and has the unidirectional polarization in the ceramics. This design was found to provide 30 W power with an efficiency of 98% and 30 °C temperature rise from the room temperature. An electro-mechanical equivalent circuit model was developed to describe the characteristics of the piezoelectric transformer. The model was found to successfully predict the characteristics of the transformer. Excellent matching was found between the computed and experimental results. The results of this study will allow to deterministically design unipoled piezoelectric transformers with specified performance. It is expected that in near future the unipoled transformer will gain significant importance in various electrical components.

A Methodology for Automatically Deriving Simple Electromechanical Equivalent Models from FEM-Models

FEM is a very important tool for getting the numerical solution of many engineering problems. It has been widely used in solving structural, mechanical, heat transfer, and fluid dynamics’ problems as well as problems of other disciplines such as piezoelectricity. Since the complexity of many problems leads to the formation of models of large dimension, which are described with many degrees of freedom, their numeric solution makes for the highest demands. The number of degrees of freedom is often unnecessarily large to represent the structural response in a limited bandwidth and therefore, in such a case, a reduction should be conducted. The systematic reduction of complex FE models on simple electromechanical equivalent circuit models (with less mechanical degrees of freedom) is the subject of this paper. The aim of the work is to make the reduction in such a way that the characteristics of the systems input/output descriptions are approximated within a pre-selectable frequency range with sufficient accuracy. A transducerwedge- system is used as an example for the method, to extract a state space model of the systems piezoelectric input/output description and to derive the parameters of the electromechanical equivalent circuit directly from the modal finite element analysis. In the present paper we describe the general methodology as well as its application to piezoelectric transducers as used in ultrasonic engineering.