Feedback

Feedback is the principle in which the output of a blackbox is redirected to the input in order to let the output be dependend of itself. This is called feeback. Mostly, feedback is used to create a stable signal amplifier.

OPAMP Feedback
OPAMPS, as we know, have two inputs, a inverting input and a non invertin input also known as the - input and the + input. The output of a OPAMP is generally defined as:

$$\ V_{out}=A(U_+-U_-)$$

When one of these inputs in controlled by some kind of electrical signal and the other at least partially by the output, the equation for Vout will contain itself. Therefore, this equation could be considered recursive but is none the less solvable if all the Vout variables are brought to one side of the equal sign.

Feedback in OPAMPS takes place as a $$\beta$$ factor. In that situation the amplified system is a sum of two inpunts from which one is the output signal multiplied by a bèta factor. Therefor in the case that the inverting input is being controlled by the feedback signal, the transferrate is equal to: $$H=\frac{1}{\beta}$$ This in only the case when the amplification factor is assumed infinite. When it's not, the transferrate is equal to: $$H=\frac{A}{1+\beta A}$$

These type of feedback systems are usually not as perfect as the previous equation describes. In a lot of cases A and bèta are both frequency dependent and in that situation instability might occure. This situation happens when $$A\beta$$ is equal to $$-1$$. This was a problem in electronics for a long time because men did not know how to apply feedback without having a situation where $$A\beta=-1$$. ... was the first person to mathmatically solve this problem by introducing ....