Vibration analysis of length extensional mode quartz crystal resonator with plural vibration bars

Abstract

AbstractA length extensional mode quartz crystal resonator of small size and good antishock performance and which functions at relatively low frequencies of 200 kHz to 1.536 MHz has been used in pagers and IC cards. An on/off repetition in quartz resonators of this type is common and therefore the start‐up transient performance becomes important.This paper describes a length extensional mode quartz crystal resonator with plural vibration bars which has a short start‐up time. The objective of this paper is to clarify both theoretically and experimentally motional inductance L1, frequency characteristics and temperature dependence of resonance frequency, and also electric properties of the resonator.Motional inductance L1 is derived first. Especially, L1 is found theoretically to be inversely proportional to the number of bars. Next, a vibration analysis of bars and supporters is made by taking into account the lateral motions based on an energy method and then a frequency equation is derived. The frequency characteristics, temperature dependence of resonance frequency, and electric properties are analyzed and compared with experimental results. The calculated results are found to be in agreement with the experimental ones. Finally, it is shown that a length extensional mode quartz resonator exhibits a short start‐up time, since L1 and R1 are compared to the single‐bar case. Such resonators are believed to be manufactured in a small form and also exhibit a good anti‐shock performance since vibrational and supporting portions can be made as one solid body by an etching method.