PWM信号如何转换为模拟量信号？专家说这是最好的解决方案

shatongb

有一个测量位置变化的位置传感器，我用万用表电压档测量传感器的输出信号，结果显示的是模拟量信号，即位置和信号输出大小呈线性关系。但是，我用示波器（Picoscope 4227）测量传感器的输出信号，显示的却是PWM信号（脉宽调制），即位置不同，输出PWM信号的占空比不同。
PWM信号的参数是：200 Hz, 低电平为0V,高电平为18V。
现在可以确定，我的传感器输出信号是PWM信号。PWM信号需要输入到控制器I/O中，但是控制器I/O口不具备直接采集PWM信号的功能。


一、解决方案：

设计个电路，将PWM信号转化为模拟量信号，然后将转换后的模拟量信号输入到控制器模拟量I/O口。


二、转换电路

1. 二阶压控有源低通滤波电路。
设计一个深度滤波电路。滤波电路图为：


低通滤波频率公式为：f=1/(2π*RC),我最后选择R=1K，C=10uf，算出的低通截止频率f=15.9HZ。
滤波电路后端是一个运算放大器，放大倍数公式：A=1+Rf/R1。我不希望电压被放大，所以我选择A=1.1。又因为R1//Rf=2R（R1，Rf两者并联的值等于R串联值），最终：Rf=220欧，R1=2.2k，R=1k。
2. 积分电路（无源滤波电路）
低通滤波电路前面是一个二级积分电路（将两个电容都接地），R=1K，C=10uf。下图是一级积分电路，设计的积分电路是将两个下图电路串联构成二级积分积分：


为验证电路效果进行的测试,我使用的设备是PicoScope4227，由于该设备最大只能生成正负1V的电压信号，就生成了幅值为1V（低电平0V，高电平1V）,频率为200HZ的PWM信号作为积分电路的输入信号。各种效果图如下：
1、示波器直接采集发生器生成的PWM信号，波形如下：


2、示波器从二阶滤波电路输入端采集信号，波形如下。发现该号波形与上图的波形相比已经发生了变化。


3.示波器从一阶滤波电路输出端中采集到的信号波形，即滤波电路从左往右数，第一个电阻与第一个电容交点的输出波形：


4、滤波器从二阶滤波电路输出端采集到的信号波形，即最终输出信号波形


5、最终输出波形的参数：


三、问题

1：为什么万用表电压档测量传感器输出信号，结果是模拟量信号，而示波器看到的是PWM信号？我该相信哪个结果？
答：这个问题牵涉到测量输入口的分辨率问题。万用表输入口的分辨率低（通过此例看低于200HZ），而示波器输入口的分辨率高，可达几千，甚至几兆赫兹频率，所以输出的结果不同。我们要相信示波器显示的结果。我理解PWM信号本质还是希望达到模拟量的效果，只是表现形式不同。
2：关于计算公式
答：在低通滤波电路中，有个频率公式f=1/(2π*RC)， 它计算的是低通截止频率（-3dB）。而在积分电路中，有个公式T=RC。 这个 T 是指电容充放电需要的时间。选取 T 时，根据一般经验公式，T>10 * T'(T'表示信号周期)。
在本例的积分电路中，RC=10ms，只有两倍的信号周期，但是通过测试，信号效果还是比较理想的。如果将更多的积分电路串联，效果会更好。
3：PWM 信号被控制器采集还有其他方案吗？
答：方案一：将PWM信号倍频，就是提高PWM信号的频率，但是占空比不变化。PWM倍频后的频率大于控制器I/O的分辨率，就可以被控制器默认为做模拟量，从而可以输入到模拟量I/O。
方案二：通过软件办法计算PWM的占空比。在控制器中编写程序，首先定时，测量这段时间内PWM信号中高电平的时间，从而计算出占空比。
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