A VIBRATION ANALYSIS OF TORSIONAL QUARTZ-CRYSTAL RESONATORS TAKING ACCOUNT OF LATERAL MOTION

This paper describes a torsional quartz crystal resonator taking accou nt of lateral motion. The objective of this paper is to clarify a term of lateral motion, resonant frequency and frequency temperature coeff icient of a torsional quartz crystal resonator which is caused by late ral motion. An equation of motion including lateral motion is, first, shown and from the equation of motion resonant frequency is given as a function of a term of lateral motion. The term of lateral motion is, next, calculated, so that the resonant frequency is found to be very d ependent upon a thickness-to-width ratio R(zx) and a thickness-to-leng th ratio R(zy). Finally, the first order temperature coefficient a var ies with 1.3x10(-7)/degrees C in the experiments and 1.7x10(-7)/degree s C in the calculation according to a variation of R(zy)=0.033 to 0.16 5, when R(zx)=0.825.