Mathematical proof for positive feedback

[anb2020]

Is there a mathematical proof that the positive feedback makes the op-amp saturated?

http://i.imgur.com/71PNh.png

 

[the_emi_guy]

Do you understand why it saturates (non-mathematical seat of the pants explanation)?

 

[skeptic2]

Let's clarify this by specifying positive DC feedback drives the opamp into saturation. Positive AC feedback makes it oscillate.

 

[anb2020]

Do you understand why it saturates (non-mathematical seat of the pants explanation)?

Yes of course

 

[alphysicist]

There is indeed a mathematical proof that positive feedback can cause an operational amplifier (op-amp) to become saturated. This can be seen by analyzing the gain equation for an op-amp in a positive feedback configuration.

The gain equation for an op-amp in a closed loop configuration is given by A = A0 / (1 + βA0), where A0 is the open loop gain and β is the feedback factor. In a positive feedback configuration, the feedback factor is greater than 0, meaning that the denominator of the gain equation is less than 1.

When the feedback factor is small, the gain of the op-amp is approximately equal to the open loop gain A0. However, as the feedback factor increases, the gain decreases and eventually becomes 0 when the feedback factor is equal to 1. This means that the output voltage of the op-amp will be equal to the input voltage multiplied by the open loop gain A0, resulting in saturation.

Furthermore, the gain equation also shows that as the feedback factor approaches 1, the gain of the op-amp approaches infinity. This is known as the "infinite gain" phenomenon, where even a small change in the input voltage can cause a large change in the output voltage, leading to saturation.

In conclusion, the mathematical proof for positive feedback causing op-amp saturation lies in the gain equation, which shows that as the feedback factor increases, the gain decreases and eventually becomes 0, resulting in saturation.