In this final lecture, to wrap things up we're going to talk a little bit about some of the details of the guitar amplifier kit. Now, we saw that a lot of people did actually buy these, and we hope that they have fun putting it together. But, I want to take a little time in the first part of this lecture to talk about some of the details of circuits in the kit. And you should be able to look back at that and make sense of all of it now. And then in the second part of this lecture Dave Anderson PhD, student here. Is going to go over some of the practical details of building the Guitar Amplifier. So to start off, I'm going to just go back and revisit the schematic for a minute. And then, I want to talk in a little bit of detail about how the tone circuit works. And then, with a little more detail about how the gain and distortion control part of the, design works. And then finally, we'll say a little bit about the speaker cabinet design. it turns out that, the guitar amplifier speaker cabinet really us a, a very simple kind of affair. And there's not a lot to say about that particular design. But let's go on and start talking about the schematic in general. Now here is the Full Schematic of the guitar amplifier kit. this was posted right at the top of the course website. And so this should be, this is available to you. There's a little manual that describes the guitar amplifier. So, it's a very simple, three stage circuit with a Tone control front end that has some gain as well. And then there is a Gain distortion stage in the circuit that gives you kind of the guitar crunch sort of sound And then the last part of this is the simplest, this is the power amplifier. This is a TDA 2003, it's very simple. kind of ubiquitous, amplifier used for like car stereos and things of that sort. So it's a 10-watt car stereo amplifier. If you just look up on the Internet, TDA 2003, data sheet, you can download the data sheet on the thing. And there's really nothing to say about this other than it's set up As a non-inverting configuration. So here's the feedback to the negative output coming from the midpoint of these two relatively low-resistance resistors. So this is just set up to have a modest amount of gain, around 10 or so. And, the, capacitors are really nothing more than just DC blocks. They're essentially short circuits for the signal, the AC, frequencies of the signal. But they, isolate, like the inverting input from whatever the DC voltage is here. So that's why you see capacitor all over the place, and this capacitor is isolating this input from the DC voltage. And this little chunk right here is just an LED so there's an LED that's on when the amplifier's on. There's nothing worse than turning something on, and if the light doesn't come on you have no idea if the thing's alive or not. So we stuck the LED on there just for fun. So in the next few slides, I just want to talk about the tone circuit first, and then the gate circuit. Now the other thing if you were building a kit, this TL072 Op Amp is two Op Amps in one package. And so we use half of one of the Op Amps for tone control, and the other one for the gate control. So that's why it's one half of that, it's a dual Op Amp chip. Okay, so we're going to start by looking at the tone control circuit. Now it's just a Op Amp setup in an inverting amplifier configuration, so the input goes through the input resister to the inverting input of the Op Amp. The non-inverting input is grounded, and then there's feedback from the inverting input from the output back to the inverting input. And the network that goes on the, in the feedback path Is this parallel combination of a capacitor, 10 nanofarad capacitor, and a 50 kiloohm resistor. Now, the resistor is not just a resistor, it's a potentiometer. And the center wiper on the potentiometer is connected to one den, one end of the capacitor. So, what happens is, let's say that the wiper is all the way to this end up here. And so I have the parallel combination of a 50 kilo-ohm resistor, and a 10 nanofarad capacitor, that the signal is going to encounter. So what happens there is, the capacitor is going to look like a smaller impedance for higher frequencies. And therefore the total feedback impedance is going to be reduced, so the gain is going to go down. So, for high frequencies, so when the wiper is up at this end. Then I've turned down the gain for the high frequencies. So that means that the low frequencies are accentuated. So that's like turning up the bass in, in this amplifier. Now on the other end, if I slide the potentiometer wiper all the way to this end of the resistor. Well now I have just a short circuit in parallel with the capacitor. So I've essentially taken the capacitor out of the circuit, because when the current, after it passes through the resistor, it comes to this junction point. And it can either go through a 0 resistance to the output, or though some finite resistance or finite impedance through the capacitor. And of course all of the current is going to go through the zero resistance path. So sliding, moving the slider all the way to this end then makes the, gives the circuit its full bandwidth. There's no loss of gain for the higher frequencies because the capacitors just taken out of the circuit. And so that has the effect of turning up the treble control, so it kind of accentuates the high frequencies. So this end, it's bass boost, this end, it's treble boost. So let's look at this at a little more detail. The, now in general, the inverting Op Amp configuration, with the input impedance and a feedback impedance. We can, when we first talked about up amp, way back like in week two, we just looked at simple DC circuits where we just used resistors. Now all of that analysis carries over to replacing resistances with impedances. And these impedances in general are complex, because if you have capacitors inductors, that gives you complex impedances. And the gate formula, if i just take the magnitude of the gate, i don't care about phase shifts for this purpose. the magnitude of the gate is just the magnitude of the feedback impedance over the input impedance. So this is exactly the same formula when you just have simple resistors for the feedback resister and the input resister. Now let's take a look at this feedback network a little bit more. Now, let's say that the gain slider, or the, the tone slider position, is given by g. And g can go from zero to one. So, when it's all the way turned down at zero. All the way up, it's the full, all the way at one end, then it's one. Now what I have, then, is, depending upon the value of G, this is going to be a resistor up to the slider point. And then it becomes the parallel combination of a resistor and a capacitor. And so the amount of the resistor that is before the slider point. So here is the, this node represents where the slider is touching on the, along this resistor. So, let's say that the amount of resistance appear as 1 minus g. So, if g is turned up to 1, then, I move the slider all the way up here, and the, this goes to zero. And then from this point on, I have the rest of the resistance, which is g times RF, so this, 1 minus g times RF plus g times RF, this equals RF. So the sum of those two are always RF, But then I have this resistor gxRF in parallel with the feedback capacitor. So here is effectively what this little network is. As a function of the potentiometer settings, which of course has to be between 0 and 1. So I can compute the impedance of this little network. It's the series combination of this resistor. So here it is, plus this impedance. Now this impedance is the parallel combination of the feedback capacitor And this piece of the, resister, gRF. And so the parallel combination of those two is the product of their impedances. So here's the impedance of the feedback capacitor. Here's the resistance, divided by the sum of the two. So that's just the parallel impedance addition formula. So the expression for the gate, the magnitude of the gate is just the feedback impedance divided by the input resistance. And I take the magnitude of the whole thing, and so here it is. Here Zn is just a resistor that I call Rn. And then the feedback impedance is this whole, the feedback path impedance is this entire expression. And I just want the magnitude of that.q Now notice that this is a function of frequency now. And so the gain is going to be a function of frequency.