Accurate evaluation of the real and imaginary material constants for a piezoelectric resonator in the radial mode

The standard IEEE procedure for determining the piezoelectric, dielectric, and elastic constants associated with the radial mode resonance of piezoelectric materials neglects the imaginary components of these constants. A method is presented to determine the complex form of the above constants. These constants are calculated from the experimental values of the first and second series resonant frequencies, the first parallel resonance frequency and appropriate half band frequencies, and the low frequency admittance of the material, all of which can be measured on one disk sample. The method was also used to automate the current IEEE procedure for determining the real parts of the material constants. The method was applied to three test cases to test the limitations of the fit. The technique is limited at very high and low quality factors. The technique was also applied to a lead zirconate titanate sample, and the results and fit were found to be in excellent agreement.