Feedback

So now I want to talk a little bit about the concept of feedback. This is a really important concept. It was developed in the 1920s, the idea of using feedback, and it was done at Bell Labs, Bell Telephone Laboratories. Remember we talked about this on the op amp? This being the non-inverting input. So, if this voltage went up, this voltage went up, and the negative sign is the inverting input.

So, these voltages here and here move in opposite directions. The key to understanding what feedback is, is to pay attention to this inversion path and then these non-inverting paths. We're going to start over here with just isolating the voltage divider part of our circuit. So that's copied over here, and we think about let's look at what happens if V out goes up and what happens to V minus in this case.

Well, V minus goes in what direction in a voltage divider? It goes up. So this is a non-inverting structure. If V out goes up, then the thing we care about, V minus, goes up as well. Likewise, if V out goes down, then V minus goes down. So that's isolating just on this part of it; we have no inversion happening around here.

So we go around here now, and let's look at what happens on this path here. If we go up in V in, then we know that V out goes up. If we then change colors to, let's try this, if V minus goes up, then V out goes down. That's the inverting path. So there's one inversion in this circuit, and it happens right here where V minus goes to V out. So that's where the inversion is.

So now let me set up just an example circuit. We'll set R1 equal to R2, and from the last video, we developed a gain expression. We said that V out equals R1 plus R2 over R2 times V n. With these resistor values, V out equals 2 times V in. All right, so this is equal to 2 times V in.

And what does that make this point here, V minus? This is V minus, and from our voltage divider, we know a voltage divider says that V minus equals V out times R2, which is just R over R plus R, or V minus equals one half V out. So we have let's put a voltage on here. Let's put a real voltage on here. Let's say this is at one volt.

All right, and going through our amplifier, we know that V out equals two volts, and that means that V minus equals one half of V out, so V minus is one volt. So this is one volt here. So let's say for the moment that something happens to this circuit, like we heat it up or something like that, and let's say the gain goes up a little bit.

Now what that means is that this amplifier, which is amplifying this voltage difference right here, is going to be a little higher. So the voltage here is going to go up a little bit. Let's use this color, A goes up a little bit, and that means that this output voltage is going to go up a little bit.

And we already decided from looking at this voltage divider that if this point goes up, then this point will go up. It goes up half as much, but it goes in the up direction. When this voltage goes up, that means this voltage goes up, and now we find ourselves, we're at the inverting input.

We're at the inverting input to the amplifier, and that means what? When the change at the inverting input goes up, that means the output goes down, and that's in the opposite direction of the original change. So this is the mechanism of feedback. A went up a little bit. We thought that V out would go up a bit, which meant this point goes up, which meant it gets fed back to the input, to the inverting input, and then it goes back down.

This balancing act that's going on right here, that is the mechanism. That is what we call feedback. You get this feedback effect when this connection is made right here back to the inverting input to the op amp. In particular, because it's the inverting input, this is called negative feedback.

So this is the mechanism of feedback, in particular negative feedback, and what it does for us is it provides us a way to exploit and to use this enormous gain that these amplifiers have to create really stable, really nicely controlled circuits that are controlled by the values of the components we attach to the amplifier.

So that's the idea of feedback; a really powerful idea and really at the heart of analog electronics.