We're ready now to analyze the first simple Op Amp circuit, which is called a voltage follower, or simply a buffer amplifier. Now, this is about as simple as it gets with the op amp. The ye, the non-inverting and the inverting terminals shown here, the outputs here. What you do is you connect the output to the inverting input of the op amp. And, that's it. That's the whole op amp circuit. And so, what we want to do is analyze this entire circuit. If I put a voltage source with some internal source impedance on the input side and then put a load resistor on the output side. I'd like to compute the gain of this circuit and see what it, what it does. Now, we're going to use the idealized op amp model to analyze this circuit. So that really simplifies things a great deal. Now, [COUGH], the first thing is to notice that we have intentionally connected the output to the inverting input. So that means that VN here, has to equal V0. So, we're forcing that by connecting a wire there. Now, iP is zero. This is the ideal op amp assumption that there's no current flowing into either of the inputs. So, if iP is zero, that means there's no current through this resistor. So, there's no voltage drop across that resistor. So the voltage on this side and that side are exactly the same. So, if that's the case, then VP is just equal to VS. So, using Kirchhoff's law, we go from 0 to VS, then there's no voltage drop across RS. And then here we are at VP, so VP equals VS. Now, the ideal op amp model also tells us that VP equals VN. So, there's no voltage difference between [INAUDIBLE], the non-inverting and inverting inputs. Therefore, V out has to equal, Vs. So, that's all there is to it. So, the output of this is equal to the voltage of that source. And we say that the output is simply following the input voltage. Now, that seems like, big deal, who cares about an amplifier that does nothing. I could have just measured the voltage here and and that would be it. But what this does is it isolates the input from the output side. There's no current being drawn from this source here, so there's no current here. So, we have we don't have any voltage drop across the source resistor, because there's no current. And so, this voltage is mirrored on the output of the amp-, amplifier. So it's, what we say is we've buffered this input from the output. And the, the utility of this kind of circuit is that we're If this happened to be a very high impedance internal source like a guitar pickup for example, this could be 10 kilo-ohms. we can measure the voltage here with the up-end circuit without having to worry about there being any internal voltage drop through that large source impedance. And so we can have source that provides very small, actually zero current, and then the output of this the op amp is able to drive a substantial amount of current through a load resistor. And so, you have in this idealized model, there's, there's no current here and there's a finite current here. So, there's actually infinite gain infinite power gain. But in practice, it's obviously not that. But the idea is that we buffer the input from the output, and the up amp is able to drive much more current than would have been available from, the original source.