PSpice modeling of capacitive microfabricated ultrasonic transducers.

Capacitive microfabricated ultrasonic transducers (cMUTs) are the newest and potentially the most promising devices to convert electrical into acoustic signals and vice-versa. These devices are based on the capacitance modulation of a microcondenser which is obtained by microfabrication onto a silicon substrate. The aim of this paper is to describe a PSpice model of the cMUT, based on an analytical distributed model previously reported (IEEE Trans. UFFC 49 (2) (2002) 159-168), which can be used to simulate the performances of a general ultrasound system, either in frequency or time domain. The PSpice model consists of a capacitor with a parallel resistor, which represent the static capacitance and the loss and bias resistances of the transducer, respectively, plus two quadrupoles (GLAPLACE) modeling the mechanical impedance of the membranes and the radiation impedance of the medium. The usefulness of a PSpice model is the possibility to simulate and optimize the cMUT transducers in transmission and reception, along with driving and receiving electronics, in a general ultrasound system. Experimental measurements on a 5 MHz cMUT operating in pulse-echo are in good agreement with model predictions.

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.

A matrix model of the axle vibration of a piezoelectric motor

In this work, a matrix model of the axle vibration of a piezoelectric motor is proposed. The stator of this motor is composed of a thin piezoelectric membrane and a steel axle fitted at the center of the membrane. The rotor consists of a cylinder-shaped permanent magnet, pressed in contact with the other end of the axle by means of the magnetic forces. A travelling wave is excited in the membrane by using four electrodes and four, properly delayed, driving signals. The rotating flexural displacement of the membrane produces a wide precessional motion of the axle. In this way, a continuous slipping takes place between the axle and the rotor, and therefore, a torque is transmitted to the rotor. In this paper, the precessional motion of the axle is modeled as the composition of two transverse vibrations belonging to two perpendicular planes passing through the axle. The axle, vibrating in its transverse mode, is modeled as a two-port system: the input is the bending moment supplied by the membrane, and the output is the transverse force at the terminal end of the axle. With this model, we have computed the trasmission transfer function as a function of frequency, and the transversal displacement along the axle at its resonance frequency. The computed results are in reasonable agreement with experimental interferometric measurements carried out on a prototype.

Two-dimensional modelling of multifrequency piezocomposites.

The multifrequency composites of 2-2 connectivity modelled in this work are made with groups of piezoelectric elements of different lateral dimensions, periodically reproduced in the structure. These composites have potential to improve the performances of standard piezoelectric composites with the same materials and ceramic fraction, on account that they have different resonators coupled mechanically along the structure. A one-dimensional model was developed to study their performances in a first approximation. In order to obtain a design model, a two-dimensional model, previously used to describe multielement array transducers, has been extended to the case of 2-2 polymer-piezoceramic composites. Several composite samples, having piezoceramic strips with different width-to-thickness ratios, have been built, and their resonance behaviour compared with the model prediction. Finally, the model has been extended to the case of 2-2 multifrequency composites. For multifrequency composites having in the same composite structure two or three piezoceramic strips with different lateral dimensions, the comparison between experimental and predicted results shows good agreement. The model has been used to optimise a double composite in comparison with a standard one with the same volume fraction and constituents.

Analysis of the radial symmetrical modes of thin piezoceramic rings.

In this work, the radial symmetric vibration modes of thin piezoceramic rings have been analyzed by means of a previously proposed theoretical model. Both the resonance frequencies and the effective electromechanical coupling factor (k(eff)), as a function of the aspect ratio G between the inner and outer radii of the ring, were computed. The results have shown that the disk structure (G-->0) has only one radial symmetrical mode (with its harmonics), but, for the ring structure (G-->1), two different modes are clearly distinguished: the ring mode, which has no harmonics, and a width-like mode, with its harmonics. Moreover, the results show that the ring structure can be assumed to be definitely reached for G>0.6. An analysis of the material coupling factor in the ring geometry is reported as well.

A piezoelectric motor using flexural vibration of a thin piezoelectric membrane.

This paper describes a new implementation of a disk-type piezoelectric motor, whose stator is a commercial available piezomembrane composed of a nickel alloy disk to which a piezoceramic disk is bonded. The two disks are concentric, and the total thickness is very small. Ultrasonic motors are based on the concept of driving a rotor by mechanical vibration excited on a stator, via the piezoelectric effect. The rotor is in contact with the stator, and the driving force is the frictional force between rotor and stator. To transform the mechanical vibration of the stator in the rotor rotation, a traveling wave must be excited on the stator surface. The proposed motor can be regarded as a disk-type, single wavelength motor in which the traveling wave is due to the natural flexural vibration of the piezomembrane at low frequency. The behavior of the stator is analyzed both theoretically, by using the theory of isotropic and homogeneous vibrating plates, and by means of a commercial finite element computer code, finding a good agreement with the experimental results. The main features of the motor are very small thickness, appreciable torque, and high speed, obtained with low input power at low voltage; the intended application is to substitute the moving-coil in analogic instrumentation.

An approximated 3-D model of cylinder-shaped piezoceramic elements for transducer design.

In this paper an approximated 3-D model of cylinder shaped piezoceramics is described. In the hypothesis of axial symmetry, the element vibration in the extensional and radial directions is described by two coupled differential wave equations. The model is obtained choosing, as solution of these equations, two orthogonal wave functions, each depending only on one axis, corresponding to the propagation direction. The mechanical boundary conditions are applied imposing continuity between the stresses and the external forces on the surfaces of the element in an integral way, while, as far as the electrical boundary condition is concerned, two possibilities are explored: to neglect the piezoelectric constant in the transverse direction and to impose an integral condition also for the electric field. Comparisons with experimental results show this last approach to give better results. The model predicts with sufficient accuracy only the first radial and the first thickness modes of the cylinder-shaped piezoceramic element of arbitrary aspect ratio; but, for these modes, it is able to compute all the relations between the input applied voltage and the output forces and velocities on every external surface. Because only these two modes are of relevance in the practical applications of piezoceramic elements as ultrasonic transducers, the model can be used as a simple and useful tool in transducer design and optimization. Experimental validations of the model are also shown in the work.

A new approach for the design of ultrasono-therapy transducers.

In this paper we describe a new approach for the design of ultrasono-therapy transducers. Usually, in this kind of transducer, a lambda/2 front plate is inserted only in order to ensure a good mechanical protection of the active crystal from the surrounding medium. However, with an accurate design, the plate can also be used to match the piezoelectric element to the load both in terms of gain and bandwidth. To this end we apply the technique normally used in acoustical imaging and nondestructive testing, and, by means of a distributed matrix model, we optimize the thickness and impedance of the plate in order to obtain a strong response and a large bandwidth at the working frequency. Using a front plate of thickness about lambda/3, the model predicts better performances than the ones obtained with the classical design, also in terms of efficiency. An experimental comparison between a transducer realized according to the proposed design and a commercial half wave transducer shows better performances the former and therefore validates the new design criterion.