Study on the vibrational characteristics of ultrasonic transducers using tapered piezoelectric ceramic elements

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Study on the vibrational characteristics of ultrasonictransducers using tapered piezoelectric ceramic elements

Rupa Mitra and T. K. SaksenaUltrasonics Section, National Physical Laboratory, Dr. K. S. Krishnan Road, New Delhi-110 012, India

~Received 19 November 1994; revised 29 July 1996; accepted 3 September 1996!

Any nonuniformity in the flatness of a crystal element used in an ultrasonic transducer may lead tosignificant variations in transducer response. An accurate estimation of such variations couldobviously be a measure of the nonuniformity involved, whatever its extent may be. Studies arereported on the effect of nonparallelism between two major plane surfaces of the crystal element ontransducer response by studying the normal displacement amplitude pattern and its distribution overone of the vibrating~plane! surfaces at resonance. Measurements are carried out in air using aphase-locked laser interferometry technique where the effect of tapering in disk thickness on thetransducer performance is manifested through the variation in vibrational patterns. Results of thesemeasurements are compared with those obtained from electrical~conductance! response to highlightthe importance of the former. Other comparison measurements, such as the conventional method ofdetermination of acoustic response and pulse waveforms of the radiated signals in water, are alsoreported as a function of tapering in disk thickness. A correlation is discussed between resultsobtained from different measurements. ©1997 Acoustical Society of America.@S0001-4966~97!02401-6#

PACS numbers: 43.38.Fx, 43.38.Ar, 43.35.Yb@SLE#

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INTRODUCTION

Uniform thickness piezoelectric crystals are employedconventional ultrasonic transducers for use as transmiand receivers. Such transducers produce a narrow-btransmit response when operated at resonance. A svariation of any crystal parameter such as disk thicknessmay be introduced in the processing of the disk, howevleads to a significant variation in transducer response1–8

which in turn could help in detecting the extent of nonuformity involved in transducer dimensions.

Tapering of the transducer could be caused inadvertaor could be introduced with a definite purpose. In the formcase, the nonuniformity in thickness is small, whereas inlatter it may assume larger proportions. Nowadays thepered transducers are finding increasing applications in Nand medical fields. For example, a linearly tapered pieelectric disk can be used as a broadband transducernearly uniform transmit response5–10 even without employ-ing a lossy backing layer. Using such tapered disks, the cplicated and relatively expensive backing treatmentavoided. Moreover, localized concentration of vibration ocrystal can be achieved fairly easily by tapering the disk. Tdisplacement amplitude of such a vibrating disk has bshown to be higher at the thicker part even for a very slitaper. As a specific case, a point source transducer madesigned using a centrally thick tapered transducer. In themode, a varying frequency can selectively excite resonportions of tapered ceramic and thereby achievfrequency-controlled acoustic beam translation. A tapephased array has been found to offer an accurate and effiheating of deep-seated tumors with the least heating ofrounding normal tissues and thus is useful for hyperthertreatment.11 An accurate knowledge of the vibrational chaacteristics of tapered transducers would therefore be esse

323 J. Acoust. Soc. Am. 101 (1), January 1997 0001-4966/97/10

ribution subject to ASA license or copyright; see http://acousticalsociety.org

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to obtain the right performance of the transducer and canused as an important design parameter.

Although a geometric measurement of taper is easymake, it cannot provide precise information about the traducer construction because of factors such as bondclamping, etc., in transducer construction. One has to trecourse to an acoustical method. The measuremenacoustic pressure has often been used for such studies. Ipresent work the object of investigation is to examiwhether vibrational amplitude measurements can be utilito provide necessary information about the tapered traducer. The point-to-point study by vibration amplitude mesurements would complement the overall study madeacoustic pressure measurements and give a connectivsight for better understanding of design perspectives. Moover, whereas the acoustic measurements give only a msure of the damping of transducer performance causedtapering, the vibration measurements provide a numbeparameters that can be used to distinguish transducerswith very slight difference of thickness gradient.

Vibrational characteristics of transducers having a laof parallelism between the major plane surfaces of piezoramic elements can be accurately and conveniently stuby the measurement of the normal displacement amplitpatterns near resonance using phase-locked laser interfeetry technique with high accuracy~3%–7%!.12,13 The mainfeature of this technique is that the effect of relatively lofrequency~up to 10 kHz! high amplitude~;mm! environ-mental vibrations on the low amplitude~;nm! high-frequency~;MHz! ultrasonic vibrations~to be measured! isminimized.12 It is proposed in the present work to study thvibrational characteristics of tapered transducers along wacoustic response and pulse waveforms in the vicinityresonance or its overtones and to examine the effect o

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pering in disk thickness on transducer response. Transdconductance is also studied in the preassigned frequerange and results are compared with those obtained fvibrational measurements. An attempt is then made to colate the variation in transducer~disk! dimensions with corre-sponding variations in the transducer response thus obtaSuch studies could be of significant use in the estimationdesign configuration of specific ultrasonic transducerscussed above and in the detection of slight tapering thatbe introduced inadvertantly. Each transducer used emplongitudinal thickness drive vibrations of thick wedgshaped disks of lead-zirconate titanate ceramic.

I. EXPERIMENT

A. Laser interferometer system

Figure 1 presents the block diagram of the phase-loclaser interferometer system that employs an He–Ne labeam of wavelength 632.8 nm and power 5 mW. The baarrangement is very similar to that of the Michelson interfometer, but modified for compensation of the effect of lofrequency ~&10 kHz! ambient vibrations in the signabeam.12,14–16The technique utilizes the electro-optic Pockeeffect17,18 by introducing a Pockels cell unit consistingsuitably oriented KD*P crystals in the path of circularly polarized laser light. Use of this unit and an appropriate feback system in between the reference and signal beamcuitries makes it possible to shift the frequency of treference beam by the same amount as the shift generatthe signal beam by low-frequency ambient vibrations.15,17

The feedback circuit, having a characteristic time constwhich is small compared to the time of one cycle of enronmental vibration, is unable to respond to the higfrequency ultrasonic signals to be detected at the outputhe interferometer.12 As the signal and reference beams aorthogonally polarized, the amplitude fluctuations from intference can be detected by a second polarizing beam spplaced at 45° to the plane of polarization of the beams. Wcorrect gain in the feedback loop, the interferometer is banced and very sensitive to small ultrasonic displacem~j! in the range 0–150 nm are found, which are compuusing the following relation

j~ t !5sin21@~Vi /V0!•~l/4pn!#, ~1!

whereVi is the output signal of the interferometer.V0 is thereference or fringe voltage,l is the wavelength in vacuum othe laser light used~632.8 nm!, andn is the refractive indexof the medium concerned. Forj!l/4. Equation~1! may beexpressed as

j~ t !5@~Vi /V0!•~l/4pn!#, ~18!

which has been used in the present study to computerequired displacement amplitude.

B. Measurements of vibrational amplitude, acousticoutput, and electric conductance

To study the vibrational amplitude patterns, each traducer was excited with a Wavetek~model 166! function gen-erator connected with a pulse generator~Systronics, model

324 J. Acoust. Soc. Am., Vol. 101, No. 1, January 1997


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1110/D! to generate the required sinusoidal tone-burst sigof 0.8-ms duration. The excitation voltage is mentionedeach corresponding figure~Fig. 3!. As the transducers produced relatively weaker peak amplitudes at higher harmics, the excitation voltage at those frequency ranges ascreased to obtain prominent vibration amplitude. The poinwhich the excitation voltage was increased is denoted bdashed vertical line in the figure.

For the measurement of acoustic response in water

FIG. 1. ~a! Schematic block diagram of optical phase-locked laser interometer.~Quarter wave plates are indicated byl/4.! ~b! Sectional view ofmounted transducer 4.~c! Schematic of excitation of the transducer.~d!Schematic of the measurement of acoustic response of the transducera probe hydrophone.

324R. Mitra and T. K. Saksena: Tapered ceramic elements


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far field axial point, the transducer was excited by the simprocess@Fig. 1~c!#, as described above, and a PVDF prohydrophone~Medisonics, needle type! connected with a preamplifier ~Medisonics Mk II, 30-dB gain! and an oscillo-scope was used as a receiver@Fig. 1~d!#. The tip of the hy-drophone was placed at an axial distance of more than 2a2/lfrom the transducer surface, where ‘‘a’’ and ‘‘ l’’ are, re-spectively, the radius of the transducer and the wavelengtradiation in water. The transducer impulse responsestudied by driving it with spike signals obtained fromKrautkramer ~model USIP-11! flaw detector operating aspecific frequencies. For acoustical measurements the trducer was connected through a two-way key@Fig. 1~c!# toarrange for the excitation either by tone-burst signalsspike signals. The vibration amplitude measurements wtaken in air and the transmitting response measuremenwater because of the high absorption coefficient and the csequent absorption correction in air.

Electrical conductance of the transducers has been sied in the frequency range 100–1000 kHz covering the fdamental and higher harmonics, at a step frequency okHz. A vector impedance analyzer~Hewlett-Packard 4192A!was used for this measurement which provides the maximexcitation voltage of 1.1 V to the transducer concerned.

C. Fabrication of the transducers

Each transducer consists of an axially polarized cylindcal disk of lead-zirconate-titanate ceramic with zero or lintapering in thickness. The ceramic disks were fabricatedthe National Physical Laboratory, India, and have the elaand piezoelectric properties equivalent to those of standPZT-5A ceramic having the dielectric constantk3

T51700 anddielectric loss factor tand50.025. The sectional view of thtransducer with highest tapering is shown in Fig. 1~b!. Oneof the two major~plane! surfaces has been optically polisheand then silver plated for use in the interferometer. Telectrical terminals have been taken from the two silplated surfaces where an air-drying conducting silver pawas used to make electrical contacts. The dimensionspiezoelectric charge constants~d33! of the four disks em-ployed in the study are tabulated in Table I. The study thcomprises the evaluation of performance characteristicultrasonic transducers with a different degree of taperingdisk thickness.

TABLE I. Physical parameters of transducer elements. Diameter (D) ofeach disk53060.02 mm.

Transducerserial number

Tapering in diskthickness (t)

in mm

Thicknessgradient

(m5Dt/D)

Charge const.~d33!pC/N

1 11.5~const.! 0 3202 11 to 12 0.03 3363 6 to 10 0.13 3104 4 to 11 0.23 298



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II. RESULTS AND DISCUSSSIONS

Studies were carried out on the vibrational charactetics together with the electrical as well as acoustical behaof the four transducers in the frequency range 100–1kHz, which covers the fundamental resonance and highorder overtones. Results of measurements of various paeters are reported in the following subsections.

A. Study on electrical conductance ( G)

Figure 2 represents the conductance patterns of thetransducers in the preassigned frequency range. Transdu

FIG. 2. Variation of conductance with frequency for different tapered traducers.



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with no tapering in disk thickness~with a tolerance of60.02mm! shows a fairly monochromatic response@Fig. 2~a!# witha prominent resonance peak at 167 kHz which is surrounby two smaller peaks~214.5 dB with respect to the maione! appearing in a frequency band of 80 kHz~Table II!.Transducer response at the third harmonic~at 551 kHz! ap-pears with the peak amplitude 5 dB lower than that offundamental one. A fifth harmonic peak at 917 kHz~29.9dB! is also observed.

The conductance pattern of transducer 2 with slightpering in disk thickness~the thickness gradient being 0.03!produces the main resonance peak at 169 kHz@Fig. 2~b!#accompanied by two close-by subsidiary peaks~213 dB ref-erence to the main one! of slightly higher amplitude com-pared to that of the corresponding ones appearing in thevious case. Moreover, the frequency spread for smaller pe~95 kHz! is also higher compared to the previous caTransducer response at the third harmonic is found tomuch weaker~211.4 dB! compared to that at the fundametal and also with reference to the corresponding amplituobserved for zero tapering. The fifth harmonic peak~at 898kHz! is still weaker~212 dB!. Electrical measurements thupresent the differences in transducer characteristics for trducers with slight variation of tapering, through the amptude ratio between main-to-subsidiary peaks near fundamtal resonance and through that between fundamentaharmonic ones. Unlike the two cases discussed,conductance pattern of transducer 3 with a thickness gradof 0.13 presents a number of smaller peaks@Fig. 2~c!# in thefundamental resonance region in a frequency spread ofkHz ~Table II! which is much broader than that observedthe two cases discussed earlier. The transducer thus shomultiresonance characteristic at the fundamental withmain peak at 270 kHz and almost negligible responsehigher harmonics. An introduction of an additional dampito the transducer by employing a suitable backing couldsult in a flatter vibrational pattern and thus lead to a broband response at the fundamental region. The transdwith highest tapering in disk thickness~the gradient being0.23!, transducer 4, produces several secondary peaknearly the same order of amplitude which appear in funmental resonance region in a frequency range of 315 kThe transducer shows no response at higher harmonics.further noticed that the peak value of the fundamental renance conductance (Gm) in this case is much less~,6 dB!than that observed in each of the earlier three cases stu

TABLE II. Comparison of the electrical responses of different tapethickness transducers.

Transducerserialnumber

Taperingin diskthicknessin mm

No. ofsecondarypeaksnear

resonance

Ratio in dBbetween mainpeak ampl. toav. of secondarypeak ampl.

Frequencyspreading ofpeaks nearresonance

~kHz!

1 11.5~const.! 2 14.5 802 11 to 12 2 13.0 953 6 to 10 4 5.9 1704 4 to 11 6 4.8 315



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although the values of piezoelectric charge constant~d33! ofall the disks are of the same order~Table I!. The low value ofGm could be attributed to the processing condition for tpresent disk. The response of this transducer is observehave the widest frequency spread for the discrete peaksresonance, among all the four transducers concerned.

The electrical response of the transducers thus makobvious that a tapering in disk thickness results in the mtiresonance pattern, i.e., an inhomogeneous broadening infrequency-domain response. It also leaves a transduceractive at the harmonic region.

B. Study on the vibrational amplitude ( j)characteristics

The displacement amplitude patterns of the four traducers in the preassigned frequency range, measured ocentral points of radiating surfaces, are depicted in FigEach transducer was excited with a sinusoidal tone-burstnal of duration 0.8 ms and a p–p driving voltage (VD) asmentioned in each corresponding figure.

The displacement amplitude pattern of transducer 1~notapering! @Fig. 3~a!# produces nearly a similar sort of response as obtained from the conductance [email protected]~a!#. Apart from the main resonance peak at 167.1 k~with amplitudejm556.8 nm orjm/VD52.03 nm/V! and afew discrete peaks in its vicinity, there appears a continudistribution of average amplitude of 7.5 nm in the frequenrange 130–200 kHz~Table III!. Such a vibrational characteristic implies that the transducer does vibrate up to anservable extent over this frequency band, which cannotdetected from the corresponding electrical measurem@Fig. 2~a!#. This could be mainly due to the low excitatiovoltage ~1.1 V, which is the maximum limit of the experimental setup for the HP 4192A impedance analyzer! appliedin the latter case. The displacement amplitude measuremis thus found to be more nearly precise and informative copared to the electrical measurements. It may be mentiothat a uniform parallel-plate transducer is expected to pduce a sharp resonance with negligible spurious vibrationits vicinity. It thus appears from the vibrational amplitudpattern of transducer 1 that there exists some nonuniformin the disk employed for it.

Figure 4 displays the traces of displacement amplituprofiles on resonating transducer surfaces~at main resonancefrequencies! as measured along a diameter connecting poon maximum and minimum thickness. The increasing thiness or the positive thickness gradient~1veDt! is indicatedin Fig. 4~b!–~d! through arrow marks. The displacement amplitude profile for transducer 1@Fig. 4~a!# is observed to benonuniform, although axially symmetric with a central maxmum and no side lobes. Similar forms of profiles have bereported in the literature by earlier authors like Shaw,19 Ly-pacewicz and Filipczinski,20 and Arnold and Martner21 forshort barium titanate and PZT transducers.

Transducer 2, the slightly tapered one~with gradient0.03!, produces the fundamental resonance~at 169.3 kHz!with jm/VD51.61 nm/V @Fig. 3~b!# which is accompaniedby a few discrete peaks along with a continuum of averadisplacement amplitude 6 nm in the frequency range 12



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230 kHz~Table III!. A comparison between Fig. 3~a! and~b!reveals a spreading of the continuum of transducer vibranear resonance and an observable lowering of highermonic amplitude caused by slight tapering. In a more neaideal case of transducer 1, which in the present case is lito have some nonuniformity in its configuration, the abocomparison would produce a clearer distinction betweenvibration patterns of the two transducers concerned. Theplacement amplitude profile on the surface of transducenot only represents a nonuniform distribution ofj but anaxial asymmetry is noticed with more concentration of vibtion in the thicker part of the disk. An identical distributiowas theoretically estimated by Loutzenheiser aDenkmann1 for a truncated, linearly tapered quartz crys

FIG. 3. Variation of vibrational amplitude with frequency for different tpered transducers.



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strip in thickness vibration. It is noticed that although the tw6-dB points are equally separated in the profile fromcentral peak for transducer 1@Fig. 4~a!#, there is a differenceof 2 mm for the corresponding values of transducer [email protected]~b!# where the peak is shifted slightly toward the highthickness side. The displacement amplitude characterisas studied by optical phase-locked laser interferometry, tprovide significant information regarding the true vibratiopatterns of the transducers. Use of a slightly tapered dsuch as that used in transducer 2, reveals an estimation oobtainable precision of present experimental setup.

Figure 3~c!, the displacement amplitude pattern of tranducer 3, exhibits several prominent peaks~with the highestone ofjm/VD51.4 nm/V! of varying amplitude~15–40 nm!in the fundamental resonance region. This multiresonapattern is again superimposed over a continuum of displament amplitude in a wider frequency range~130–350 kHz!.The transducer response does not show any prominentat higher harmonics. The displacement amplitude pro@Fig. 4~c!# in this case shows more nonuniformity in thdistribution of normal displacement amplitude comparedthe previous case.

Variation of j with frequency for transducer 4, formewith the highest tapered disk@Fig. 3~d!#, presents severapeaks in the fundamental resonance region, the pattern shing great resemblance to the corresponding electrical

FIG. 4. Displacement amplitude profiles on resonating transducer surfa

TABLE III. Relative performance of the four tapered transducers asserved from displacement amplitude measurements.

Transducerserial number

Ratio in dB of mainpeak amplitude tothat of continuous

distribution

Freq. spread of continuousdistribution ofpeaks in kHz

1 17.3 702 16.8 1103 16.2 2204 16.0 310



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sponse@Fig. 2~d!#. The highest one at 240.3 kHz appeawith jm/VD51.15 nm/V. An observable continuum of relatively high displacement amplitude appears over thequency range 150–460 kHz, the spread being the highethis kind studied here~Table III!. The transducer, thereforecan be fairly operated through a wide frequency rangeconsiderably high uniform output over which the discrepeaks are superimposed. The transducer, however, showresponse, at higher harmonics. The displacement ampliprofile @Fig. 4~d!# shows the maximum nonuniformity observed thus far in the present study. The gradual decreajm/VD with increasing tapering can be explained in the flowing way. As the number of resonance peaks or the ctinuum near resonance spreads with increasing taperingacoustic energy of the transducer at resonance gets disuted among all the peaks instead of being concentratedsingle resonance peak. This could lead to the lowering ofmain peak amplitude.

The effect of tapering in disk thickness on the vibrtional characteristics of ultrasonic transducers is observethe appearance of multiresonance patterns in the fundamresonance region and in the widening of frequency spreathe continuum of vibration amplitude around the resonafrequency. Additionally, the displacement amplitude profion the resonating transducer surface becomes axially asmetric, showing higher concentrations of vibration in tthicker part.

Vibrational amplitude measurements thus providefollowing three parameters for the analysis of transducer pformance:

~i! Frequency spread of resonance peaks or a continof j;

~ii ! Asymmetry in profile with higher amplitude in thickepart;

~iii ! Lowering of the higher harmonic peak amplitudetapered transducer.

C. Study on the acoustic output of the transducers

Vibrational characteristics of a transducer are commostudied through its temporal and frequency response wemployed as a transmitter. Several experimental studieacoustical measurements with tapered ultrasonic transduand their theoretical interpretations are reported inliterature1,7,8where the impulse response~pulse waveform ofacoustic output! and frequency response are mainly dscribed. For example, in their study on tapered ceramics8 byBarthe and Benkeser, the theoretically evaluated electricput impedance, spectral content, pulse, and continuous-wpressure profile responses obtained by using a model wfound to agree well with the measured response of a tappiezoelectric transducer. In the present work it is proposeexamine whether there is any correspondance betweenresults on vibrational patterns and those obtained from cventional acoustical measurements with tapered ultrastransducers, to throw light on transducer design aspects fthe knowledge of vibrational characteristics. To find that crespondence the effect of tapering in disk thickness has bstudied by observing the impulse response, i.e., pulse w



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forms of different transducers when driven with a spike voage. Transducers with uniform thickness~transducer 1!,slightly tapered~transducer 2!, and highly tapered~trans-ducer 4! disks have been used for this purpose. Photograof the pulse waveforms obtained by using a probe hydphone placed at a far-field axial point for each of the abothree cases are shown in Fig. 5~a!–~c!. It is very clear fromthe figure that a transmitter with parallel faced element girise to an output signal having the longest duration~the 6-dBdiminution of peak amplitude is obtained at a duration ofms!. A slightly tapered transducer@Fig. 5~b!# produces ashorter time response~6-dB diminution at 10-ms duration!,whereas the corresponding time is least for the highlypered@Fig. 5~c!# transducer for which the 6-dB diminution iachieved at 4ms. A comparison of Figs. 3, 4, and 5 thureveals that the shorter the time response of acoustic oufrom the transducer, the wider the frequency spread ofcrete peaks or the continuum near resonance and the mnonuniform the profile corresponding to a highly taperdisk.

FIG. 5. Photographs showing the pulse waveforms from different transders: ~a! transducer 1~t511.5 mm!; ~b! transducer 2~t511–12 mm!; ~c!transducer 4~t54–11 mm!.



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In the next step, tone-burst sinusoidal excitation withsingle cycle was employed to drive the transducer operaas a transmitter, and the frequency response near resonwas measured for vibration in water. Studies were carriedat a far-field axial point of each transducer using the saprobe hydrophone~Medisonics! and the results are depictein Fig. 6. With increasing tapering the 3-dB bandwidth icreases, resulting in a lowering of theQ factor of the trans-ducer. A significantly high acoustic output is obtained withhighly tapered transducer. This could be because of thethat tapering by gradually diminishing the thickness alondiameter results in a reduction of mass of the whole dConsequently, the relatively lighter transducer is capablevibrating with a higher amplitude and thereby transmittimore acoustic energy into the surrounding medium, ewhen driven by the same excitation voltage as applied tomore uniformly thick-disk transducers. An increase in renance frequency (f r) is also observed in each case for tmeasurements in water. Although an increase in loadingpedance is expected to decrease the value off r , an increasein this value caused by specific backing or loading, whichrather unexpected, has also been reported in the literatu22

III. CONCLUSION

The effect of tapering on the disk thickness of ultrasopiezoelectric transducers on their characteristics is mamanifested by a frequency spread of resonance peakscontinuum in the vicinity of resonance, as observed frvibrational amplitude and conductance patterns. The traducer becomes less active at higher harmonics becaustapering. Tapering also causes the displacement ampliprofiles on resonating transducer surfaces to be axially asmetric, where the vibration is more concentrated towardthicker part. As it is observed that even a slight taperaffects the vibrational pattern up to an observable extent,vibrational amplitude measurements would be very usefor detection of any tapering that may be introduced evenoversight.

FIG. 6. Transmitting response of different transducers.



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ACKNOWLEDGMENTS

The authors are thankful to the Director, National Phycal Laboratory, India, for giving permission to communicathe paper for publication. One of the authors~R.M.! is grate-ful to the Council of Scientific and Industrial Research, Indfor providing her financial assistance in the form of a rsearch fellowship.

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Documents

Study on the vibrational characteristics of ultrasonic transducers using tapered piezoelectric ceramic elements