Finite element simulation of TT cut torsional quartz crystal resonators

This paper describes a vibration analysis of TT cut torsional quartz crystal resonators of tuning fork-type with finite element method. The influence upon vibrations of vibrational portions due to a shape and a dimension of the supporting portion which is connected to two lead wires is clarified for the fundamental mode vibrating in torsion. As a result, the shape and the dimension of the supporting portion are found to give the great influence on various characteristics, and also an optimum designed resonator is provided.