Effects of Three Side Ratios of the Rectangular Substrate on the Resonant Characteristics of the Ultra-small Size Resonator Using Its Length Extensional Vibration

사각 기판의 길이진동을 이용하는 초소형 공진자에 있어서 사각 기판의 세변의 길이비가 공진특성에 미치는 영향

The length extensional vibration mode of a piezoelectric ceramic substrate is used in fabricating the ultra-small size resonators and filters. In general, the three side ratios of the rectangular substrate affect the resonant characteristics of the resonator using its length extensional vibration. In this paper, their relationships are studied. We know that changing the ratio of its length to its width makes possible to change the resonant frequency of the width vibration without degrading the length extensional vibration. And frequency constant for length extensional vibration becomes slightly small as the substrate thickness becomes thin, but it does not change as its length changes. Electro-mechanical coupling factor for length extensional vibration, k$\_$31/ does not change as its length changes within length/width$\geq$4, but it becomes small as its width increases.