传感器与检测技术 复习题
3.画出电容式传感器的差动电桥测量电路图，并说明C。、△C表示什么量值？ 4.画出差动式电容加速度传感器结构原理图。并标往各组成部分的名称。 5.电容式传感器通常用来测量（ ）。
A.交流电流 B.电场强度 C.重量 D.位移 6.电容式传感器还可以测量（）。
A.压力 B.加速度 C.电场强度 D.交流电压
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传感器与检测技术 复习题
计算题
1. 某压力传感器的校准数据如下表如示。试用端基法求其基准直线，并确定该压力传感器的灵敏度和线性度。
压力(MPa) 输出电压（mV） 0.00 -2.7 0.02 0.6 0.04 4.0 0.06 7.4 0.08 10.9 0.10 14.4
2. 设一力传感器可作为二阶系统来处理，已知传感器的固有频率为?0=200Hz，阻尼比?=0.6，静态灵敏度为k=9.6，
试求：
（1） 该传感器的动态输入输出方程； （2） 该传感器的频率传递函数；
（3） 如果该传感器用于测量力F=sin(400t)，试求该传感器的稳态输出； （4） 试分析当测量的外力为2000KHz时，此传感器的稳态输出。
3.设有两只力传感器，均可作为二阶系统来处理，自振频率分别为800Hz和1200Hz，阻尼比ξ均为0.4，今欲测量频率为400Hz正弦变化的外力，应选用哪一只？并计算将产生多大的振幅相对误差和相位误差。
4. 电阻应变片的灵敏度定义为
k??R R?其中ΔR为作用应变ε后应变片的电阻变化，R为应变片的电阻。如果一阻值为120Ω的应变片灵敏度为k=2.0，将该应变片用总阻值为12Ω的导线连接到一测量系统，求此时应变片的灵敏度。
5.一应变片的电阻R=100Ω，灵敏系数k=2.10，用作应变为1000με的传感元件
(1)求ΔR和ΔR/R；
(2)若惠斯登电桥初始时已平衡，电源电压U=4V，求在此应变下的输出电压UO；
-422
6.如将两个100Ω电阻应变片平等地粘贴在钢制试件上，试件截面积为10m，弹性模量E=100GN/m，由100kN的拉力所引起的应变片电阻变化为1Ω。把它们接入交流电桥中，电桥电源电压为1V，求应变片灵敏系数和电桥输出电压。
7.有一台变极距非接触式电容测微仪，其极板为圆形，半径为r=3mm，假设与被测工件的初始间隙为?0=0.5mm，试求：
1) 若极板与工件的间隙变化量为??=10?m，电容的相对变化量（即
?C）为多少？ C02) 若测量电路的灵敏度为Ku=100mV/pF，则在??=1?m时的输出电压为多少？ 已知空气的介电常数为
??1?10?9F/m?9?10?12F/m 36?原始极距为为其转换电路(如右图桥的两个桥臂，并接有为相同的固定电容
8.在压力比指示系统中采用差动式变极距型电容传感器，已知?1=?2=0.25mm，正方形极板的边长为a=20mm，采用电桥电路作所示)。电容传感器的两个电容分别接R=5K?的电阻后作为电效值为U1=50V的电源电压，其频率为f=400Hz，电桥的另两臂C=0.002?F，试求
3) 电容传感器的电压灵敏度（单位为V/m）；
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传感器与检测技术 复习题
4) 当电容传感器的输出电压U0=1V时，电容传感器活动极板的位移（单位为?m）。
9.试推导差动电容式传感器接入变压器电桥（如右图所示），当变均为U时，其空载输出电压Uo与电容Cx1，Cx2的关系式。若采用变初始极距均为?0，极距变化??后，空载输出电压Uo与??的关系式。
10.当差动式变极距电容传感器动极板相对于定极板位移了容C1=C2=80pF，初始极距?=5mm，试计算其非线性误差，若将差动容，初始值不变，其非线性误差有多大？
压器二次侧电压有效值极距型电容传感器，设
??=0.5mm时，若初始电电容改为单只平板电
11. 表4.1中单组式变面积型平板形线位移电容传感器，两极板相互覆盖的宽度为4mm，两极板的间隙为0.5mm，极板间介质为空气，试求其静态灵敏度？若极板相对移动2mm，求电容变化量？
12. 现有一只0～20mm的电容式位移传感器，其结构如下图所示。已知L=25mm，R1=6mm，R2=5.7mm，r=4.5mm，CBC构成固定电容CF，CDC随活动导杆的伸入而变化，拟采用理想运算放大器测量电路，试回答：
（1） 要求运算放大器测量电路的输出电压与输入位移x成正比，在测量电路中CF与Cx应如何连接？ （2） 活动导杆每伸入1mm所引起的电容变化量为多大 （3） 输入电压U=6V时，输出电压U0为多少 （4） 固定电容CF的作用何在
（5） 传感器与测量电路的连接线对传感器的输入有无影响
13.在右图中，电感L=200mH的纯电感线圈中通入一个不断变化的电流i。电流i为一正弦信号，其幅值为2，频率f=200Hz，当
t=0时，相位为
?。2试求：在线圈上产生的自感电压为多大？
2
14.一个铁氧体环形磁心，平均长度为10cm，截面积为2cm，平均相对磁导率?r=2000，求：
（1）均匀绕线1000匝时的电感； （2）匝数增加1 倍时的电感。
-8
取真空磁导率为1×10H/cm。
15. 试推导右图所示差动型电感传感器电桥的输出特性UO=f(?L)，已知电源角频率为?，Z1、
Z2为传感器两线圈的阻抗，零位时Z1=Z2=R+j?L。若以变气隙式传感器接入该电桥，求灵敏度表达式k=UO/??为多大（本题用有效值表示）。
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传感器与检测技术 复习题
16. 某压电晶体的电容为1000pF，电荷灵敏度为Kq=2C/cm，连接电缆电容为Ce=1000pF，示波器的输入阻抗为1M?，
并联电容为50pF，求
（1） 压电晶体的电压灵敏度； （2） 测量系统的高频响应；
（3） 如系统允许的测量幅值误差为1%，可测量的最低频率是多少？
（4） 如频率为10HZ，允许误差为1%，用并联连接方式，电容值为多大？
2
17. 石英晶体压电式传感器，面积为1cm，厚度为1mm，固定在两金属板之间，用来测量通过晶体两面力的变化。
1014
材料的弹性模量为5×10Pa，电荷灵敏度为2pC/N，相对介电常数为5，材料相对两面间电阻是10?。一个10pF的电容和一个100M?的电阻与极板并联。若所加力F=0.01sin(1000t)N，求： (1)两极板间电压峰值； (2)晶体厚度的最大变化。
18.分析压电式加速度传感器的频率响应特性。又若测量电路的C总=1000pF，R总=500M?，传感器固有频率f0=30KHZ，相对阻尼系数?=0.5，求幅值误差在2%以内的使用频率范围。
Visa-free policy brings Chengdu biz, tourism boost. Making national headlines several times, Chengdu's 72-hour visa-free policy has attracted wide attention from both Chinese and foreign experts and businessmen since it took effect on Sept 1 last year. The program permits citizens from 51 countries and regions including the United States, Australia, Canada and Japan who have valid visas and flight tickets to a third country to spend three days in the city. The capital of Sichuan province is the first city in the western region of China to offer foreign tourists a three-day visa and the fourth nationwide to adopt the policy following Shanghai, Beijing and Guangzhou. Li Zhiyong, deputy dean of the tourism institute at Sichuan University, said the move \number of overseas tourists and raises the city's level of internationalization\cultural legacies and is also a paradise for panda lovers with the world's largest breeding and research center. Three days are long enough for foreign visitors to visit those iconic tourist spots,\cheng Mountains and the Du jiang yan irrigation system. Qing cheng has long been recognized as the birthplace of Taoism, China's ancient indigenous religion, while Du jiang yan is considered to be the oldest functioning water-control project in the world. Chengdu ranked third in tourist facilities, management and services among 60 Chinese cities in a develop more tourism products, improve Yun, chairwoman of British Chamber of convenient. \British client once flew here customer satisfaction survey released last year. But, Li added that efforts are still needed to English services and provide accurate translation of traffic signs and scenic billboards. Zhao Commerce Southwest China, told China Daily that his colleagues found the policy very and stayed for just one day to check her ordered goods,\province, but she has lived in Chengdu for more than 10 years. \before,\hometown,\72-hour visa-free policy and compelling conditions in transportation, climate and cuisine, he said. Foreigners also gave positive feedback on the spokesman from Dell Inc said the company has a global hub of operation Chengdu, so the three-day visa \on with the culture, policy. A in the company's business development\Canada, said his work requires frequent travel to Chengdu and the policy \public security bureau shows some 100 foreign visitors enjoyed the 72-hour policy by the end of March, most of them from the United States, the United Kingdom and Germany. Chengdu also reported robust growth in its overall tourist industry last year. Official statistics show that it received some 150 million tourists last year, an increase of 28 percent from 2012. Around 1.7 million came from abroad, an increase of 12 percent. Total revenue from tourism surpassed 133 billion yuan ($21.7billion). During his visit to Kazakhstan in and Central Asia join hands to build a Silk Road economic belt to boost Asian countries, becoming an encouraging blueprint for Chinese areas than 2,000 years. In the next three weeks, China Daily reporters will travel September, Chinese President Xi Jinping proposed that China cooperation. The idea has been widely echoed in Central along the Silk Road that has linked Asia and Europe for more through the belt in China and in Kazakhstan, Uzbekistan and Turkey. They will show the progress and expectations of the countries, businesses and peoples on the route. Shaanxi - the start of the ancient Silk Road - has positioned itself as the new starting point for the development of the Silk Road Economic Belt, which will strengthen China's cooperation with Central Asian countries, a senior official said. Shaanxi Governor Lou Qinjian said the province is fresh, rich and unique, as it was when it anchored one end of the ancient Silk Road. 第 8 页 共 8 页
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