Abstract: In this paper, under Kirchhoff's assumptions, a theory of the thin shell o'f radially-polarized piezoelectric ceramic cylinder has been developed. Using the methods of the Green's function and separation of variables the scattering of a plane wave by the cylinder has been solved. The normal mode series expressions of the velocity distribution of the surface of the cylinder and of the total sound field have been obtained and from those an exact analytical expression of the transfer function of the cylinder as a sound receiver has been given. Arbitrary transient response of the cylinder can be calculated from the transfer function by using FFT.
For PZT-5 piezoelectric ceramic cylinder, the transfer function, impulse response and step response have been calculated. The results show that the impluse response appears a typical minimum phase behaviour and so the cylindrical piezoelectric receiver belongs to the minimum phase system. Therefore, the phase spectrum of transfer function of the receiver can be reconstructed from its amplitude spectrum by using the Hilbert transform. The phase spectrum obtained by such a method is in good agreement with that calculated from the analytical expression of transfer function directly.
Obviously, it can be deduced that if a transducer has the minimum phase property then the phase spectrum of its transfer function can be reconstructed from the measured values of the amplitude spectrum by using the Hilbert transform.
The phase reconstruction of transducer is of importance in engineering applications, especially because o’f various difficulties of the phase measurement.