THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

From Equation (16.28) we haveorF = Ae V = α T VlF = a T V16.5 Transducers 465The mechanical compliance C m is analogous to the electrical capacitance C, i.e.,C m = slF = slσ A = YlAWhen an applied force F causes a strain s, mechanical energy W m is stored in thetransducer, according towhereW m = 1 2 Fsl = 1 2 F 2 C m = 1 2 α2 T V 2 C m = 1 2 CV2 (16.32)C = α 2 T C mThe electrical capacitance C e between the electrodes of the transducer followsthe relationship:C e = ε A(16.33)lThe corresponding electrical energy W e is equal to 1 / 2 C e V 2 . From Equations(16.32) and (16.33) the ratio of mechanical energy stored in a piezoelectric transducerto the electrical energy provided to it is given byW mW e= C C e= α 2 TC mC e= k 2 eHere the electromechanical coupling factor ke 2 constitutes a measure of the efficiencyof the transducer.The Q FactorThe Q factor of either a mechanical or an electrical system determines the contourof the frequency response curve for that system. A low value of Q results ina resonance spreading over a wide frequency band. At higher values of Q, aresonance will be confined to a considerably narrower frequency band. Two Qfactors exist in a transducer, one mechanical and the other electrical, denoted byQ m and Q e , respectively. The mechanical Q factor is defined byQ m = mω rR mwhere ω r represents the resonance frequency of the transducer, m its mass and R mthe mechanical resistance. In the simplest case for the radiating transducer surface,