摘要石英晶体微天平 (QCM) 作为一种非常敏感的传感器，利用英晶体谐振器的压电特性，将石英晶振电极表面质量变化转化为石英晶体振荡电路输出频率的电信号变化，进而通过计算机等其他辅助设备获得高精度的数据。QCM对过程质量和体系性状（密度、粘度、电导率、介电常数等）变化非常敏感，能够检测微观过程中的微小变化，为研究微观变化过程中各种特性的变化提供了一种强有力的手段。正因为如此，QCM近年来获得了迅速发展，已广泛用于化学、材料、生物和医学等多个领域的研究。65572

本文正是针对QCM电路模型及其电极表面带有负载时的等效电路模型进行研究。首先通过了解QCM的基本原理，推导无负载情况下的电路模型，研究其特性。再进一步推导不同待测物质（包括刚性薄膜、牛顿液体、粘弹性薄膜）情况下的等效电路模型，给出其对传感器谐振频率的影响规律。并利用MATLAB对QCM电路模型进行仿真，结合仿真结果验证推导的电路模型及其幅频特性。

毕业论文关键词  QCM  等效模型 待测物质 MATLAB

毕业设计说明书（论文）外文摘要

Title  Research on Equivalent Circuits Model of QCM with Load on the Surface of Electrode

Abstract

As extremely sensitive sensors, quartz crystal microbalances (QCM) take advantage of the piezoelectric property of quartz crystal harmonic oscillators to transform the change of mass on the electrode surface of the vibration to the change of digital signals of the output frequency of the circuit. Then, assistive equipment like computers are used to acquire high accuracy data. QCM is very sensitive about process mass and system properties such as density, viscosity, conductivity and dielectric constant. The tiny change during the microcosmic process can be detected by the QCM. And a powerful way is provided by QCM to study the change of characters during the process. As the reason mentioned above, QCM, booming in the past few years, is widely applied in multiple areas like chemistry, material, biology and medicine. 

Research about the equivalent circuits about the model of QCM circuit with load on its surface was done. The basic theory of QCM is understood during the process. The ratiocination of circuit model without load is done. And character is studied. After that, equivalent circuit model with different material for test is also derivate. The rule of the sensor oscillation frequency is also given. And the QCM circuit model is simulated in the Matlab. The simulation result is used to prove the circuit model and its character of amplitude frequency.

Keywords  QCM（Quartz Crystal Microbalance） Equivalent Model  Load    MATLAB  

目  录

1  引言 1

1.1 QCM概述 1

1.2 QCM基本原理2

1.3 QCM传感器的用途及发展现状3

1.4 研究本课题的意义以及结局问题的方法5

1.5 小结5

2  QCM等效电路模型推导与分析6

2.1 QCM等效电路模型的推导 6

2.2 元件参数对幅度和相位的影响 8

2.3 利用Matlab对QCM电路模型进行仿真10

2.4 小结 17

3  不同待测物质情况下等效电路模型推导18

3.1 刚性薄膜 18

3.2 牛顿液体 19

3.3 粘弹性薄膜 20

3.4 小结 22

4   不同待测物质模型的仿真与分析 23

4.1  Matlab简介23

4.2  利用Matlasb对不同负载情况下的等效电路进行仿真25

4.3  小结29

结论 30