Analysis of the Theoretical Error for Electromechanical Coupling Coefficient of Low Q m Piezoelectric Resonator

The electromechanical coupling coefficient is usually determined from the relative frequency spacing of the resonance and anti resonance.The conventional formula is derived from the equations describing the electrical behavior of an ideal lossless piezoelectric resonator.In this paper, the influence of the intrinsic material losses on the frequency shift of the resonance and anti resonance, and therefore on the accuracy of the conventional formula to determine the electromechanical coupling coefficient is analyzed. The exact admittance or impedance model of the piezoelectric resonator with different vibrating mode, with a rigorous account of the intrinsic material losses, has been taken as a reference, instead of the frequently used lumped approximate equivalent circuit.The results show that the electormechanical coupling coeffcient determined from the frequencies of resonance and antiresonance is less than the intrinsic electromechanical coupling coeffcient, and the error increases for high losses material with weak electromechanical coupling. The detailed results are presented in this paper,the accuracy and the range of application of the conventional formula to determine the electromechanical coupling coefficient is established.