Sandwiched piezoelectric ultrasonic transducers oflongitudinal-torsional compound vibrational modes

Sandwiched piezoelectric ultrasonic transducers of longitudinal-torsional compound vibrational modes were studied. The transducers consist of coaxially segmented, longitudinally and tangentially polarized piezoelectric ceramic rings, a back metal cylinder, and a front exponential solid metal horn. Based on the plane-wave approximation, the equivalent circuits of the longitudinal and torsional vibrations in the sandwiched transducer were obtained and the resonance frequency equations of the transducer in longitudinal and torsional vibrations were derived. By means of choosing the radius decay coefficient of the front exponential horn, the longitudinal and torsional vibrations are made to resonate at the same frequency in the transducer. Sandwiched piezoelectric ultrasonic transducers of longitudinal-torsional compound modes were designed and fabricated according to the frequency equations. It is demonstrated that the measured resonance frequencies of the transducers are in good agreement with the theoretical results, and the measured resonance frequencies of the transducers in longitudinal and torsional vibration modes are also in good agreement with each other. Theoretical and experimental results show that this kind of transducer can be used in ultrasonic welding, ultrasonic machining, ultrasonic motors, and other ultrasonic applications which need large displacement amplitudes     

Radiation impedance of collapsed capacitive micromachined ultrasonic transducers

The radiation impedance of a capacitive micromachined ultrasonic transducer (CMUT) array is a critical parameter to achieve high performance. In this paper, we present a calculation of the radiation impedance of collapsed, clamped, circular CMUTs both analytically and using finite element method (FEM) simulations. First, we model the radiation impedance of a single collapsed CMUT cell analytically by expressing its velocity profile as a linear combination of special functions for which the generated pressures are known. For an array of collapsed CMUT cells, the mutual impedance between the cells is also taken into account. The radiation impedances for arrays of 7, 19, 37, and 61 circular collapsed CMUT cells for different contact radii are calculated both analytically and by FEM simulations. The radiation resistance of an array reaches a plateau and maintains this level for a wide frequency range. The variation of radiation reactance with respect to frequency indicates an inductance-like behavior in the same frequency range. We find that the peak radiation resistance value is reached at higher kd values in the collapsed case as compared with the uncollapsed case, where k is the wavenumber and d is the center-to-center distance between two neighboring CMUT cells.     

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.     

Fabrication and characterization of piezoelectric micromachined ultrasonic transducers with thick composite PZT films

Ferroelectric microelectromechanical systems (MEMS) has been a growing area of research in past decades, in which ferroelectric films are combined with silicon technology for a variety of applications, such as piezo-electric micromachined ultrasonic transducers (pMUTs), which represent a new approach to ultrasound detection and generation. For ultrasound-radiating applications, thicker PZT films are preferred because generative force and response speed of the diaphragm-type transducers increase with increasing film thickness. However, integration of 4- to 20-microm thick PZT films on silicon wafer, either the deposition or the patterning, is still a bottleneck in the micromachining process. This paper reports on a diaphragm-type pMUT. A composite coating technique based on chemical solution deposition and high-energy ball milled powder has been used to fabricate thick PZT films. Micromachining of the pMUTs using such thick films has been investigated. The fabricated pMUT with crack-free PZT films up to 7-microm thick was evaluated as an ultrasonic transmitter. The generated sound pressure level of up to 120 dB indicates that the fabricated pMUT has very good ultrasound-radiating performance and, therefore, can be used to compose pMUT arrays for generating ultrasound beam with high directivity in numerous applications. The pMUT arrays also have been demonstrated.     

New equivalent lumped electrical circuit for piezoelectric transformers

A new equivalent circuit is proposed for a contour-vibration-mode piezoelectric transformer (PT). It is shown that the usual lumped equivalent circuit derived from the conventional Mason approach is not accurate. The proposed circuit, built on experimental measurements, makes an explicit difference between the elastic energies stored respectively on the primary and secondary parts. The experimental and theoretical resonance frequencies with the secondary in open or short circuit are in good agreement as well as the output "voltage-current" characteristic and the optimum efficiency working point. This circuit can be extended to various PT configurations and appears to be a useful tool for modeling electronic devices that integrate piezoelectric transformers.     

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.     

Acoustic impedance matching of piezoelectric transducers to the air

The purpose of this work is threefold: to investigate material requirements to produce impedance matching layers for air-coupled piezoelectric transducers, to identify materials that meet these requirements, and to propose the best solution to produce air-coupled piezoelectric transducers for the low megahertz frequency range. Toward this end, design criteria for the matching layers and possible configurations are reviewed. Among the several factors that affect the efficiency of the matching layer, the importance of attenuation is pointed out. A standard characterization procedure is applied to a wide collection of candidate materials to produce matching layers. In particular, some types of filtration membranes are studied. From these results, the best materials are identified, and the better matching configuration is proposed. Four pairs of air-coupled piezoelectric transducers also are produced to illustrate the performance of the proposed solution. The lowest two-way insertion loss figure is -24 dB obtained at 0.45 MHz. This increases for higher frequency transducers up to -42 dB at 1.8 MHz and -50 at 2.25 MHz. Typical bandwidth is about 15-20%.     

Air-coupled piezoelectric micromachined ultrasonic transducers for surface stain detection and imaging

This paper proposes an air-coupled piezoelectric micromachined ultrasonic transducer(PMUT)for detection and imaging of surface stains.A 508 kHz PMUT array is de...     

Electric equivalent circuit for flexural vibrations in piezoelectric materials

General expressions for the values of the components of an electric equivalent circuit are derived for flexural vibrations. These expressions are applied to some interesting electrode configurations. The obtained values are in good agreement with experimental values and values specified by manufacturers of watch crystals. It is noted that solving Laplace's equation for the dielectric field is sufficient in order to obtain the values of the vibration amplitude, the piezoelectric current, and the equivalent components. The piezoelectric part of the electric field need only be considered if very accurate values of the resonance frequencies are desired. It is shown how accurate estimates can be obtained without the need of advanced calculation tools.     

An ndt method using piezoelectric polymer transducers and computerized vibrational spectroscopy

The normal mode vibrational spectrum of a particular object contains a wealth of information about the mechanical integrity of the object. The non-destructive evaluation of objects by observation of their vibrational spectra is facilitated by the combination of recently developed low mass, high compliance piezoelectric polymer transducers; a synchronized method for exciting the sample; and a small minicomputer capable of making digital Fourier transforms which convert the complicated, oscillatory, decaying signal from the transducer into the intensities and frequencies of normal modes.     

Ring piezoelectric transducers radiating ultrasonic energy into the air

Ring piezoelectric transducers generating ultrasonic energy in air were designed and tested experimentally and numerically. The radiation pattern of the transducer is very narrow (4 degrees ) and its frequency response has a broadband character. Resonant frequencies of the transducers were determined experimentally and verified theoretically. Applications of the proposed ring transducers in a robotic ranging system were examined.     

Narrowband impedance matching layer for high efficiency thickness mode ultrasonic transducers

A new matching layer design concept has been proposed for narrowband continuous wave (CW) devices. Analysis has shown that the mechanical impedance of a resonant-type transducer in thickness mode CW operation does not equal its acoustic impedance ρVs but roughly equals ρVs/Q, where ρ is density, Vs is acoustic velocity, and Q is the mechanical quality factor. The value of ρVs/Q is much lower than the acoustic impedance of water for any transducer material, including lead zirconium titanate (PZT), single crystals, or polyvinylidene fluoride (PVDF). With this new approach, the impedance of the matching layer must also be between water and ρVs/Q, but there are few such practical low impedance materials. To realize equivalent low impedance structure, a novel double layer design is presented: a relatively low impedance material (such as polyethylene or polyurethane) on the inside and a relatively high impedance material (such as polyester or metal) on the outside. A high power CW transducer structure was designed and fabricated with PVDF-TrFE (polyvinylidene fluoride trifluoroethylene) to operate at 1.4 MHz     

Fabrication and characterization of annular thickness mode piezoelectric micro ultrasonic transducers

Micromachining techniques, in combination with low temperature ceramic composite sol-gel processing, have been used to fabricate annular array thickness-mode piezoelectric micro ultrasonic transducers (Tm-pMUTs). The processing techniques of low temperature (710 degrees C) composite sol-gel ceramic (sol + ceramic powder) deposition and wet etching were used to deposit and structure 27-microm thick lead zirconate titanate (PZT) films on silicon substrates to produce annular array Tm-pMUTs. Using these techniques, high quality PZT materials with near bulk permittivity have been obtained. The Tm-pMUT devices were shown to resonate at approximately 60 MHz in air and 50 MHz in water. From resonance measurements k(t) values ranging between 0.2 and 0.47 have been calculated and shown to depend on the level of porosity within the film. Lower values of kt were observed for films with higher levels of porosity, which was attributed to the relative decrease in the effective piezoelectric coefficient epsilon(33) with respect to stiffness and permittivity as a function of increasing porosity. This paper presents the successful micro-fabrication of a Tm-pMUT device and discusses the optimization of the poling conditions and effect of PZT microstructure on the coupling coefficient k(t). Pulse echo measurements in water, showing a -6 dB center frequency of 53 MHz and 47% -6 dB bandwidth, using a target 15 mm away from the transducer, have been included to demonstrate successful operation of the device. Full analysis of these results will be conducted in later publications.     

A simple equivalent circuit for interdigital transducers based on the coupled-mode approach

The coupled-mode approach is a powerful tool for analyzing surface acoustic wave (SAW) periodic structures such as reflectors and interdigital transducers. The relations among the terminal quantities at two acoustical ports and one electrical port of an interdigital transducer (IDT) are derived from coupled-mode equations. A simple distributed-parameter equivalent circuit representing the entire IDT is proposed. A few examples of applications of this equivalent circuit to analysis of SAW devices are presented.     

A universal equivalent circuit model for the impedance response of composites

An equivalent circuit model has been developed to describe the impedance response of composites with insulating or conductive particles or fibers. Required inputs are the matrix conductivity, the intrinsic conductivity of the particles, and their volume fraction. The model has general applicability to systems involving moderately conductive matrices, insulating or conductive particles/fibers, and, in the case of conducting particles, the presence of a high impedance coating element on the particle surfaces. Ramifications for the use of impedance spectroscopy in the characterization of composite properties and the monitoring of their performance under load are discussed.     

Dynamic characteristics of 2-2 piezoelectric composite transducers

Lateral resonant modes associated with specific lateral structures in piezoceramic-polymer composites are the main drawback that interferes with performance of ultrasonic transducers utilizing the composites as driving elements. This paper presents a field solution to characterize dynamic behavior of lateral modes in composite transducers with 2-2 connectivity. The solution is derived based on a concept of Lamb wave propagation along piezoceramic and polymer layers in the thickness direction of the composite transducers. The behavior of 2-2 composite is investigated over a broad spectrum ranging from quasi-static stage up to mode transition zones. Dispersion curves for various modes were calculated and compared with experimental results. A safe zone can be identified from the dispersion curves where the interference of lateral modes to thickness oscillation is negligible. Strong interactions between thickness modes and lateral modes are observed in the transition zones where two modes merge together in the frequency domain. Electromechanical thickness coupling coefficient, k_t, is calculated for the first time to include the effect of aspect ratio of the composite. Results show that the coupling coefficient, k_t, varies dramatically as a function of both ceramic volume fraction and the aspect ratio. As k_t reaches its maximum value, the vibration of the ceramic phase is completely decoupled from that of the polymer phase     

An improved equivalent circuit model of radial mode piezoelectric transformer

In this paper, both the equivalent circuit models of the radial mode and the coupled thickness vibration mode of the radial mode piezoelectric transformer are deduced, and then with the Y-parameter matrix method and the dual-port network theory, an improved equivalent circuit model for the multilayer radial mode piezoelectric transformer is established. A radial mode transformer sample is tested to verify the equivalent circuit model. The experimental results show that the model proposed in this paper is more precise than the typical model.