Large Transducer Research Articles

Large Nearfield Calibration Array

Farfield transmitting response, free-field sensitivity, and directivity patterns of both small and large (up to 18 ft in one dimension) underwater audio-frequency transducers have been obtained by direct measurement made in the nearfield with a special hydrophone, the NRL 33 ft × 33 ft nearfield calibration array (NFCA). Some of the measured results will be compared to the results determined by the classical farfield measurements except where only computed results were feasible. The calibrating array hydrophone consists of 2500 acoustic sensors in a square array on 8-in. spacings. These acoustic sensors were amplitude shaded according to the distribution advanced by W. James Trott in a JOURNAL article [36, 1557–1568 (1964)]. Applicable theory and fabrication design data for the special hydrophone will be briefly noted.

Excitation and Detection of Surface Elastic Waves in Piezoelectric Crystals

The amplitude of the surface elastic wave produced by the application of an alternating voltage to an interdigital arrangement of electrodes on the surface of a piezoelectric medium is determined. The electric field produced by the surface electrodes is calculated subject to the assumption that the piezoelectric coupling of the material can be neglected. This electric field acts as the forcing term for the inhomogeneous elastic equation, which is then solved to obtain the amplitude of the surface wave generated by the transducer. A reciprocal relationship between the excitation and detection problems is used to obtain the power extracted from the surface wave by an interdigital arrangement of surface electrodes. Measurements made on single crystals of quartz and cadmium sulfide are found to be in good agreement with theoretical predictions. The maximum value of the product (efficiency×fractional bandwidth) for a surface-wave transducer is calculated. For an interdigital surface-wave transducer on the basal plane of CdS, the maximum value of this product is found to be 7.8×10−2. It is shown that one can connect linear pairs of surface electrodes in an appropriate binary code so as to obtain high efficiency and large bandwidth transducers.

Transient Effects in Transducer Arrays

The familiar transient behavior of electromechanical transducers vibrating in vacuum is modified by acoustic effects when these transducers vibrate in a medium such as water. These effects are of particular interest in the large transducer arrays used in sonar, where the acoustic interactions between transducers causes different transient behavior at different locations in the array. A finite-difference iteration solution of the differential equations that describe the interacting transducers has been carried out in order to investigate some of these effects. The acoustic interactions are included in an approximate way that becomes more exact as the transducers are made smaller. The velocity of each transducer is computed as a function of time from the instant of sudden application of the driving voltages until steady state is reached. The convergence of the method has been checked by comparison with independent calculations of the steady-state velocities. Results will be given and discussed for different transducer and array parameters including cases of beam steering.

The resolution of turbulent pressures at the wall of a boundary layer

This paper is a discussion of the resolution by a piezo-electric transducer of the local pressure fluctuations at the wall of a turbulent boundary layer. The first part applies to transducers whose sensing area is large in comparison with the boundary layer thickness, and the second part to transducers whose sensing area is either of the order of, or smaller than, the boundary layer thickness. For large transducers, the main result, derived for a sensing surface of arbitrary shape and with an arbitrary spatial sensitivity distribution, is that under circumstances which are perhaps unrealistically stringent, the attenuation of a given frequency component will increase as the cube of the transducer face linear dimension. In general, it should be expected to increase only as the square of the dimension. In the second part, the probable dependence of the resolution on frequency and on transducer size is indicated by using both recent experimental evidence and physical reasoning bearing on the nature of the pressure cross-spectral density. Both approaches suggest that in a co-ordinate system translated downstream at an appropriate velocity, as the streamwise wave number increases, the spectral density in wave number-frequency space is associated with proportionately increasing spanwise wave numbers and almost proportionately increasing frequencies. Experimental evidence suggests departure from this finding if the fixed axis longitudinal wave length is very large (of the order of the boundary layer thickness) in which case both the characteristic time in convected axes and the characteristic lateral coherence length appear to reach asymptotic finite values. For shorter waves, the strong relationship between the two space scales and the convective time scale necessarily implies that the resolution of the frequency spectral density by a finite transducer continues to deterioriate as the frequency increases. It is concluded that the attenuation predictions previously published by the author are not likely to be seriously in error.

Transducers Using Forced Transitions Between Ferroelectric and Antiferroelectric States

Abstract : The use of resonant piezoelectric composite structures for acoustic radiation into fluid media is well established. At low frequencies, desirable for long distance acoustic transmission, resonant structures are extremely large and expensive. Frequency lowering can be accomplished by a variety of means involving use of bending structures or mass-loading, but the resulting transducers are vulnerable to pressure effects due to deep submersion. A possible alternative to present transducer structures is the use of the electric field-forced transition from antiferroelectric to ferroelectric. A number of Pb(Zr, Sn, Ti)O3 compositions have been developed which experience these transitions at relatively low electric field(7-15 kV/cm) and typically generate volume strains near 0.1%. There is therefore not necessarily a requirement for acoustic shielding, and since the developed strain is independent of frequency, resonant structures are not needed. Construction is therefore simplified and the size and weight of low frequency transducers may be reduced. Operating characteristics of the antiferroelectric transducer are discussed in detail, but no large low frequency transducer arrays have yet been built.

Underwater-Sound-Transducer Calibration from Nearfield Data

Farfield transmitting response, freefield sensitivity, and directivity of large audiofrequency transducers can be obtained directly from measurements made in the near field (Fresnel zone) of a transducer array especially designed to radiate a plane wave of constant amplitude within a portion of the Fresnel zone. The theory of the measurements and of the design of the special measuring array are supported by experimental data. Design data for building suitable measuring arrays are given.

Underwater Acoustic Tank Facility for Nearfield Measurements

This paper describes a large tank facility that has been in operation since the first of the year at the Fullerton site of the Hughes Aircraft Company. This facility was designed primarily for making nearfield measurements of large underwater acoustic radiators. (The 30-ft-diam by 20-in.-high redwood tank is completely enclosed in a corrugated-metal building.) Unique features and capabilities of this installation are described. These include provisions for the reduction of both airborne and ground-transmitted acoustic noise; a truck entry from which large transducers can be lifted directly to the tank top level; a movable bridge for mounting transducer fixtures that may be positioned anywhere above the water surface or rolled clear of the tank for special test purposes; a complete complement of electronic instruments, including a Hughes-designed pulsing and gating unit, for making precise measurements of pressure amplitude and phase. Acknowledgment is made of the helpful and continuing encouragement and advice of Dr. Elias Klein of the Defense Research Laboratory, Austin, Texas.

Determination of far-field characteristics of large underwater sound transducers from near-field measurements : Baker D. D. 1962. J. Acous. Soc. Amer., 34(11):1737–1744

Determination of far-field characteristics of large underwater sound transducers from near-field measurements : Baker D. D. 1962. J. Acous. Soc. Amer., 34(11):1737–1744

Computation of Farfield Characteristics of Phased Portions of a Cylindrical Transducer from Nearfield Measurements

Kirchoff's formula, with a simple approximation for the normal pressure gradient, was used to compute directivity patterns of two phased portions of a large cylindrical transducer from near-field-pressure measurements made over a cylindrical surface. In one case, 16 staves of the 48-stave transducer were phased to a plane and shaded to give 20-dB minor lobe suppression in the farfield. Nearfield-pressure amplitude and phase mensurements were made by receiving with the 16-stave array while transmitting with a line hydrophone that was rotated around the transducer. The transducer was mounted with the axis vertical, and the horizontal directivity pattern for the plane passing through the center of the transducer was computed. In the second case, several staves of the transducer were driven with phasing to produce a beam depression of about 30° Nearfield measurements were made by receiving with a probe hydrophone that was rotated around the transducer at several vertical levels. There is good agreement between the computed patterns and the equivalent measured ones in both cases. This is significant because one of the original restrictions on the gradient approximation in use was that the measurement surface closely fit the radiator. The approximation has been shown to be better than it was thought to be because in the present work the surfaces used were cylindrical and the radiators—due to phasing—were portions of a plane and a truncated cone.

Computation of Farfield Characteristics of a Transducer from Nearfield Measurements Made in a Reflective Tank

The directivity pattern and source level of a large cylindrical transducer were computed from nearfield pressure amplitude and phase measurements made under conditions simulating those in a reflective tank of diameter about 1.5 times that of the transducer. The measurements were made on the leading edge of the received pulses—before steady-state conditions were reached. This caused the pressure-amplitude data to be a few dB below the equivalent steady-state amplitudes. Computed directivity patterns agreed well with measured ones, but computed source levels were about 3 dB low. A correction term was derived from the first portion of the pulse-risetime curves and was applied to the source-level values to give good agreement with measured ones. The present results indicate that accurate transducer calibrations can be obtained in reflective tanks considerably smaller than those used in previous work.

Resolution of Pressure in Turbulence

The finite size of a transducer-sensing element limits its space resolution of a pressure field associated with a local turbulent flow. Such pressure fields are translated at a speed comparable to the characteristic velocity of the flow. Consequently, a lack of resolution in space causes an apparent inability to resolve in time. This problem—an example of the mapping of a random function of several variables by a linear operator—is examined here. With the help of a formalism which has been previously discussed and of some recent experimental information about the spatial structure of turbulent pressure fields in boundary layers, the mapping or distortion of statistical quantities associated with the second-order moments of the pressure field is given. The attenuation of the frequency spectral density and of the cross-spectral density is given explicitly in table form and in asymptotic form. The numerical results indicate that the attenuation caused by the finite size of transducers is generally more severe than previous computations had suggested, mainly because the lateral correlation of pressure is highly frequency-dependent, a typical turbulent pressure-wave component being inclined to the stream direction at roughly 45 degrees. The results are applied to an evaluation of contemporary measurements of turbulent pressure fields in shear flows. It is shown that the transducer size used introduces undesirable large errors in these measurements, which lead to doubts even about the magnitude of the intensity of turbulent pressure fluctuations. Asymptotic formulas for the attenuation of large transducers are given which yield estimates of the degree to which a flush-mounted sonar receiver immersed in a boundary layer is able to reject the background noise provided by turbulent pressure fluctuations.

Determination of Far-Field Characteristics of Large Underwater Sound Transducers from Near-Field Measurements

It has recently become necessary to find a way to determine far-field characteristics of large underwater sound transducers from measurements made in the near field of the transducer (at ranges small compared to the transducer dimensions). It is possible to compute far-field directivity patterns and source levels from pressure amplitude and phase measurements made in the near field. This can be done by using Kirchhoff's formula with a simple approximation for the normal component of the pressure gradient. Pattern computations were made on line, plane-array, dipole, and line-and-cone transducers from measurements made in open water. Extensive pattern and source level computations were made on a large, multistave cylindrical transducer from measurements made in open water and in a highly reflective tank. Agreement with measured far-field patterns and source levels was good throughout and was within ±1 dB in the more recent work with the cylindrical transducer. Particularly significant is the fact that successful measurements were made in a tank of diameter only 2.9 times that of the transducer. These measurements were made near the leading edge of the received pulses in order to avoid interference due to reflections. Preliminary work on a simplified near-field test for a cylindrical transducer has also been done. Such a test would enable one to use near-field data to make certain judgments about the far-field performance of a transducer without computations.

Computation of Far-Field Characteristics of a Transducer from Measurements Made in a Reflective Tank

The directivity pattern and source level of a large cylindrical transducer were computed using the Kirchhoff formula with a simple approximation for the normal pressure gradient. The integration was performed numerically over a finite cylinder. Nearfield pressure amplitude and phase data were made over the surface of integration by rotating the transducer and measuring the output of a line hydrophone less than one wavelength from the active face. These measurements were made in a highly reflective sheet-steel tank of diameter 2.9 times that of the transducer and wall thickness much less than a wavelength. The amplitude and phase were measured on the leading portion of the received pulses. Directivity patterns were computed in a plane normal to the axis of the transducer. They were compared with the equivalent patterns measured in open-sea conditions. Agreement was good both in pattern shape and source level. It is felt that this work shows that it is possible to calibrate such a transducer in a tank that is relatively small and highly reflective.

Experimental Determination of the Depth of Focus of Transducers Using Elliptical and Modified Parabolic Reflector Systems

When operating in the near zone of a large aperture transducer, one must use a focusing technique to realize the far-field resolving power of the aperture. For many applications the depth of focus is an important consideration. Experimental data will be presented showing the beam width, minor-lobe suppression, and sensitivity as a function of range near the far focus of an elliptic reflector. Data for similar conditions will also be presented for parabolic reflectors with the focal element shifted to obtain optimum directivity conditions. (This work is supported by the Bureau of Ships.)

Computation of the Directivity Pattern and Source Level of a Transducer from Near-Field Measurements

Kirchhoff's formula is used to compute the directivity pattern and the source level of a large cylindrical transducer from measurements made near the transducer. Directivity patterns are computed for a plane normal to the axis of the cylinder and a plane which contains the axis of the cylinder. The normal pressure gradient required in the formula is obtained by a simple approximation, and the computations are carried out by means of a numerical integration over the surface of a circular cylinder of finite length. Data have been taken by making various numbers of passes around the transducer at different positions along the axis with a probe hydrophone, or by making one pass with a line hydrophone. There is good agreement between measured and computed patterns and source levels. (This work is supported by the Bureau of Ships.)

Composite Spherical Sonar Transducers

This paper describes the construction of and behavior of a large spherical transducer formed as a mosaic of ceramic elements with no inactive material Formulas are shown that describe the several elements which form the building block of the assembly. The developed techniques indicate spheres up to 30 in. in diameter can be easily constructed and a modification of the basic element will permit much larger spheres to be built. Complete evaluation of a 10-in.-diam sphere is shown with efficiencies approaching 100%. Correlation between its evaluation and the theoretical report of S. Hanish at NRL is shown. Behavior in water indicates a good acoustic loading and wide-band operation.

Computation of Far-Field Radiation Patterns from Near-Field Measurements

The Helmholtz formula for the wave equation is used to compute the far-field radiation pattern of a large cylindrical transducer from pressure measurements made near the transducer. Radiation patterns are computed for a plane normal to the axis of the transducer by means of a numerical integration over the surface of a circular cylinder of finite length. The normal gradient of the pressure required in the formula is obtained by a simple approximation. The computed patterns compare favorably with measured far-field patterns. (This work is supported by the Bureau of Ships and the Office of Naval Research.)

Determination of Far-Field Radiation Patterns from Near-Field Measurements

The Helmholtz formula for the wave equation is used to determine the far-field radiation patterns of large transducers from measurements of the near-field pressures. It is shown that under suitable circumstances the normal component of velocity that is required in the formula can be related to the pressure. With the aid of this approximation, the far-field radiation pattern is computed from near-field pressure measurements for two transducers of different shapes. It is shown that the resultant patterns agree closely with the observed far-fields. (This work was supported by contract with the Bureau of Ships.)

Design of Large Variable Resonant Frequency Transducers

The transducer design described in this paper employs a mercury column of variable length intimately coupled to an electrically driven piezoelectric element so that a composite vibrating system is formed whose resonant frequency is capable of continuous variation. A large radiating area is realized by combining a number of such composite elements in the form of a matrix. This matrix arrangement is attached to a container which supports the mercury column. One dimension of this column is varied by means of a mechanically driven piston. The entire assembly is enclosed in a steel tank with a sound rubber window to permit its use as an underwater sound transducer.

A Note on the Effect of Test Distance on Directivity Patterns of Underwater Sound Transducers

In underwater sound work that requires large transducers with beams of only a few degrees, a problem often arises in regard to obtaining accurate calibrations with limited testing distances. At many of the available testing sites, directivity patterns must of necessity be made with the transducer either in the Fresnel region or in the critical region for true Fraunhofer diffraction. Several papers appear in the literature relating to corrections that can be made to measurements made on the acoustic axis of the beam, but little has been said regarding the effect on the directivity pattern for other orientations since it is very tedious to compute any such corrections. This paper presents some of the results of an experimental investigation as to the effect on beam width and secondary lobe structure. Measurements were made using both piston radiators and line source hydrophones.