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Radiating Wideband Sonar Pulses with Resonant Sandwich Transducers by Designing the Driving Voltage Waveform P. Cobo, C. Ranz, and M. Siguero Instituto de Acústica, CSIC. Serrano 144. 28006 Madrid. SPAIN A technique to radiate short length, high resolution, pulses with conventional piezoelectric transducers is described. It consists on designing the driving voltage waveform so that the radiated pulse has a zero-phase cosine-magnitude spectrum compatible with the natural frequency response of the transducer. According to Berkhout [1], zero-phase cosine-magnitude pulses have the minimum length, maximum resolution, within a prescribed frequency band. When applied to a 9 kHz sandwich transducer, this technique decreases the pulse length from 1 ms to 0.13 ms, increases the bandwidth from 1.4 kHz to 11.25 kHz, and lowers the Q factor from 6.2 to 1.23, at the cost of 33% of amplitude loss. INTRODUCTION H *( f ) X e ( f ) Ye ( f ) , (2) H( f ) 2 p 2 An underwater transducer is driven usually by a tone-burst. However, Winter et al. [2] and Mazzola 2 and Raff [3] showed that is possible to use Fourier where p is a regularisation constant, and * denotes techniques to find the electrical driving function so conjugate complex. Therefore, the electrical function that the transducer radiates a prescribed acoustic which must be synthesized is waveform. Holly et al. [4] reported that a transducer driven with a shaped function responded in two '$ '4 ]1 ]1 H *( f ) octaves, with an amplitude loss of 15 dB. xe (t) X e ( f ) %Ye ( f ) 5 (3) 2 2 Cobo [5] applied this technique to synthesize zero- &' H( f ) p 6' phase cosine-magnitude, gaussian, and bionic pulses, with a conventional sandwich transducer. According where ]1 denotes inverse Fourier transform. Zero- to Berkhout [1], zero-phase cosine-magnitude phase cosine-magnitude pulses are given by waveforms provide minimum length, therefore maximum resolution, pulses within a prescribed $ ! f f 1 frequency band. ' 0 ? ? cos " 2 f1 f f2 Ye ( f ) % # B 3 (4a) ' METHODS & 0 f f1, f f 2 and A transducer can be modelled as a linear system, e ( f ) 0 (4b) with a transfer function H(f), which can be measured. In conventional performance, the transducer is driven where Y ( f ) and ( f ) are the magnitude and by an electrical input, and radiates an acoustical e e waveform. However, an acoustical waveform can be phase spectra, respectively, is a trade-off parameter prescribed, Ye(f), and the corresponding electrical between main and side-lobes on the shaped pulse [6], driving function, Xe(f), can be accordingly ( f1 , f 2 ) is the frequency band, f0 ( f 2 f1 ) / 2 is synthesized the central frequency, and B ( f 2 f1 ) is the bandwith. Y ( f ) e Thus, the shaped waveform depends on four X e ( f ) .(1) H ( f ) parameters: S ( f1 , f 2 ) , the lower and upper frequencies of Since acoustical transducers are band limited, Y(f) the band. have to be chosen compatible with their frequency S , the trade-off parameter. response band. Also, for the shake of stability, Eq. (1) S p2, the regularisation parameter. must be modified to These parameters are chosen according with the mechanical frequency response of the transducer. Table 1. Summary of properties of the conventional and RESULTS synthesized pulses Time Frequency To illustrate the technique, let’s apply it to a Ampl. Length B Q transducer resonant at 9 kHz. The transducer is a (V) (ms) (kHz) Tonpiltz with 4 PZT-4A ring ceramics sandwiched Tone-burst 9.47 1.015 1.4 6.2 between backing (steel) and matching (aluminium) Zero-phase 6.29 0.135 11.25 1.23 layers. Figure 1 shows the acoustic waveforms cosine- radiated by this transducer when it is driven by tone- magnitude burst (4 cycles at 9 kHz) and synthesized electrical functions, as well as the corresponding envelopes. The 60 synthesized function was designed to radiate zero- 2 tone-burst phase cosine-magnitude pulses with f1, f2 , , p = 50 {6 kHz, 20 kHz, 0.25, 2.5}. Figure 2 shows the log- magnitude spectra of both pulses. Notice as this 40 technique flattens (equalises) the response of the zero-phase cosine-magnitude transducer within its natural frequency band. Table 1 30 summarises the characteristics of both pulses, in the time and frequency domains. The drastic reduction in 20 pulse length (widening of the frequency band) (dB) LOG-MAGNITUDE involves, as a counterpart, an amplitude loss. 10 10 0 (a) tone-burst 8 10 12 14 16 18 8 FREQUENCY (kHz) 6 FIGURE 2. Log-magnitude spectra of the tone-burst and zero-phase cosine-magnitude zero-phase cosine-magnitude pulses 4 2 CONCLUSION 0 -2 A drastic improvement of the vertical resolving AMPLITUDE (V) AMPLITUDE -4 power of acoustic pulses can be gained by driving the transducers with a more sophisticated electrical -6 waveform. -8 -10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ACKNOWLEDGMENTS TIME (ms) This work was funded by Cervera Centre, S.A. 10 (b) (Spain). 9 tone-burst 8 REFERENCES 7 6 zero-phase cosine-magnitude 1. Berkhout, A.J., Seismic Resolution. Geophysical Press. 5 London 1984. 4 2. Winter, T.G., Pereira, J., and Bednar, B. Ultrasonics, 13, AMPLITUDE (V) AMPLITUDE 3 110-112 (1975). 2 3. Mazzola, C.J. and Raff, A.I. Journal of Sound and Vibration, 53, 375-388 (1977). 1 4. Holly, A.C. Journal of the Acoustical Society of America, 0 75, 973-976 (1984). -1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5. Cobo, P. Journal of Sound and Vibration, 188, 131-144 TIME (ms) (1995). 6. Cobo, P., Ranz, C., and Cervera, M. Geophysical FIGURE 1. Tone-burst and zero-phase cosine- Prospecting, accepted for publication (2001). magnitude pulses (a) and envelopes (b) Transverse current monitoring in a range dependent ocean Igor B. Esipova, Oleg B. Ovchinnikova, Yury I. Tuzhilkina, Konstantin A. Naugolnykhb, Ola M. Johannessenc aN. Andreev Acoustics Institute, 4 Schvernik St., Moscow, 117036, Russia bCooperative Institute for Research in Environmental Science (CIRES), University of Colorado/ Environmental Technology Laboratory,National Oceanic and Atmospheric Administration(NOAA)/ZelTech 325 Broadway, Boulder, CO 80305, USA cNansen Environmental and Remote Sensing Center, Edvard Griegsvei 3A, N-5037 Bergen, Solheimsviken, Bergen,Norway, Space-time scintillation analysis [1] offers a promising method of remote acoustic sensing of current in ocean. The evolution of the scintillation pattern at receiving array is related to the advection of the inhomogeneous medium through the sound beam, thus providing a basis for flow velocity measurement. In a range dependent ocean the sound signal structure changes due to variation of rays configuration. The source/environmental information smeared in mode space -- that means the information given by a single mode at receiving array is not presented by this mode. However, using the average characteristics of signal arrivals provides the opportunity to apply the signal scintillation technique for the transverse current measurement in complex environment. ACOUSTIC SCINTILLATION reflects the compression or dilatation of the arrivals METHOD pattern, it consists of defining the trend in the signal- arrival spectrum caused by the sound speed profile changes in the stratified ocean. Sound signal passing through the ocean fine structure is modulated, producing an irregular pattern of amplitude and travel time variations at the receivers. These variations evolve as the intervening medium NUMERICAL MODELING changes. Under assumption that the fluctuations in the medium are produced mainly by the advection of a Oceanographical data frozen fine structure field (Taylor's model of As an example of range-dependent ocean, the Fram turbulence), evolution of the signal pattern can be Strait environment is considered in the present paper. directly linked to the motion of the medium. This Two major components of the Greenland and allows determination of transverse component of the Norwegian Seas circulation determine the Fram Strait current by measurements of the time lag between the environment: the West Spitsbergen Current (WSC) and signal variations at two closely spaced receivers. The the East Greenland Current (EGC). The WSC consists application of the array of the transivers allows to of warm, saline water with a temperature of 2 – 50 C make the spatial filtering of acoustic scintillation and even in winter and a salinity of about 35.5‰, reflecting to get the spatial distribution of the current velocity its origin far to the south, and occupies approximately [1,2]. the region between 30 30' E up to 9030' E. In the region In a range dependent ocean the sound signal of the WSC, the shallow shelf extends from the structure changes due to variation of rays Spitsbergen coast westward to about 80 30', where the configuration. The source/environmental information is depth increases sharply. The total volume transport of smeared in mode space -- that means the information the WSC scaling is in a range of 3 - 10 and varies when given by a single mode at receiving array is not measured during a period of several months. The presented by this mode, but each mode made a model of the current velocity distribution in the strait is contribution at each distance. Conventional space-time presented in Fig. 2 by the solid line. It is important to scintillation analysis is not applicable in this case. provide the permanent monitoring of the mass and However, it is possible to find some stable heat flux through the Fram Strait that can be made by characteristics of the sound signal such as collective the application of acoustic methods. The temperature time or cumulative sum of arrivals [3,4].
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