Analysis of Various Characteristics for Length Extensional Mode Quartz Crystal Resonator Comprising Plural Vibration Bars

Abstract

This paper describes an analysis of various characteristics for a length extensional mode quartz crystal resonator comprising plural vibration bars. An object of this paper is to clarify motional inductance L_1, frequency characteristics and frequency temperature behavior for the resonator. Another object is to provide a resonator with very short start-up time in an oscillator circuit. First, it is shown theoretically and experimentally that motional inductance L_1 is inversely proportional to number of vibration bars. Start-up time becomes very short in proportion to L_1. Finally, resonant frequency and frequency temperature behavior for a resonator comprising plural vibration bars are found to be approximately the same as that with one vibration bar.