用电测法测量非电学量时,首先必须将被测的非电学量转换为电学" />
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电容传感器的原理及应用

时间:2019-03-16 00:00 编辑:[db:编辑] 点击:
span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">用电测法测量非电学量时,先必须将被测的非电学量转换为电学量而后输入之。通常把非电学量变换成电学量的元件称为变换器;根据不同非电学量的特点设计成的有关转换装置称为/span>span style="color: rgb(51, 51, 51); font-family: arial, ????; font-size: 14px; line-height: 28px; white-space: normal; background-color: rgb(255, 255, 255);text-decoration:underline;">传感器/span>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">,而被测的力学量(如位移、力、速度等)转换成电容变化的传感器称为电容传感器。/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">a href="http://www.hgwp.cn/product/16_16.html" target="_self">电容传感器/a>的工作原理是利用力学量变化使电容器中其中的个参数发生变化的方法来实现信号变换的。根据改变电容器的参数不同,电容传感器可有3类:/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">电容传感器的原理及应用1. 改变板遮盖面积的电容传感器/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">图1是3种这类传感器的原理图,图1(a)中是利用角位移来改变电容器板遮盖面积。假定当2块板完全遮盖时的面积为S,两板间的距离为d,板间介质的介电常数为ε。当忽略边缘效应时,该电容器的电容量为:/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197006746268.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">如果其中块板相对另板转过θ角,则板间的相互遮盖面积为:/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197007234370.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">可见,此电容量的变化值和角位移成正比,以此用来测量角位移。/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">图1(b)中是利用线位移来改变电容器板的遮盖面积的。如果初始状况板全部遮盖,则遮盖面积S=ab,当2块板相对位移x时,则板的遮盖面积变为S=b(a-x)。在介电常数和板距离不变时,电容量分别为:/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197007471322.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">可见,此电容量的变化值和线位移x成正比,用他来测量各类线位移。/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">图1(c)所示电容变换器是图1(b)所示电容器的变种。采用这种锯齿形电的目的在于提高传感器的灵敏度。若锯齿数为n,尺寸如图1(b)所示不变,当运动齿相对于固定齿移动个位移x时,则可得:/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197007850059.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">比较式(2)和式(3)可见,灵敏度提高了n倍。/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197008649105.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">电容传感器的原理及应用2. 改变介质介电常数的电容传感器/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">图2是2种改变介质介电常数的电容式传感器的原理图。图2(a)常用来检测液位的高度,图2(b)常用来检测片状材料的厚度和介电常数。/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197008959073.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">图2(a)中由圆筒1和圆柱2构成电容器两,假定部分浸入被测量液体中(液体应不能导电,若能导电,则电需作绝缘处理)。这样,板间的介质由2部分组成:空气介质和液体介质,由此而形成的电容式料位传感器,由于液体介质的液面发生变化,从而导致电容器的电容C也发生变化。这种方法测量的精度很高,且不受周围环境的影响。总电容C由液体介质部分电容C和空气介质部分电容C两部分组成:/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197008354783.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">x — 电容器浸入液体中的深度;/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">R — 同心圆电的外半径;/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">r — 同心圆电的内半径;/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">ε — 被测液体的介电常数;/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">ε — 空气的介电常数。/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">当容器的尺寸和被测介质确定后,则h,R,r,ε和ε均为常数,令:/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197009516496.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">这说明,电容量C的大小与电容器浸入液体的深度x成正比。/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">图2(b)是在个固定电容器的板之间放入被测片状材料,则他的电容量为:/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197009613047.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">式中:S — 电容器的遮盖面积;/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"> d — 被测物体上侧至电之间的距离;/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"> d — 被测物体的厚度;/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"> d — 被测物体下侧至电之间的距离;/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"> ε — 被测物体上侧至电之间介质的介电常数;/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"> ε — 被测物体的介电常数;/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"> ε — 被测物体下侧至电之间介质的介电常数。/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">由于d+d=d-d,且当ε=ε时,式(5)还可写为:/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197009111018.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">式中d — 两板之间的距离。/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">显然,在电容器板的遮盖面积S,两板之间的距离d,被测物体上下侧至电之间介质的介电常数ε和ε确定时,电容量的大小就和被测材料的厚度d及介电常数ε有关。如被测材料介电常数ε已知,就可以测量等厚教材料的厚度d;或者被测材料的厚度d已知,就可测量其介电常数ε。这就是电容式测厚仪和电容式介电常数测量仪的工作原理。/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">电容传感器的原理及应用3. 改变板间距离的电容传感器/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">图3是这类传感器的原理图,图3(a)由2块板构成,其中板2为固定板,板1为与被测物体相连的活动板,可上下移动。当板间的遮盖面积为S,板间介质的介电常数为ε,初始板间距为d时,则初始电容C为:/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197010387634.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">当活动板1在被测物体的作用下向固定板2位移Δd 时,此时电容C为:/span>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197010237900.jpg" style="padding: 0px; margin: 0px; border: 0px; font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>span style="padding: 0px; margin: 0px; font-size: 14px; line-height: 28px; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);">当电容器的活动板1移动小时,即Δd</span><d时,上式按泰勒数展开为:br style="font-size: 14px; line-height: 28px; white-space: normal; font-stretch: normal; font-family: Simsun; background-color: rgb(248, 252, 253);"/>img border="0" src="/Uploads/image/20180328/1522197011146634.jpg" style="padding: 0px; margin: 0px; border: 0px;"/>img border="0" src="/Uploads/image/20180328/1522197011536280.jpg" style="padding: 0px; margin: 0px; border: 0px;"/>这时电容器的变化量ΔC才近似地和位移Δd成正比。其相对非线性误差为:img border="0" src="/Uploads/image/20180328/1522197011872730.jpg" style="padding: 0px; margin: 0px; border: 0px;"/>显然,这种单边活动的电容传感器随着测量范围的增大,相应的误差也增大。在实际应用中,为了提高这类传感器灵敏度、提高测量范围和减小非线性误差,常做成差动式电容器及互感器电桥组合结构,如图3(b)所示。两边是固定的电板1和2,中间由弹簧片支承的活动板3。2个固定板与互感器两端及交流span style="text-decoration:underline;">电源/span>U相连接,活动板连接端子和互感器中间抽头端子为传感器的输出端,该输出端电压ΔU随着活动板运动而变化。若活动板的初始位置距2个固定板的距离均为d,则固定板1和活动板3之间 ,固定2和活动板3之间的初始电容相等,若令其为C。当活动板3在被测物体作用下向固定板2移动Δd时,则位于中间的活动板到两侧的固定板的距离分别为:img border="0" src="/Uploads/image/20180328/1522197012966179.jpg" style="padding: 0px; margin: 0px; border: 0px;"/>由上述推导可知,活动板和2个固定板构成电容分别为:img border="0" src="/Uploads/image/20180328/1522197012330858.jpg" style="padding: 0px; margin: 0px; border: 0px;"/>当他们做成差动式电容器及互感器电桥组合结构时,其等效电容为:img border="0" src="/Uploads/image/20180328/1522197012441490.jpg" style="padding: 0px; margin: 0px; border: 0px;"/>虽然电容的变化量仍旧和位移Δd成非线性关系,但是消除了数中的偶次项,使线性得到改善。当img border="0" src="/Uploads/image/20180328/1522197013148605.jpg" style="padding: 0px; margin: 0px; border: 0px;"/>时(在微小量检测中,如线膨胀测量等,般都能满足这个条件),略去高次项,得:img border="0" src="/Uploads/image/20180328/1522197013252690.jpg" style="padding: 0px; margin: 0px; border: 0px;"/>比较式(9)和式(7)可见,灵敏度提高了1倍。比较式(10)和式(8)可见,在img border="0" src="/Uploads/image/20180328/1522197013148605.jpg" style="padding: 0px; margin: 0px; border: 0px;"/>时,非线性误差将大大下降。

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