All right, in this section here, we're talking about filters. And the first one we're going to talk about is a low pass filter. Meaning as we show here, his mic cut off, right? From here back, my frequencies are low and from up here, going this way my frequencies increase. And if you look at our circuit, we just got a small circuit, very basic. We've got a resistor and a capacitor.

All right? Well, the value or the resistance of the resistor is constant. It's not frequency dependent. So we've got a value of 10 kilo ohm. That's going to stay until it 10 killem. Period doesn't matter what the frequency is, but look What X sub c is, alright?

X sub c is a frequency dependent components a capacitor. And as frequency increases, X sub c decreases. So, looking at my output, because I'm taking my output across my capacitor right there. What happens? If my frequency is zero? Well C is zero, then zero, right here, we're going to have an infinitely high impedance or resistance, where is all my voltage going to be across my capacitor?

Alright. As frequency increases, X sub c decreases. So what's going to happen at this point here, where we call it the frequency of cutoff Where my curve is 70.7% of my maximum voltage. In this case, it's 10 volts. So this is going to be 70.7% of that. So actually, it's going to be 707 volts.

All right. At that point, I start to roll off because then what happens is X sub c starts getting smaller. Where does all my voltage get dropped across the resistor? Because the 10 K is constant, it doesn't change. All right. All right, even though we don't say it here.

I should have put it up here. But I'll put it up here. Now, at this point here. Yeah, I know we've got this formula to tell us what the frequency is. But it's actually in this case, it's going to be r equals X sub c. All right. So since R is a constant at that frequency here, x sub c is going to be 10 k. Now I know this phase reserve reversals, it may not be 100%.

Maybe it's 98%. But it's good enough to look at the circuit to see what it's doing. All right. All right. All right. So that's the point I'm trying to make.

All right. So on a low pass filter when I have an our NSC, our NSC a, let me stop, clear the slide off. Okay, in a low pass filter when I have an R and a C, all right, the cutoff point is, is the is the fancy, is the fancy formula, but it's actually when x sub c equals R, and in this case, it would be 10 k Okay, when x sub C and R are 10 K, that's when that's going to happen. All right. So now I kids my frequency of cutoff, I can figure V out. If you want to go there, V out.

It's the voltage divider formula that we looked at, basically, in circuits, one when I taught you that. Yeah, if you're looking at it, it's it's x sub c, because we're taking the voltage across the capacitor, divided by the total z at a circuit right there, times v n, in this case, vn is 10 volts. That's it. Everything's the same is my face angle. All right. And it's going to be one.

So it's one. What's my face angle gonna be? Gonna be 45 degrees, like I show you right there. Okay. That's where it's gonna be. And I go through the math.

You're welcome to look at that. I mean, we've done a lot of these That's it. So this is this is the nuts and bolts. Okay? Yeah, you can go through them out. But let's try to understand it intuitively.

Okay, my resistor is constant as x sub c, as frequency increases, X sub c goes down. This X sub c goes down more my voltage gets, gets dropped across the resistor, my output goes low, as I'm showing you here. That's it. Okay, we still have a low pass circuit, our filter here. If you look at the circuit, here, we have an inductor and a resistor. And now we're taking my output across the resistor.

Again, the resistor is not a frequency dependent component, but I have an inductor and an inductor is a frequency dependent component. Here's my formula two pi FL. So what happens As frequency increases, X sub l increases. So what's going to happen? Well, this is going to stay current at one K. But what happens as my frequency increases, the reactance of this inductor right here is going to get larger. All right, and when it gets larger, more of my AC voltage is going to be dropped across that inductor.

Again, my my frequency of cutoff RFC is when XL equals R. And in this case, it's going to be what one K. And again, is the formula to find that V out is the same as the previous example, the only thing we've done is instead of dealing with x subsea, we're dealing with XML here. You think It might be 45 degrees there, huh? Because they're equal. Yeah, right there. Okay, and V out. I solve for it.

It's it's going to be 70.7% of the supply voltage. And FC is right there. All right, you can go through that. That's it. Okay. That's it.

Basically the same thing. But again, intuitively looking at the circuit, yeah, I can go through math, but look at the circuit and see what it's doing. Okay. And this is very simple. But if I'm, if I can start getting you to look at circuits, because at some point, we're going to be building circuits, putting them together, we're going to be doing some lab work to Alright, I want you to intuitively understand what a circuits doing. Yeah, math is great and we can get the right answers but Intuitively, what's it doing?

If you look at that circuit, I know I've got an inductor basically in series with a resistor right here. Alright? When the frequency goes up, XML goes up. If XML goes up, I get more voltage across this. This is a constant, I get less voltage across that. And I see a curve like this when I'm showing you.

That's it. Okay, Nuff said. Let's go to the next one. Okay, on this circuit here, it's still a low pass right there. Okay. But you'll notice we've got a resistor network right here.

What happens? Let's look at this. If I disconnect this, right, right there and look at that, what what do I know? I know that that's a voltage divider, right? Because they're both the same value resistances. So if I take that off, all right, I've got 10 volts peak to peak I'm going to get equal voltage across each resistance because they're, they're equal.

So what happens now when I look at this with my capacitor on there? Well, again, low pass filter, if I'm at zero hertz, this resistance is infinitely high. All right. So basically, what's going to happen is I'm going to have the same amount of resistance here is here, all right? But as frequency increases, what happens? x sub c goes up.

So I've got a 10 K resistor right here. I've got a capacitor that is frequency dependent. What happens as my frequency increases X sub c goes down as x sub c goes down, the total Z of this R and C goes down. And I get a roll off as frequency goes higher up this way. My frequency of cutoff is here, and it's determined by two pi r squared R, our two divided by 10. Because this starts to roll off here, when this the X sub c of this C is one 10th of 10 K or one K, that that's it.

So we start off here. As my capacitive reactance starts equal equaling the resistance in parallel, I start to swing off here. And this right there is my frequency of cutoff. That basically is where our again, our will equal x sub c. In this case, our will be 10 K. So that will be 10 K. All right, we're good, thanks. Okay, now we're talking about high pass filters. And if you look at this circuit, it's it's kind of like the first one we did only would take in our output across the resistor instead of across the capacitor like we did at the very first low pass.

The other thing we've done is we've stopped DC level in here, and that's just to make out a point, you'll see what I mean. But again, alright, as frequency goes up, X sub c does what goes down. So as x sub c goes down here. All right, more since we have our resistor, resistor is not frequency dependent. So as this goes down here, I get more voltage across my resistor here, and then we get a curve like this. So we were not passing low frequencies, but as frequency increases, we're passing high frequencies.

A capacitor blocks DC. So even though if you look here in here, I've got an ace an AC voltage on a DC component, this capacitor right here will block that. And the only thing I'll see across this resistor is my AC component. And again, that's dependent upon frequency. We calculate the cutoff frequency right there as we done before, V outs the same and my, my face angle is the same, so everything's the same. This is basically the same circuit as the very first one we did.

We just stuck a, a battery in there just to emphasize that capacitor blocks VC. But instead of taking my output across my capacitor, I've just swapped the components and I take it across the resistor. That's it. That's it. All right. Let's go on to the next one.

Okay, on this circuit here we're talking about high pass and Look, we've got an inductor there, and we've got a resistor. Okay, as we know an inductor is a component that's depended upon frequency. So we know that x sub l equals two pi FL, right. So as frequency increases, XML increases. So since my resistor is constant one K, as my frequency increases, the reactance of my inductor increases so I get more AC voltage across it. And that, that's given me my curve that increases as frequency goes up.

All right, frequency of cutoff is right there. And we know that that's when x L equals R. In this case, we can calculate the frequency with this formula here. I've done it for you and it's 2.65 hertz, which is right here. So that's pretty much it. Let's look at it. And that's it.

I mean, I can't really say much more on this. And this will end this, this, this module and the end of this course. And we've got one more in what I call my core courses. One more. All right, one more course. And then I've done what I call the core courses.

That will be the foundation, my gut feeling is if if, if people take these core courses from me, you will build the foundation to understanding electronic circuits. And then on the second phase here, what I'm going to do is I'm going to put circuits up there, I'm going to put them all together. And we're going to talk about circuits, how circuits work. operational amplifiers, transistor amplifiers oscillators on I keep telling you, I'm going to do one in vacuum tubes and that's coming. And then we're going to throw some labs up there and stay with you, you're gonna get a good grasp of electronics. Now, these courses that I do have these slides, they're time consuming.

Okay, it takes me about, Oh, I'd say 2030, maybe 40 hours to create the slides, do the research and so forth on these. So it is time consuming. Please bear with me. My intentions are good. I want you understand the vocational electronics. So stay tuned.

And thank you all for staying with me at this point. With that said, I wish you all the best. We'll see you in the next course. Take care