Ultrasonic Transducer Characterization at the NBS

The design of high-frequency high-efficiency underwater acoustic transducers with good impulse response is discussed. Cross correlation of the impulse response of a particular design with that of an ideal transducer provides a parameter whose maximization is sought. Results indicate agreat flexibility in the choice of material combinations for quarter wavelength matching layers. T HE BROADENING of the frequency response of piezoelectric disk transducers radiating into a water load by use of single or multiple acoustic impedance matching layers is well known [ l ] . The best pulse response is obtained when a zero acoustic reflection coefficient exists over a wide frequency range at the disk-surface/load-medium interface together with the complete absorption of any acoustic energy incident on the backing medium, However, such an arrangement is both difficult t o realize and would be of low sensitivity. If the disk is air-backed, then, excepting losses, all the acoustic energy generated eventually enters the load-medium, giving a high sensitivity transducer. The use of transition layers between the disk face and the load-medium to improve the pulse response while retaining the high sensitivity of an air-backed disk is explored in detail. An equivalent circuit representation of the transducer, built around the Mason model [2] was employed to obtain a quantity x( t ) , defined as the inverse Fourier transform of the complex ratio F/V (see Fig. (I)) at discrete time intervals of (4f0)-’ S , fo being the piezoelectric disk thickness frequency. The quantity x ( t ) is termed the transducer impulse response. Limitations of the equivalent circuit in representing a piezoelectric disk are essentially those listed by Kossoff [ l ] . Manuscript received August 15, 1978;revised September 12, 1978. The author is with the Geophysics Group, School of Physics, Univer‘Throughout the paper, this term refers to the acoustic reflection at sity of Bath, England. the radiating surface of the piezoelectric disk. Fig. 1. Schematic diagram of transducer indicates where electrical input voltage V and output force F are measured. The performance of a particular transducer configuration is assessed by comparing its impulse response x 2 ( t ) with the impulse response of an air-backed piezoelectric disk radiating into an infinite medium of characteristic acoustic impedance equal to that of the disk material; the latter impulse response is here designated the ideal impulse response x1 (t). Quantitative comparisons of performance are available through R 1 2 , the maximum value of the normalized cross correlation function between x , ( t ) and x 2 ( t ) . It is well known that an acoustic match between the disk and the load-medium is obtained at the same number ( N ) of frequencies as there are quarter wavelength transition layers if the transition layer acoustic impedances Pi are all the geometric mean of those of their two contiguous materials. That is PN-i= dPN+I-iPN-,-i; i = O ; . . , N 1 (1) where i = 0 refers to the load (water) and i = N t 1 to the piezoelectric disk (PZT-SA): Po = 1.5 * lo6 and PN+ I = 33.7 . lo6 kg m-2s-1. The zero’s of the reflection coefficient’ can be made to coalesce at&, the frequency at which the layers are quarter wavelength, if the Pi are selected by what might be termed the binomial method: PN-~=PN+I-~(P~/P~+I)~~; i =O,N1;