Losses, dispersion and field dependence of piezoelectric materials

The impedance equations for high loss piezoelectric resonators have been derived from the linear equations of piezoelectricity using complex material constants. The effects of dispersion and the biasing of the samples with a DC electric field are modeled. Techniques to analyze losses, dispersion, and higher order coefficients of the unbounded piezoelectric resonator in the radial, thickness, thickness shear, length, and length thickness extensional modes are presented. A circuit model is presented that can be calculated directly from the complex material constants and which is in excellent agreement with simulated and measured data about the fundamental resonance of the various modes. A full characterization of a Lanthanum doped Lead Zirconate Titanate material (PZT Motorola 3203 HD) is presented to illustrate the extent of these techniques. The complete reduced elastic, dielectric, piezoelectric matrix including losses for this PZT (C...