Let's go on and look at another amplifier, this is a inverting amplifier configuration. Now, we're actually going to use this one in the guitar amplifier. So, what we do in this case is you take the negative terminal, the inverting input of the op amp. And that is connected to the output with this feedback resistor, R2. Now again, we have a source with assumed well a source in series with some resistance R1. And that's connected to this terminal, as you will, the inverting terminal. So, you got the feedback resistor and the input resistor both connected to this terminal. And the non-inverting terminal of the up end is grounded. So, we want to analyze this circuit and compute V out as a function of the signal, the signal voltage. So, we're going to start by looking at this node that we've labeled A, and apply Kirchhoff's current law to that node. Now, Kirchhoff's current law says that the algebraic sum of all the currents flowing into that node is 0. So, i1 is flowing in, i2 is flowing in, so they're both positive. And iN is flowing out, so that's negative. So, those three have to sum up to zero. Now, [COUGH] I can then write an expression for i1 and i2 in terms of the voltages. Now i1, the current through this resistor, is just going to be the difference of Vs minus Vn. So, Vs is the voltage on this side of the resistor. The voltage on this side of the resistor is Vn. And so, the current i1 is just that voltage difference, Vs minus Vn over R1. Then, the second current, i2, the voltage difference across that is V out over here. The m over here, and so the current, i2, is V out minus VN over R2. So, that's the second term. And then in is leave it as it is. Now, we're going to now use the assumptions that are part of the ideal op amp model. the first one is that Vp and VN are equal. And the second one is that there's no current flowing into either of these. the non-inverting or the inverting input. So, these are both zero. So, that's the ideal op amp assumption. Okay, so with those assumptions and that equation, remember that we're looking back up here. We made Vp equal to 0 and Vp equals VN, so VN has to be zero. So, I can go back in this equation and set VN equal to zero everywhere I see it. And the equation at node then reduces to this simple equation, Vs over R1 plus V out over R2 equals 0. And so, I can solve that for V out as a function of Vs, the source of voltage, and it's just minus R2 over R1. And so, the voltage gain of this, the output voltage divided by the input voltage is negative. The ratio of the feedback resistor to the input resistor. So, if I put in a small sinusoidal signal what's going to come out of this is a sinusoidal signal that is amplified by a factor of R2 over R1, and it's going to be inverted. So, I get a larger sine wave that is also inverted. So, you can build a gain stage with this sort of amplifier configuration. And you can control the gain of the stage just by choosing the values of R2 and R1. And in the first stage of the Kathrein amplifier that we built this gain is around five or six. I forget exactly but this R2 is maybe five or six times bigger than R1. So, this is an extremely useful an ubiquitous configuration for op amps. So this is worth remembering. Thank you.