ON THE POWER LIMITATIONS OF SONIC TRANSDUCERS

When the mechanical quality factor Q of a transducer is less than the optimum value, the maximum power output of the transducer at resonance is electric- (or magnetic-) field-limited. When Q is greater than this optimum value, the transducer power is stress-limited. Traditional estimates of the field and stress limits and of the optimum Q, based on a simple equivalent circuit, are often too high for the field limit and too low for the stress limit and the optimum Q. Consideration is given to two extra compliance elements that are useful in flextensional transducer models and in representing glue-joint and stress-bias-rod compliances that occur in practical transducer configurations. When these compliances are included in the transducer equivalent circuit, the effect is to introduce a scale factor alpha (so that alphaQ is substituted for Q in the expressions for the power limits) and a second parameter beta whose practical effect is less important. The result is that the field limit is reduced by the factor alpha while the stress limit is increased by approximately 1/alpha. At the same time, the optimum value of Q is also increased by approximately I/alpha, but the maximum power (at the optimum Q) is little changed. An illustration of this effect is given by a lead zirconate titanate (PZT) barrel-stave flextensional transducer with alpha = 0.34 and beta = 0.53.