Useful Formulas for Piezoelectric Ceramic Resonators and Their Application to Measurement of Parameters

Abstract

Electrical characteristics of a lossless ceramic resonator with fully covered electrode can be expressed by three basic parameters: clamped capacitance, electromechanical coupling factor, and the gravest resonant frequency or antiresonant frequency. Unified formulas are derived for various modes of vibration with longitudinal and transverse electric field. The formulas are valid for a very wide range of frequency, but the calculation is not simple because of transcendental functions involved. Hence, approximate formulas are derived that are simple and easy to calculate. The accuracy of the approximation is far better than the accuracy of conventional lumped-constant equivalent circuit representation. A novel method for determining three basic parameters of a ceramic resonator with transverse electric field is developed based on the present approximate formulas. The method requires only the measurement of resonant frequencies, before and after the insertion of a series capacitance, and eliminates the need for both the measurement of antiresonant frequency and the measurement of low-frequency capacitance, which are required in a conventional practice.