Mechanical Q m factor of bulk crystal plate measured by GHz pulse-echo technique with modulated input impedance

A new method for evaluating the mechanical quality factor Q m of bulk crystal plate specimen is proposed. This method is based on a pulse-echo technique without using a coupler. A piezoelectric ScAlN film transducer is deposited on the bulk specimen for evaluation. The round-trip attenuation α in the bulk specimen is estimated by analyzing the difference between the first and second echoes reflected from the bulk specimen. However, when the electrical impedance of the transducer is well-matched to the 50 Ω input impedance of the network analyzer, efficient piezoelectric conversion of the reflected wave in the transducer causes a significant error in attenuation measurement. Several high impedance values were intentionally introduced to experimental S 11 parameters to create an impedance mismatch, resulting in precise attenuation determination. This improvement in precision was also confirmed through theoretical simulations based on Mason’s model. Q m is calculated from the estimated attenuation α using the relation Q m = πf/αV a. The effect of diffraction was also taken into account when estimating Q m. In this study, Q m at 2 GHz of 7000, 2400, and 2300 were determined in LiNbO3, Ti, and SiO2. Q m were also estimated for various other bulk crystal materials.