The conventional thickness mode equivalent circuit of the piezoelectric transducer is analyzed when one face is perfectly well terminated. It is shown that the impulse response of the transducer can be made ideally time limited by inserting a linear network in the electrical circuit. This ideal solution is achieved without the need for severe electrical or mechanical damping and applies even when the transducer is used in both the transmit and receive mode. Consequently it is also shown that in the ’’transmit’’ mode the transducer’s impulse response is independent of k, the electromechanical coupling coefficient.