低Qm 压电振子机电耦合系数的标准计算方法的原理误差分析

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

压电材料的机电耦合系数通常由谐振及反谐振频率之间的相对间隔确定。常用的ＩＥＥＥ标准计算公式，是由描述理想无损压电振子的电行为方程推导得出的。本文给出了压电材料的固有损耗产生的谐振及反谐振频率的偏移及由此引起的标准公式的误差。代替以往分析时常用的等效电路方法，本文采用把损耗考虑在内的严格的压电振子导纳或阻抗模型。分析结果表明：由测得的谐振及反谐振频率用标准公式得出的耦合系数小于材料的固有耦合系数；误差随固有损耗的增加及耦合的减弱而增加。文中给出了较为详细的分析结果。

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.