TABLE OF CONTENTS High power projectors are often operated in the vicinity of resonance where the output motion is magnified by the mechanical Q of the transducer. At this frequency the mechanical mass and stiffness reactance cancel and, if the transducer is also electrically tuned, the input electrical impedance is resistive at resonance. At frequencies off resonance the impedance becomes partially reactive, reducing the power factor and increasing the volt-ampere product required for a given power output. Transducers with a high effective coupling coefficient require less volt-ampere product and consequently smaller power amplifier capacity for a given power output.
Below resonance, the input electrical energy density is U e = ? TE 2/2, and Eq. (1.19) shows that the energy density converted to mechanical form is U m = 
where ? T is the free dielectric constant, E is the electric field intensity, and k e is the transducer effective coupling coefficient. For magnetostrictive transducers the mechanical energy density is U m = 
where ? T is the free permeability and H is the magnetic field intensity. As discussed in Chapter 2, the mechanical power density at resonance is P = ? rQ mU m, and for piezoelectric ceramics
where Q m is the mechanical Q and ? r is the angular mechanical resonance frequency. If the ceramic is sufficiently compressed, so that it is not dynamically stress limited, then the power output is...
