An analysis of pulsed ultrasonic transmit-receive systems for medical diagnostics

This paper presents a method for the calculation of the shape and size of pulses radiated and received by ultrasonic transmitting-receiving systems used in medical diagnostics. Using an equivalent electrical circuit for the transducer, the transfer functions for different working conditions of the transducer were calculated and, on the basis of these functions the acoustical and electrical behaviour was calculated. Because of the complicated nature of the mathematical relations, continuous Fourier transform (CFT) was used to describe the systems. This was then replaced by a discrete Fourier transform (DFT), thus preparing the relations for numerical calculations. The DFT was in turn calculated using the fast Fourier transform (FFT). Calculations were made for a number of practically realized cases. The paper also gives the results obtained from an analysis of the operation of a transmitting transducer for different types of acoustic matching, for a wedged transducer, and for a divided one.