A lumped-parameter model of the free-flooded ring transducer array.

The free-flooded ring (FFR) transducer is an extensively used ring-type acoustic transducer in underwater environments owing to its broad operating frequency bandwidth and small size. However, achieving high sound pressure levels with a single FFR transducer is often difficult, thus necessitating the construction of vertically arranged FFR transducer arrays. This study presents a comprehensive analysis of the electrical and acoustic characteristics of an FFR transducer array by considering the mutual radiation load and the effects of gaps between adjacent piezoelectric rings. The lumped-parameter models of the piezoelectric ring, cylindrical cavity, cylindrical gap, and radiation impedance constitute an entire impedance matrix. The radiation impedance matrix for the FFR transducer array is calculated using the Helmholtz-Kirchhoff integral formula by considering the interaction of the FFR surfaces with the surrounding fluid medium. The proposed model predicts the resonance peaks in the admittance and transmitted voltage response (TVR) with a relative error of 5%, and the TVR level within a 3 dB range. Detailed analyses of a four-FFR transducer array reveal that a wider gap between each FFR leads to a decreased chance of negative conductance and broader operating bandwidth. The proposed model offers valuable insights into the design of FFR transducer arrays.

A lumped parameter model of the single free-flooded ring transducer.

A free-flooded ring (FFR) transducer can generate low-frequency sound in a small device and has a wide operating frequency bandwidth. Many studies have been performed that can predict the characteristics of an FFR transducer using analytical techniques and an equivalent circuit model (ECM), and methods to predict properties using numerical simulations have recently been developed. However, an ECM, a type of lumped parameter model (LPM), is still widely used to interpret the properties of such transducers in the design process. In this study, the authors investigated an ECM of an FFR transducer. The ECM consists of three parts: the piezoelectric ring, the cylindrical cavity, and the radiation load. Moreover, it can be included readily in a circuit to drive an FFR transducer. Additionally, an LPM was proposed, considering the mutual radiation loads, to improve the accuracy of the model. Each model was tested in comparisons with the finite element method; it was confirmed that an LPM could predict the properties of an FFR transducer with much better accuracy than an ECM. The LPM developed can save much time in designing FFR transducers.

A micromachined efficient parametric array loudspeaker with a wide radiation frequency band.

Parametric array (PA) loudspeakers generate directional audible sound via the PA effect, which can make private listening possible. The practical applications of PA loudspeakers include information technology devices that require large power efficiency transducers with a wide frequency bandwidth. Piezoelectric micromachined ultrasonic transducers (PMUTs) are compact and efficient units for PA sources [Je, Lee, and Moon, Ultrasonics 53, 1124-1134 (2013)]. This study investigated the use of an array of PMUTs to make a PA loudspeaker with high power efficiency and wide bandwidth. The achievable maximum radiation bandwidth of the driver was calculated, and an array of PMUTs with two distinct resonance frequencies (f1 = 100 kHz, f2 = 110 kHz) was designed. Out-of-phase driving was used with the dual-resonance transducer array to increase the bandwidth. The fabricated PMUT array exhibited an efficiency of up to 71%, together with a ±3-dB bandwidth of 17 kHz for directly radiated primary waves, and 19.5 kHz (500 Hz to 20 kHz) for the difference frequency waves (with equalization).

The impact of micromachined ultrasonic radiators on the efficiency of transducers in air.

The use of micromachined thin-film ultrasonic radiators to improve the efficiency of conventional in-air acoustic transducers is investigated. We conduct a theoretical investigation of the parameters that determine the efficiency of thin-film transducers, using a lumped parameter model, and show that the efficiency can be improved by choosing a radiating plate thickness that can be realized by micromachining. We also identified the problems that should be overcome to design and fabricate a micromachined ultrasonic transducer with the theoretically predicted efficiency. Based on the lumped parameter model, we showed that the problems can be resolved via an appropriate design scheme. A piezoelectric micromachined ultrasonic transducer is designed and fabricated to demonstrate the impact of the proposed design method. Test results for the fabricated radiator indicated that it provided an electroacoustic efficiency of 58.4%, up to 300% greater than either the unit previously fabricated by the authors or conventional unimorph ultrasonic transducers. An array of the proposed transducers was also designed, fabricated, and tested as a source transducer for a parametric array, since transducer efficiency is important for practical applications of a parametric array. The test results for the proposed transducer demonstrate its potential for improving the practicality of parametric array sources, such as parametric loudspeakers and directional ultrasonic ranging sensors.

A micro-machined piezoelectric flexural-mode hydrophone with air backing: a hydrostatic pressure-balancing mechanism for integrity preservation.

Although an air-backed thin plate is an effective sound receiver structure, it is easily damaged via pressure unbalance caused by external hydrostatic pressure. To overcome this difficulty, a simple pressure-balancing module is proposed. Despite its small size and relative simplicity, with proper design and operation, micro-channel structure provides a solution to the pressure-balancing problem. If the channel size is sufficiently small, the gas-liquid interface may move back and forth without breach by the hydrostatic pressure since the surface tension can retain the interface surface continuously. One input port of the device is opened to an intermediate liquid, while the other port is connected to the air-backing chamber. As the hydrostatic pressure increases, the liquid in the micro-channel compresses the air, and the pressure in the backing chamber is then equalized to match the external hydrostatic pressure. To validate the performance of the proposed mechanism, a micro-channel prototype is designed and integrated with the piezoelectric micro-machined flexural sensor developed in our previous work. The working principle of the mechanism is experimentally verified. In addition, the effect of hydrostatic pressure on receiving sensitivity is evaluated and compared with predicted behavior.

A micro-machined piezoelectric flexural-mode hydrophone with air backing: benefit of air backing for enhancing sensitivity.

A micro-machined underwater acoustic receiver that utilizes the flexural vibration mode of a silicon thin plate and piezoelectric transduction material was investigated. In particular, air was used as the backing material for the hydrophone in order to improve sensitivity in the audible frequency range. To evaluate the effects of air backing on receiving sensitivity, a transduction model incorporating mechanical/electrical/acoustical design parameters was used in designing a piezoelectric micro-machined hydrophone. The sensitivity and displacement responses of the sensor were simulated using the model for air backing and water backing cases, and the benefit of using air backing to enhance sensitivity was confirmed. The micro-machined piezoelectric transducer was fabricated, assembled in the shape of a hydrophone, and tested to ascertain its characteristics as an underwater sensor. These characteristics, such as frequency response and sensitivity, were measured and compared with the simulated results.

A stepped-plate bi-frequency source for generating a difference frequency sound with a parametric array.

An ultrasonic radiator is developed to generate a difference frequency sound from two frequencies of ultrasound in air with a parametric array. A design method is proposed for an ultrasonic radiator capable of generating highly directive, high-amplitude ultrasonic sound beams at two different frequencies in air based on a modification of the stepped-plate ultrasonic radiator. The stepped-plate ultrasonic radiator was introduced by Gallego-Juarez et al. [Ultrasonics 16, 267-271 (1978)] in their previous study and can effectively generate highly directive, large-amplitude ultrasonic sounds in air, but only at a single frequency. Because parametric array sources must be able to generate sounds at more than one frequency, a design modification is crucial to the application of a stepped-plate ultrasonic radiator as a parametric array source in air. The aforementioned method was employed to design a parametric radiator for use in air. A prototype of this design was constructed and tested to determine whether it could successfully generate a difference frequency sound with a parametric array. The results confirmed that the proposed single small-area transducer was suitable as a parametric radiator in air.

Design of an ultrasonic sensor for measuring distance and detecting obstacles.

This paper introduces a novel method for designing the transducer of a highly directional ultrasonic range sensor for detecting obstacles in mobile robot applications. The transducer consists of wave generation, amplification, and radiation sections, and a countermass. The operating principle of this design is based on the parametric array method where the frequency difference between two ultrasonic waves is used to generate a highly directional low-frequency wave with a small aperture. The aim of this study was to design an optimal transducer to generate the two simultaneous longitudinal modes efficiently. We first derived an appropriate mathematical model by combining the continuum model of a bar and countermass with the compatibility condition between a piezoelectric actuator and a linear horn. Then we determined the optimal length of the aluminum horn and the piezoelectric actuator using a finite element method. The proposed sensor exhibited a half-power bandwidth of less than+/-1.3 degrees at 44.8 kHz, a much higher directivity than existing conventional ultrasonic range sensors.

A micro-machined source transducer for a parametric array in air.

Parametric array applications in air, such as highly directional parametric loudspeaker systems, usually rely on large radiators to generate the high-intensity primary beams required for nonlinear interactions. However, a conventional transducer, as a primary wave projector, requires a great deal of electrical power because its electroacoustic efficiency is very low due to the large characteristic mechanical impedance in air. The feasibility of a micro-machined ultrasonic transducer as an efficient finite-amplitude wave projector was studied. A piezoelectric micro-machined ultrasonic transducer array consisting of lead zirconate titanate uni-morph elements was designed and fabricated for this purpose. Theoretical and experimental evaluations showed that a micro-machined ultrasonic transducer array can be used as an efficient source transducer for a parametric array in air. The beam patterns and propagation curves of the difference frequency wave and the primary wave generated by the micro-machined ultrasonic transducer array were measured. Although the theoretical results were based on ideal parametric array models, the theoretical data explained the experimental results reasonably well. These experiments demonstrated the potential of micro-machined primary wave projector.

Effects of mutual impedance on the radiation characteristics of transducer arrays.

The mutual resistance of transducer arrays is investigated in order to design arrays with improved performance for high intensity sounds at a given frequency. This work proposes the theory that the mutual resistance is related to the loading effects of pressure waves propagated from a piston driver on the surface of another driver. Using this interpretation, the important characteristics of the mutual resistance of two piston drivers are explained and the conditions for local maxima in the mutual resistance are easily determined. On the basis of analyses of the interactions between a driver and acoustic pressure waves, we propose a method to determine the driver radius and the distance between two drivers that give maximum mutual radiation resistance. To evaluate the proposed method, the total resistance of a transducer array is calculated using the formulas for mutual and self-resistance established by Pritchard. The results of the calculations of the total resistances of arrays with many drivers show that a transducer array with drivers arranged sparsely can achieve a larger value of the radiation power per unit area as well as better radiation efficiency than an array in which the drivers are in a closely packed arrangement at a given frequency.