64 



TESTING TECHNIQUE 



that, it these reversible transducers did not obey the 

 reciprocity principle, one would obtain the same cali- 

 bration by the use of each. 



7. If a calibrated resistor is available so that cur- 

 rent can be measured by measuring the voltage drop 

 across the resistor in series with the transducer, one 

 need not have an absolutely calibrated voltmeter to 

 perform a reciprocity calibration. For, if one sub- 

 stitutes E,/R for I T in equation (62), it can be seen 

 that only the ratio of voltages, and not their absolute 

 magnitudes, enters into the formula. 



5.5.8 



Motional Impedance Methods 



There have been proposed and applied several 

 methods of absolute calibration, based on the meas- 

 urement of the impedance of the transducer, which 

 can be applied to transducers obeying the reciprocity 

 principle. It is sufficient here to indicate how one of 

 these methods leads to an absolute calibration. It 

 one considers a transducer which has a sharp me- 

 chanical resonance at some frequency, the impedance 

 shows a rapid variation with frequency in the neigh- 

 borhood of the resonant value. If one plots the re- 

 sistance and reactance as a function of frequency, 

 smooth curves can be drawn connecting the portions 

 of the resistance curve and the reactance curve far 

 above and far below resonance. These curves are re- 

 ferred to as the blocked resistance and reactance, 

 since they correspond to the impedance which would 

 be measured if the diaphragm of the transducer were 

 prevented from moving. 



The difference between the actual impedance and 

 the blocked impedance is referred to as the motional 

 impedance. If the motional resistance is plotted 

 against the motional reactance in rectangular co- 

 ordinates, with frequency as parameter, a figure is 

 obtained known as the motional impedance circle. 

 If one measures the diameter of the motional im- 

 pedance circle in ohms for the instrument immersed 

 in water and then in air, calling the quantities D w , 

 and D A respectively, one can show that the efficiency 

 E of the transducer in water, that is, the ratio of 

 acoustic power output to electric power input, at 

 resonance, is given by 



*-!%}-%] 



(63) 



where R is the actual resistance of the device in water. 



The directivity pattern and thus the directivity in- 

 dex of the transducer can be measured with an tin- 

 calibrated transducer. From equation (8), Chapter 4, 

 one can see that, if the efficiency and directivity index 

 of a transducer are known, its response can be deter- 

 mined. In this way, the device can be absolutely cali- 

 brated at its resonant frequency from the motional 

 impedance circle (which gives the efficiency) and a 

 directivity pattern (which gives the directivity index). 



Since this method furnishes an absolute calibration 

 at only one frequency, it is not of great value as a 

 general calibration method, but it is useful for ob- 

 taining the efficiency of a device at resonance by 

 purely electrical impedance methods. Some of the 

 other methods of motional impedance analysis are 

 more refined and allow calibration over an extended 

 frequency range, but in general they are not so con- 

 venient to use as the reciprocity method. 



5.5.9 Relative Calibration of Transducer 



Even the reciprocity method entails more effort 

 than is desirable for the calibration of most devices. 

 The comparison method, involving the calibration 

 of one transducer against another which has already 

 been calibrated, provides a practical means for the 

 rapid calibration of most devices. In the comparison 

 method the magnitude of the sound field is first estab- 

 lished by means of a previously calibrated standard. 

 This is then followed by the calibration of the device 

 to be tested in this known sound field. 



It is presumed in a calibration by comparison that 

 the reference standard is sufficiently stable in con- 

 struction and operation so that its calibration is re- 

 tained in the interim between its own calibration and 

 its application in a relative calibration. Either a 

 transmitter or a receiver can be used as a reference 

 standard, the former to establish a known sound 

 field, the latter to measure the magnitude of the 

 sound field produced by an uncalibrated transmitter. 

 It has been found by USRL that properly constructed 

 receivers are somewhat more reliable than transmit- 

 ters as reference standards, but the difference is not 

 great. In fact, by using both a calibrated receiver and 

 a calibrated transmitter in a comparison test, a cross 

 check on the stability of the standards may be ob- 

 tained in conjunction with the test. 



The procedure in the relative calibration of a re- 

 ceiver is the following: A transmitter is placed at one 

 point in the water and driven by a constant voltage 



