RECIPROCITY CALIBRATION OF A SONAR TRANSDUCER FROM ELECTRICAL IMPEDANCE MEASUREMENTS IN WATER AND IN AIR : THE DELTA-Z RECIPROCITY CALIBRATION METHOD S. Baker, R. Bedard, M. Patton, O. Wilson To cite this version: S. Baker, R. Bedard, M. Patton, O. Wilson. RECIPROCITY CALIBRATION OF A SONAR TRANSDUCER FROM ELECTRICAL IMPEDANCE MEASUREMENTS IN WA- TER AND IN AIR : THE DELTA-Z RECIPROCITY CALIBRATION METHOD. Journal de Physique Colloques, 1990, 51 (C2), pp.c2-1291-c2-1294. <10.1051/jphyscol:19902303>. <jpa-00230645> HAL Id: jpa-00230645 https://hal.archives-ouvertes.fr/jpa-00230645 Submitted on 1 Jan 1990
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COLLOQUE DE PHYSIQUE Colloque C2, suppl6ment au n02, Tome 51, FBvrier 1990 ler Congrgs FranCais d'acoustique 1990 RECIPROCITY CALIBRATION OF A SONAR TRANSDUCER FROM ELECTRICAL IMPEDANCE MEASUREMENTS IN WATER AND IN AIR : THE DELTA-Z RECIPROCITY CALIBRATION METHOD S.R. BAKER, R. BEDARD, M.D. PATTON and O.B. WILSON Code 61, Naval Postgraduate School, Monterey, CA 93943, U.S.A. Abstract -- A method is described by which the free-field, open-circuit voltage sensitivity of a reversible underwater acoustic transducer may be obtained from measurements of its input electrical impedance in water and in air. This method, which we have termed the Delta-Z reciprocity calibration method, is being developed for the in-service calibration of sonar transducers installed in domes which can be flooded and purged. The application of the Delta-Z method to the calibration of a single tonpilz-type piezoelectric sonar transducer is described. The resulting sensitivity obtained using the Delta-Z method agrees within approximately one decibel with that obtained by a standard comparison calibration procedure over a twooctave frequency band about the nominal operating frequency of the transducer. 1 -- INTRODUCTION A variety of methods exist for establishing the absolute receiving sensitivity of a transducer which are based upon the reciprocal property of the acoustic field /I,2/. In general, these reciprocity methods do not require the transducer being calibrated to be reversible. A reciprocity method is described herein which does not rely upon the reciprocal property of the acoustic field; rather, it relies upon the reciprocal property of a reversible transducer. In particular, it will be shown that the sensitivity of a reversible electroacoustic transducer is proportional to the square root of the difference of its input electrical impedance when loaded and unloaded; hence we have termed this method the Delta-Z reciprocity calibration method. This method is being developed for application to the in-situ calibration of sonar transducers installed in domes which can be flooded and purged. 2 -- THEORY The description of the Delta-Z reciprocity calibration method is in terms of network theory. A reversible electroacoustic transducer in an acoustic field is represented by the pair of coupled networks shown in Figure 1 /3/. Electrical Transducer Mechanical Acoustic Port Port Field TU Ti Pb Figure 1. Network representation of a reversibie electroacoustic transducer in an acoustic field. The network equations are e=zebi+ TU, p= Ti+ Z,U, where e = voltage across the transducer's electrical terminals, i = current through the transducer's electrical terminals, Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19902303
C2-1292 COLLOQUE DE PHYSIQUE p = acoustic pressure averaged over the transducer's radiating face. U = volume velocity of the transducer's radiating face, dkcted into the transducer for positive U, 2, = transducer blocked (Ud) electrical impedance, Za0 = transducer open-cwit (id) acoustical irnpedanu?, T = transduction coefficient, & = acoustical radiation impedance, pb = blocked (Ud) acoustic pressure averaged over the transducer's radiating face, D = diffraction constant, pf = incident free-field pressure, i.e. the pressure at the location of the transducer in its absence. Here, and throughout this paper, the transducer is considered to be reciprocal; the extension of the theory to the case of an anti-reciprocal transducer is straightforward and does not change the magnitude of the finalresult. By considering the three cases of: 1) the transducer unloaded 0). 2) the transducer, loaded by the acoustic radiation impedance Z, with pf= 0, and 3) a plane wave incident upon the open-circuited transducer loaded by Z, it may be shown 141 that the open-circuit, free-field voltage sensitivity of the transducer, M, is given by where AZ is the difference in the transducer input electrical impedance when the mechanical terminals are loaded by Z, and unloaded, respectively. For an underwater acoustic transducer the unloaded condition is approximated by placing the transducer in air, and the loaded condition is in water, so that is given by where Zm and ZEA are the transducer input electrical impedances in water and air, respectively. Equation 2 shows that, if D, Z, and Z, are known, the free-field voltage sensitivity of a reversible underwater transducer may be obtained from the difference in its input electrical impedance in water and in air, without the need to know the blocked eledtrical impedance. Additionally, apart from isolated frequencies of mechanical resonance, it is usually the case for underwater transducers that Z,>>Z, in which case equation 2 reduces to Hence, the acoustical impedance of the transducer only needs to be known near frequencies of mechanical resonance. This is an extremely usen result. Accurate values of D, &, and Zao as a function of frequency are required to obtain precise results using Equation 2. Analytic expressions for D and Z, may be found for only the most simple geometries ; values of D and Z, for more complicated geometries must be obtained by numerical means. 3 -- -TION OF DRTA-Z MJ?THOD TO -ON OF A TONPIr ZTYPE PrezOELECXRlC SONAR TRANSDUCER 3.1. Description of Experiment The Delta-Z reciprocity calibration method was applied to a tonpilz-type piezoelectric sonar transducer. A Hewlett- Packard Model 4192 Low Frequency Impedance Analyzer, controlled by a Hewlett-Packard Model 9826 Laboratory Computer, was used to obtain the input electrical impedance of the transducer in water and in air over a two-octave frequency band about the nominal operating frequency of the transducer. Impedance measurements were made in the large, anechoic pool at the Transducer Evaluation Center (TRANSDEC), Naval Ocean Systems Center, San Diego, CA, and in the small water tanks at the Naval Postgraduate School. A standard comparison calibration procedm was also performed at TRANSDEC. 3.2. Numerical conmutation of D and Z, by the finiteelement method The diffraction constant D and acoustical radiation impedance Z, were computed using the finiteelement computer program CNlEF /5,6/ using a model adapted from one developed by Bloman and Webman 171.
The CHIEF program computes the mechanical radiation impedance matrix, Zij = Fibj, where Fi is the acoustic force acting on the ith element, and uj is the normal component of the velocity of the j?h element, and the far-field pressure in a specified direction, pff, referred to a distance of one meter from the source. The mechanical radiation impedance matrix elements from CHIEF were combined to obtain the acoustical radiation impedance Z, according to /s/ where Ai is the surface area of the ith element, and the sum is only over active face elements. In computing Z, the velocity distribution across the active face was assumed to be uniform. The diffraction constant, D, was obtained from the computed far-field pressure at a distance d, pdd), using the reciprocal property of the acoustic field /9,10/, according to where U is the assumed volume velocity of the transducer to produce pdd), and J, = 2d/pf is the spherical-wave reciprocity parameter. Only the on-axis diffraction constant was calculated, so the resulting free-field sensitivity obtained using Equation 2 is for on-axis incidence. Because of their construction, the open-circuit acoustical impedance of a typical underwater transducer is very difficult to obtain by direct measurement. Instead, Z, was extracted from the measured values of the input electrical impedance in water and in air, ZEW and ZEA, and the computed values of the acoustical radiation impedance, Zar, using an approximate equivalent circuit model for zero incident field, shown in Figure 2 11 11. Figure 2. Approximate equivalent electrical circuit model of the transducer for zero incident field. The blocked electrical impedance ZEB in Figure 1 is modeled here by the capacitance Co; the electrical equivalent of the series combination of the transducer open-circuit acoustical impedance Z, and the acoustic radiation impedance Z, is modeled by the series LRC circuit. The acoustic field contributions to L and R (subscript AR) are taken to be zero for the transducer in air. Values of the circuit elements in Figure 2 were obtained from the in-air and in-water impedance data by a least-squares curve-fitting procedure. Then, using the fact that both the transducer and radiation field acoustical impedances transform from the mechanical port to the electrical port by the same ratio, Z, was found from the values of Z, computed using Equation 5 by 1121 4 -- RESULTS Figure 3 shows the results of applying the Delta-Z method and the results of a standard comparison calibration procedure.
COLLOQUE DE PHYSIQUE 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 flfo Figure 3. Relative, on-axis, free-field, open-circuit voltage sensitivity level of a tonpilz transducer obtained by the Delta-Z method and by a standard comparison calibration procedure. Both the frequency and the relative sensitivity scales have been normalized to the values obtained for the sensitivity peak by the standard comparison calibration procedure. The sensitivity obtained by the Delta-Z method agrees within approximately one decibel with that obtained by the standard comparison calibration procedure over a twooctave frequency band about the nominal operating frequency of the transducer. 5 -- SUMMARY AND CONCLUSIONS A method has been described, which we have termed the Delta-Z reciprocity calibration method, by which the absolute sensitivity of a reversible underwater acoustic transducer may be obtained from measurements of its input electrical impedance in water and in air. The results of the application of this method to a tonpilz-type piezoelectric sonar transducer agree within approximately one decibel with the results of a standard comparison calibration procedure over a two-octave frequency range about the transducer's nominal operating frequency. It is concluded that the Delta-Z method is a good candidate for application to the in-situ calibration of sonar transducers installed in domes which can be flooded and purged. This work was sponsored by the Naval Research Laboratory, Underwater Sound Reference Detachment, the Submarine Systems Monitoring and Maintenance Support Office of the Naval Sea Systems Command, and the Naval Postgraduate School. REFERENCES /I/ Bobber, Robert J., Underwater Electroacoustic Measurements, U. S. Govt. Printing.Office, 1970, reprinted by Peninsula Publishers, Los Altos, CA, 1988, pp. 27-45. /2/ Rudnick, Rudnick, I., "Unconventional reciprocity calibration of transducers", J. Acoust. Soc. Am. 63, 1923 (1978). /3/ Ref. /I/, p. 23. /4/ Bedard, R., "Reciprocity calibration of an underwater transducer by the Delta-Z method, M. S. thesis, Naval Postgraduate School, Monterey, CA 93943, Dec. 1987, pp. 17-25. /5/ Schenck, Harry A., "Improved integral formulation for acoustic radiation problems", J. Acoust. Soc. Am. 44,41 (1968). /6/ Benthien, G. W., and Barach, D., and Gillette, D., CHIEF User's Manual, Technical Document 970, Revision 1, Naval Ocean Systems Center, San Diego, CA 92152-5000, September 1988. /I/ Blottman, J., and Webman, K. M., Naval Underwater Systems Center letter Ser 621321615, January 02, 1987. /8/ Patton, Mark D., "Reciprocity calibration of an in-service transducer by the Delta-Z method", M. S. Thesis, Naval Postgraduate School, Monterey, CA 93943, Sept. 1988, p. 15. /9/ Bobber, Robert J., "Diffraction constants of transducers", J. Acoust. Soc. Am. 37,591 (1965). /lo/ Ref. 181, pp. 18-26. /1 11 Wilson, 0. B., Introduction to Theory and Design of Sonar Transducers, U. S. Govt. Printing Ofice, 1985, reprinted by Peninsula Publishers, Los Altos, CA, 1988, p. 26. 1121 Ref. 181, pp. 33-36.