Okay, and welcome to Al's electronic classroom. And in this module here, we're going to talk about resonance. All right. And before I go on, let me just regress here a little bit and state to really understand the material in this in this section or in this course, you need an understanding of capacitive reactance, inductive reactance and RLC circuits meaning resistance, inductive and capacitive circuits. All right. If you don't have a good grasp on that, okay, you need to go back and take my courses on X, MC, XML, and XML x subsea and our circuitry.

Are I to get a grasp on that, all right, because you You may not understand the concepts in this course, unless you have that background. So this is a bit of an advanced course now. So with that said, let's go on. So I'm going to define resonance right here. And it's this little blurb that I put up put on the slide here, when x MC which is capacitive reactance. And XML, which is inductive reactance is equal, this combined effect is to favor one particular frequency.

This is called the resonant frequency. When we tune out and see to get this particular frequency, this is called the resonant effect. And we can define the resonant frequency by this formula here. resonant frequency, C equals one over two pi, the square root of LC All right, so I'm just defining it here. Now. All right.

And now let's go to the next slide. And we're going to talk about tuning and series resonance. So hold on dx, here we go. Okay, let's look at this this definition right here okay. inductive reactance increases as the frequency is increased, but capacitive reactance decreases with the higher frequency because because of these opposite characteristics of a tuned LC combination, there must be a frequency in which Excel equals the XC as one increases while the other decreases. This case of equal and opposite reaction to this is called resonance and the AC circuit is then a resonant circuit.

One of the most important applications of a resonant circuit is tuning where one frequency selective over the other. Okay, so now that we've we've I've spelled this What does it mean? Well, this is what it means. If you remember from previous courses, okay, X sub c equals one over two pi f c and X sub l equal to pi f L. Alright, so what happens to XML? As frequency increases, X sub l will increase, what happens to x MC? As frequency increases here, x MC will go down.

So they're opposite. So, there's got to be some frequency which we call fr frequency of resonance where x sub c equals X sub l. And if we remember from previous discussions, what did I tell you, x, MC, and XML are opposite each other. They cancel each other out. So when I, in other words, if I have an X sub c equals 100 an X sub l equals 100. If they cancel each other out or their opposite, what's my result? Zero.

All right, zero. That is the again, that is the resonant effect. Again, alright, I go through this when we talk about x sub l, x sub c and our circuits. Alright. So there's where we built the background. Okay, in this module here, we're talking about resonance.

All right. So let's let me clear off this slide and let's go To the next one, okay, and remember, this formula gives me my resonant frequency. And we're going to do one or two of them later. All right, let me stop here, clear the slide off, go to the next slide. Okay, on this. On this slide here, I just just giving you an example of what I mean by tuning.

All right. That's all. So now I've got this. I've got this box that selects a signal right here. I'll call this my box. And I have all these different frequencies coming into my box.

All right, but I because of my properties, and I'm going to create a resonant circuit. All right, I create a high gain for 1000 kilohertz, or my resonant frequency because of the properties of this circuit. will allow a signal that is oscillating at 1000 kilohertz to have a very large gain, which is this one here. All right. If you look at my input, I've got 500 kilohertz, 750 kilohertz, 1000 kilohertz, 1250 kilohertz and 1500 kilohertz, but because of the properties of this circuit, I allow this input signal, which is very small here to get amplified at some rate and it attenuates the other frequencies here. So basically what I'm doing is with this resonant frequency, I am selecting a frequency and this example 1000 calories hertz, to have a very, very large gain on the output.

So this here is 1000 kilohertz and it rejects or attenuates all these other signals here. That's what I do with the property of toning. All right. Let me stop here. Okay, on this slide, we're still talking about resonance. And this here is a series resonant circuit.

If you look at this circuit here, what we have is we've got an inductor and an XML of 1500 ohms and we have a capacitor of x subsea of $1,500 If previous discussions, we know that x MC and XML are opposite, and so they cancel each other out. So just by looking at this circuit, if these two active components cancel each other out what is limiting my current Rs? 10 ohms. Alright. And we're going to calculate the resonant frequency using this formula here. And it can be a little bit convoluted when you're doing it longhand.

I suggest what I'll do is at the end of this section, I'll put a link to where you can go in there and plug the you know the values of the capacitors and and the inductors and it'll calculate the frequency for you. But honestly, you should should know how to do this. I know math is, you know, math yet, but you know, you should know how to do it. All right. So anyways, let's go through it. I'm going to go through it rather quickly, I, because you should have been honed up on your math skills by now, again, I put that course up, or you can do it any way you want.

But you need to have some math skills, which will give you an intuitive reasoning. If the answer that you get when you plug it into a calculator or you plugging into one of these tools on the internet where you can plug in the information and get the answer you'll look at and say, yeah, that's gotta be right. Because you've done it. You know how to do it. Anyways, Enough said. So I just plug in my values here.

106 Times 10 to the 12 Pico is times 10 to the minus 12. Okay, nano, I'm sorry, micro right here. 230 micro farad, just 10 to the minus six, my. So we know that Pico equals 10 to the minus 12. And micro equals 10 to the minus six, we know that all right, so now I do my math. And what I can do here is I can multiply those two numbers right here.

Keep it under my radical sign. And then when we have powers of 10, and we use multiplication, what happens? The powers of 10 add like I'm showing you here. So right now. I'm coming to this step here. All right, what 106 times 239 when I take the square root of that It comes to 159 dot two, this actually comes to 10 to the minus 18.

But when I take the square root of a power of 10, I divide by two. So I'm left with 10 to the minus nine to pi is 6.28. Because pi equals 3.14. So two times 3.14 is 6.28. We've already found that 159 dot two times 10 to the ninth. All right, and what do I get?

I get this one over 1000. When I do my multiplication, all right, you can do it to see if I'm right, times 10 to the minus nine is my answer, zero. dot 001 times 10 to the night. And that converts to 1000 kilohertz. All right. Okay, so we're right.

We're right. And again, you can plug these values in. I'll give you the link to that calculator that I was talking about at the very end of this section. And you can go plug it in see him, right, but I would like you to follow along. Alright, to try to do this. I mean, there's going to be some problems that I'm going to give you.

And yeah, you can cheat. You can go to this calculator. You can plug it in and say, Okay, here it is. But what I'd like you to do is try the formula. I'm going to give you the answers and then go to this calculator and plug it in. Everything should jive.

Alright. So again, back to this. This is a series resonant circuit. So let's clear off the slide and go on with this. Okay, so here on this section here. All right, we've got fr equals 1000 kilohertz.

That's actually one megahertz to 1000 kilohertz is actually one megahertz. Okay? x Val equals X sub c net results as resistance. Because if you remember previously, I said that x ob, XC and XML are opposites, so they subtract or we take the difference. If they're equal, my difference is zero. Isn't that correct?

So in the circuit x Savelle and SMC cancel each other out. All right, so now what's my current flow? My current flow in this circuit is only determined by that resistor. So now I use ohms law, current in circuit is 300 micro volts divided by 10 ohms. I do my mouth, and I get 30 micro amps and again, I'm not expanding these equations anymore. All right.

So now the voltage across this capacitor, V XC at resonance equals IC. That should be at at resonance times x subsea at residence. I just do my math. And the voltage across my capacitor is 45,000 micro volts. I, that's the highest frequency on sorry, that's the highest amplitude that I'm going to get. All right, even though we have reactive components, they cancel each other out.

And because of this criteria, this property that's when I have my maximum current flow that When I have my, my maximum voltage across my reactive elements, all right? All right, that is series resonance. Okay, so at that instant, okay 1000 kilohertz, the frequency of 1000 kilohertz or if I've got a sine wave of 1000 kilohertz, that's where I'm going to get its maximum amplitude, and it's going to be 45,000 micro volts. Now, just just just expand this, okay, since I don't give it a label, it's assumed that it's 45,000 micro volts RMS and I can go through my derivations, my conversions to find peak to peak peak, the average value and so forth by using the constants, okay, and again, I went over that when we did understanding voltage Current and resistance. Alright, so there you go, there you go. Okay, this is series resonance.

And what do we know, we know that when my reactive elements are equal and opposite, I get my largest AC voltage drop across my reactive elements in this example, we're taking the output across this capacitor here. But if I took that across that inductor, it would be the same, the same voltage level. All right. All right, I'm going to stop here, clear off the slide, we're going to go to the next one. Okay, this one here, we've kind of gone over this part on the previous slide, but I just kind of put a little chart up here, just for you guys to look at. If we look at this chart, I'm showing the frequencies between 600 kilohertz to 1400 kilohertz and we give you the value of x sub l and X sub c. Then we take the difference of XC minus XL and then Excel minus xe you'll notice at resonance the differences zero.

Okay, what determines my current here is our, my z is our which is 10 ohms. And if you'll notice, that is where I get my biggest voltage swings across my reactive elements. And that's what we're looking for. Okay? We want for whatever reason, maybe it's a radio station. Maybe it's a maybe for some reason, I need to select this thousand kilohertz.

Alright, for whatever reason, okay. And I've designed this circuit, that when I have a sine wave of 1000 kilohertz, I get the largest amplitude. And quite honestly, even though we didn't pound on it, it actually attenuates the others. All right, the other frequencies below it below this and above this. Alright, so I just wanted to show you this chart here. Take a look at it, go through it.

If you've got any questions, you can email me, or Yeah, at some point, we're going to be starting some questions and answer sessions. I haven't done one yet. I'm trying to get some more courses up there. But at some point, we will you'll get an email or some type of notification. And you can ask Okay, anyways, with that said, I'm going to stop here. We're going to go to the next section and see over there.

Okay, before we end this, I just wanted to put this slide up and make sure you can see what's going on here. Okay, so and residents, these are the voltage drops I have across each one of these elements, obviously there My RS which is resistive, it's it's passive, I get 300 micro volts. And maybe these, maybe these arrows are misleading. What I mean by that is V XL and V x equals 45,000 micro volts. That's across 45,000 across that element, and 45,000 across this element. That's what I mean.

And then again, there's the chart here again. So that's it. I get these voltages at resonance, all right, and they have the highest voltage. If you look at this chart, you'll see that it's the highest voltage across each one of these elements is at resonance. All right. All right.

Let's stop here. Go to my summary. Okay, here's a summary of series resonance. The current is maximum and The resonant frequency, I which is current is in phase with the generator voltage, or the phase angle of the circuit is zero degrees. The voltage is maximum across either L, the inductor, or see the capacitor alone, okay, we have to take the output across each individual component. If I take it across both of them, they cancel each other out, it's going to be zero.

The impedance is maximum. I'm sorry, the impedance of this circuit is minimum at a frequency of residence and it's equal to a low Rs. That's the resistance of this circuit. Alright, so there you go. I've capsulized it. If you don't understand something, go back and rewatch This, you can reach out to me, I'll help you as best I can.

And before I go on, I promised you the link to that calculator that will calculate the resonant frequency. It's right there. So have fun with it. We'll see in the next section where we're going to talk about parallel resonance Now, take care. See over there.