矩形AT切割石英晶体谐振器的振动分析与设计  

THE VIBRATION ANALYSIS AND DESIGN OF AT-CUT RECTANGULAR QUARTZ RESONATORS

作　　者：公勋[1] 章德[1] 

机构地区：[1]南京大学近代声学国家重点实验室,声学研究所,江苏南京210093

出　　处：《南京大学学报（自然科学版）》2000年第3期336-341,共6页Journal of Nanjing University（Natural Science）

基　　金：泰电电业公司的资助

摘　　要：随着石英体波谐振器向小型化和高性能方向的发展 ,控制晶片中的模式耦合问题便成了保证晶振性能的关键 从R .D .Mindlin的两维方程入手 ,分析了AT切石英晶片中的振动模式 首先得出了无穷大晶片中的色散关系 ,继而又得到了矩形晶片振动频率和长厚比 (晶片的长度与厚度的比值 )、宽厚比 (晶片的宽度与厚度的比值 )之间的关系 ,并与实际生产中所采用的数据进行对比 ,符合得十分好 最后以计算结果为指导 ,举例了一种Rectangular AT cut quartz resonators have been widely used in frequency control because of their smal size and extraordinary fequency temperature stability. However, a lot of spurious resonant modes such as face flexure, thickness twist, flexure and their higher order harmonics are coupled to the foundmental thickness shear mode at the edges of the plate. Traditionally only the modes propagating along the width direction are considered for two reasons. Firstly, the rectangular quartz plate dimensions used is often 2?mm×8?mm, that is, the length dimension is much larger than the width dimension. Secondly, the electrode has strong energy trap effect, which means that most of the vibration energy concentrates under the electrode. However, smaller resonators are developed recently, whose width and length dimensions are both less than 3?mm. So, it becomes necessary to take the modes propagating along both x 1 and x 3 directios into account. This paper presents the analysis of the vibration modes in AT cut quartz plate. According to Mindlin's 2 dimensional first order equations, dispersion curves for waves prorogating along x 1 and x 3 directions, in an infinite At cut quartz plate, are obtained. Moreover, after the boundary conditions are considered, standing waves are formed. Then the curves of dimensionless frqunency vs. length/thickness and width/thickness for rectangular AT cut quartz plates, i.e. mode charts, are given in this paper. There is excellent agreement between the computed results and the practical data from the factory. Finally, as an example, the design of a 4 MHz rectangular quartz resonator is shown in this paper. During the design of the resonator, the dimensions of both the width and length are carefully selected in order to avoid the existence of the spurious modes. At the same time, we can see that the computed results do not agree to the pratical data completely, especially at the high frequency range. We can improve the computed results in two ways. Firstly, because there are tw

关 键 词：模式耦合 振动分析 设计 石英晶体谐振器 

分 类 号：TN752[电子电信—电路与系统]