运放电路中电容的一些特殊用法

最近在进行实验室项目PCB设计的时候，看到一些运放电路中总有一些电容，但是由于自己非电子专业科班出身，对于这些电容的用法不是很懂。
于是就自己上网搜集资料，先总结如下，方便将来回顾。

1.https://zhidao.baidu.com/question/390123272773618365.html

回答1：

• 1、C1和R1组成具有一定频率特性的负反馈电路，如果没有C1，那么电路的频率特性是平直的，并联C1后，频带高端的负反馈增大，同时，也可以抑制高频自激。
  2、R2和R4是运放同相端的静态偏置电路，C2是为了滤除正负1.5V电源中的残余交流成分，使偏置电压更平稳。

回答2：

• 电容器的作用是同交流隔离直流。
  R1阻值太大，小的交流信号不能通过，并联一个C1就是提供一个高频小信号的负反馈电路。用于消除运放内部半导体结电容等引起的自激。

回答3：

• 消振作用和相位补偿

2.https://zhidao.baidu.com/question/494192495.html
运算放大器 积分电路 正相输入端接地 输入电压vi经电阻接 反相输入端， 电容一段接反相输入端 一端接输出v0 有一电阻和电容并联 此电路是什么作用？

回答：

• 理想积分器是不用并联这个电阻的。
  实际的积分器由于运算放大器难免会存在偏置电压，尽管偏置电压很低，还是会对电容进行充放电，时间一长，电容就饱和了(充电到正电源或负电源电压)。并联电阻的目的就是为了使给电容提供放电回路，不要饱和。
  并联电阻后的积分器的传递函数已经不是理想积分器了，但是，只要输入信号周期远远大于RC常数，可以近似为积分器。

3.https://www.amobbs.com/thread-5683381-1-1.html

回答：

• 输出端的高频信号有一部分会通过C返回到输入端。 不过返回来的信号跟输入的信号相位相反。 所以会有一部分高频信号被抵消掉了。
  最后反映到输出端的现象就是低频增益变大。 即低通滤波
  

4.http://blog.sina.com.cn/s/blog_b526d0f10102yl13.html

回答：

• CF的作用：相位补偿，防止振荡，抑制高频噪声。 Why?
  一般来说，因为布线的寄生电容，使得运放的输入端都会有一个10~20pF的寄生电容，如图CIN（我们暂且将它称为输入电容）。正是这个输入电容，会使得运放的高频噪声增益很大，从而有可能使系统不稳定。
  我们的输入信号一般为直流信号或低频信号，这个电容此时不会起作用，因而此时的增益为-R2/R1。
  引发系统不稳定的是高频噪声，所以我们可以暂且抛开信号增益，只讨论电路的噪声增益。该网络的反馈系数是R1/（R1+R2）,因而噪声增益为（R1+R2）/R1
  (这里我也不是很明白，欢迎大伙补充说明)。
  当噪声的频率比较高的时候，则需要考虑输入电容CIN对噪声增益的贡献，对于高频噪声来说，R1与CIN为并联关系，因而此时的噪声增益为：[R2+(R1//1/ωCIN)]/(R1//1/ωCIN)。
  从这个噪声公式可以看出，当噪声频率越高，噪声增益公式的分母越小，噪声增益的值就越大(是不是感觉像是伯德图中零点的作用？)，系统就越不容易稳定。
  How?
  引入CF滞后，噪声增益公式变为：[（R2//1/ωCF）+(R1//1/ωCIN)]/(R1//1/ωCIN)，当频率ω增大，噪声增益公式中分母减小的同时，分子也在减小，因而噪声增益公式整体就不会随着1/ω的增大而增大。如果从伯德图看来，这里是引入了一个极点。
  一般要求是R1 X CIN 大于等于 R2 X CF。

5.https://www.zhihu.com/question/46175336/answer/1053498177

先说结论，这个电容的目的应该是降低系统的高频增益。防止系统出现高频自激振荡之类的问题。其实图中已经推导了系统的传递函数为 那么在R2和R4上增加的电容实际上就是改变了电阻R2和R4两端的阻抗而已，所以新的传递函数为（假定两个电容容值都是C） 所以系统引入一个新的极点。合理配置该极点就能够使得系统的幅值裕度增加，避免出现自激振荡。

作者：其遇
链接：https://www.zhihu.com/question/46175336/answer/1053498177
来源：知乎
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5.https://www.sciencedirect.com/topics/engineering/feedback-capacitor

• Introduction to Spice Noise Analysis Art Kay, in Operational
  Amplifier Noise, 2012

  4.5 Feedback Capacitor Simulation Example A common op-amp circuit uses a feedback capacitor to limit the bandwidth. Limiting op-amp
  bandwidth will reduce noise, so a feedback capacitor is a common way
  to reduce noise. To understand how the feedback capacitor works,
  consider that a capacitor acts as a short to “high frequency” AC
  signals. Thus, at high frequencies the capacitor will short out the
  feedback resistor. When the feedback resistor is shorted, the noise
  gain will reduce gain to unity.

  In the circuit shown in Figure 4.26, the DC noise gain is 11. The
  gain begins to roll off at the pole fp=1/(2πC1Rf). As the capacitive
  reactance decreases, the gain decreases to unity. At higher frequency
  the gain begins to decrease because of the op-amp gain bandwidth
  limitation. Figure 4.27 shows the noise gain transfer function and
  Figure 4.28 shows the output spectral density curve. Figure 4.29
  shows the total RMS noise. Note that the region where the noise gain
  is unity contributes to the total noise. This region can be
  eliminated using an external filter (see Figure 4.30).

  

  Sign in to download full-size image Figure 4.26. Feedback capacitor
  simulation example circuit

  

  Sign in to download full-size image Figure 4.27. Noise gain vs.
  frequency for Figure 4.26
  

  Sign in to download full-size image Figure 4.28. Output noise
  spectral density for Figure 4.26
  

  Sign in to download full-size image Figure 4.29. Total noise for
  Figure 4.26

  

  Sign in to download full-size image Figure 4.30. External filter
  simulation example circuit

  Figure 4.30 shows an op-amp circuit with a filter at the output. This
  circuit has an advantage over the feedback capacitor filter because
  the external filter does not have the region where the noise gain is
  limited to unity. Figure 4.31 compares the two filtering techniques.
  Note that the external filter continues to attenuate but the Cf
  filter attenuation stops attenuating when the gain is one (0 dB).

  

  Sign in to download full-size image Figure 4.31. Noise gain vs.
  frequency for different filters

  Figure 4.32 shows the noise spectral density of both filter types.
  From Figure 4.33, you can see that the external filter is more
  effective at reducing noise. The feedback capacitance filter is most
  effective on amplifiers with high gain. Remember that the feedback
  capacitance will reduce the gain to unity at high frequency. The
  external filter is effective regardless of the gain; however, it
  increases the output impedance. The external filter is useful when
  the next stage is high impedance.

  

  Sign in to download full-size image Figure 4.32. Spectral density for
  different filters

  

  Sign in to download full-size image Figure 4.33. Total noise for
  different filters