Title :
A variational analysis of a new shape face shear mode quartz crystal resonator formed by an etching method
Author :
Kawashima, Hirofumi ; Matsuyama, Miki ; Nakazato, Hitsuhiro
Author_Institution :
Seiko Electron. Components Ltd., Tochigi, Japan
Abstract :
Variational analysis, the frequency-temperature characteristics, and the equivalent electrical circuit constants of a face-shear-mode quartz crystal resonator supported at ends, formed by an etching method are described. A vibration analysis is performed in which the equations of motion of the resonator, including both the vibrational and supporting portions, are derived using and energy method. A frequency equation is obtained by applying Galerkin´s method to solve the resulting partial differential equations and using displacement obtained from experiments on motional inductance. The resonant frequency, frequency-temperature behavior, and electrical characteristics of the resonator are analyzed by utilizing the frequency equation and displacement. The calculated results are shown to be in good agreement with the measured values
Keywords :
crystal resonators; equivalent circuits; quartz; Galerkin´s method; displacement; electrical characteristics; energy method; equations of motion; equivalent electrical circuit constants; experiments on motional inductance; face shear mode quartz crystal resonator; frequency equation; frequency-temperature behavior; frequency-temperature characteristics; model; partial differential equations; resonant frequency; shaped resonator; supported at ends; supporting portions; variational analysis; vibration analysis; Circuits; Differential equations; Etching; Inductance; Moment methods; Motion analysis; Partial differential equations; Performance analysis; Resonant frequency; Shape;
Conference_Titel :
Frequency Control Symposium, 1988., Proceedings of the 42nd Annual
Conference_Location :
Baltimore, MD
DOI :
10.1109/FREQ.1988.27581
