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標題: | 新型表面聲波濾波器之研究 A New-Type Surface Acoustic Wave Filter |
作者: | Chun-HO Chiu 邱俊豪 |
指導教授: | 周元昉(Yuan-Fang Chou) |
關鍵字: | 表面聲波濾波器,占空比,頻散曲線,週期電極,壓電材料,波動方程式, saw filter,duty-cycle ratio,dispersion curve,periodic electrodes,piezoelectric material,wave equations, |
出版年 : | 2013 |
學位: | 碩士 |
摘要: | 本論文提出調整週期電極之厚度以及占空比得以改變表面聲波在半無限域
壓電晶體上之波傳特性。 表面聲波在半無限域壓電晶體上傳遞,若在半無限域壓電晶體上鍍上週期電 極,由於電極本身為導體,且具有質量與剛性,這三個條件都將影響表面聲波的 傳遞。其中質量與剛性的影響歸類於機械效應,而表面存在電極而使基材的電位 所受的影響則是電的效應。 壓電晶體在線性範圍內可用本構方程式表示其行為,此外,在週期結構下根 據Floquet 理論來表示位移與電位,再代入波動方程式求解表面聲波在半無限域 壓電基材上傳遞的通解。所存在的表面聲波,必須要是滿足邊界條件的解,才是 自然存在的解。而邊界條件包含週期的機械邊界條件以及週期的電邊界條件。 激發器推導中在指插電極給予一交流電位輸入,由上述之方法,計算出所激 發的表面聲波振幅的頻率響應,其中可以改變電極的厚度與占空比,如此得以選 擇在適當的頻率激發下有較高的輸出。 濾波器設計放置位置於激發器與接受器之間,電極週期與表面聲波波長相同, 只有當符合此一條件的表面聲波才得以傳遞,以此達到濾波之效果。而透過電極 厚度與占空比之調整,亦可調整所要篩選的波段。 接收器推導中,假設存在一表面聲波,使得指插電極有電位差1V ,再將電 極之面電荷密度空間積分後對時間微分,將電位差1V 與所得到的電流之比值為 阻抗,此一阻抗與外接阻抗匹配時,所存在的表面聲波為自然存在之解。 搭配激發器、濾波器、以及接收器的設計,組成一個表面聲波元件,透過各 自電極的厚度與占空比的調整,可依照需求調整波傳特性。若以為機電製程技術 的良率考量,調整占空比之良率因製程較容易,因此良率亦較高。 It is proposed that the saw(surface acoustic wave) propagation characteristics in a half–space piezoelectric crystal will change as the depth or duty cycle ratio of the periodic electrodes is tuned. Considering the saw propagation in half-space piezoelectric crystal with periodic electrodes, which are conductors and have mass and stiffness, periodic electrodes affect the saw propagation with the three reasons. Mass and stiffness effects belong to mechanical effects, while being conductors affecting the electric potential of the substrate belongs to electric effects. The behavior of a piezoelectric crystal can be expressed by constitutive equations. Besides, displacement and electric field in a periodic structure are expressed by Floquet Theorem. A general form of saw propagation in a half-space piezoelectric substrate can be expressed by solving the wave equations. The homogeneous solution can be solved by a periodic BVP(boundary value problem), including periodic boundary conditions and electrical boundary conditions. An alternative voltage is given as the input to the IDT(interdigital transducer) in the derivation of the actuator. By the methods described above, the frequency response can be obtained. The frequency corresponding to the peak in the frequency response plot can be tuned by adjusting the depth or duty cycle ratio of the electrodes. The filter part is placed between two transducers, which are one actuator and one receiver. The wavelength of the saw fits the period of the electrode in the filter, so only saw meeting the periodic boundary condition exists. And one can change the selected frequency by adjusting the depth or duty cycle ratio of the electrodes. In the derivation of the saw receiver, the concept of impedance matching is applied. Assumed there is a saw that makes the electric potential difference of the IDT to be 1 volt. The charge density is obtained by integrating electric displacement. And the current can be derived by taking time derivative on the charge density. The impedance can be easily shown by the ratio of voltage difference to the current. The three parts and a pair of extra reflectors are synthesized to be the saw device. All these parts can be adjusted by tuning the depth or duty cycle ratio of the electrodes. Moreover, when it comes to the yield, tuning the duty cycle ratio is preferred due to its easier way in fabrications than tuning the depth. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58997 |
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顯示於系所單位: | 機械工程學系 |
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