Analysis of the motional capacitance of the electric equivalent circuit of quartz-crystal tuning fork using L-shaped bar model with torsion spring and in consideration of electric field distribution

We derived the motional capacitance of quartz-crystal tuning fork using L-shaped bar model with torsion spring and in consideration of both electric field distribution and the width of electrodes. If the width and the length of electrodes are taken into consideration, the calculated values of motional capacitance of the tuning fork with 100μm in thickness are good agreement with the measured ones under three boundary conditions; free-free bar, clamped-free bar, and L-shaped bar models.