A complete characterization of the piezoelectric, dielectric, and elastic properties of Motorola PZT 3203 HD including losses and dispersion

This paper reports on our determination of the small signal properties of Motorola 3203 HD, including the effects of losses and dispersion, and it shows the limitations imposed by assuming that the material is loss-less. A set of PZT 3203 HD unloaded resonators manufactured by Motorola was cut to specifications outlined in the IEEE Standard on Piezoelectricity Std 176-1987 to ensure the appropriate boundary conditions of each resonance mode. Impedance spectra of the thickness, thickness shear, length and length thickness extensional modes were analyzed at the fundamental and second resonances using Smits' method while the analysis of the radial mode resonators was accomplished using a method that we had developed earlier. Using the results from the above analysis we have determined the 10 independent complex constants (s11(E),s(12)(E),s(13)(E),s(33)(E),s(55)(E),d(13),d(33),d(15),epsilon(11)(T), and epsilon(33)(T)) that define the reduced matrix for a C-infinity piezoelectric material at the fundamental resonance frequency of the resonator. The use of complex material constants to account for the loss of linear systems is discussed and the relationship between the mechanical Q, dielecric tan delta, piezoelectric loss and the complex material constants are presented. The dispersion in the material constants, except for s(12)(E) and s(13)(E), was studied by evaluating the constants at the second resonance. The source of the major components of the dispersion has been determined to be due to external effects such as mode coupling for high impedance resonators and electrode sheet resistance for low impedance resonators. The size of loss components and the dispersion are shown to be significant and it is suggested that ignoring these effects will reduce the accuracy and predictive capabilities of transducer models.