Title :
Analysis of capacitances of electrical equivalent circuit of quartz-crystal tuning fork in consideration of electric field distribution using conformal mapping method
Author :
Ishikawa, Takahiro ; Itoh, Hideaki
Author_Institution :
Fac. of Eng., Shinshu Univ., Nagano, Japan
Abstract :
The formulas of capacitances of the electrical equivalent circuit of a quartz-crystal tuning fork at resonance were derived only for free-free bar model in consideration of the electric field distribution and the potential ratio in the section of its arm using conformal mapping method and Fourier series in Ref. [1]. We analyzed the same problem for both free-free and clamped-free bar models and compared the calculated values with measured values of capacitances of the electrical equivalent circuit of the quartz crystals which were available in practical wrist watch application.
Keywords :
Fourier series; capacitance; conformal mapping; crystal resonators; equivalent circuits; vibrations; watches; Fourier series; capacitance analysis; conformal mapping method; electric field distribution; electrical equivalent circuit; free-free bar model; potential ratio; quartz crystal tuning fork; wrist watch application; Capacitance; Capacitance measurement; Electric fields; Electrodes; Thickness measurement; Vibrations;
Conference_Titel :
Ultrasonics Symposium (IUS), 2011 IEEE International
Conference_Location :
Orlando, FL
Print_ISBN :
978-1-4577-1253-1
DOI :
10.1109/ULTSYM.2011.0573