 Hi, I'm Zor. Welcome to a new Zor education. I would like to start a new topic also related to electromagnetic waves. And that's one of the most important applications of electromagnetic waves, the radio. So this lecture will be about how to... Well, it's a very, very basic and very fundamental piece of knowledge about how people started thinking about receiving radio signals. I'm not going to talk about how to transmit it, maybe that would be a subject of another lecture. But this is about how to receive radio signal and, well, basically understand it. So we can use it like radio, for instance, to transmit the sound. Okay, so this is about some very first, very fundamental, very basic ideas which came to somebody's mind when they invented the way how we can receive the radio. By that time, people understood certain concepts about electromagnetic fields. And they did understand that we are all surrounded by electromagnetic fields which are oscillating with different frequencies, different amplitudes, different phases, etc. And there are many sources of these oscillations. Well, let's start with our Sun and Earth itself. It has a magnetic field. And it's all changing, plus all the electric devices which we are using. They're all generating certain signals, electromagnetic waves, electromagnetic oscillations. So we are all surrounded by this. Well, we do see some of them. So if electromagnetic oscillations are within certain frequencies, our eye is sensitive enough to feel it. That's what the light is. Now, the other frequencies are greater than the frequencies of visible spectrum or less than that. We don't really see, but they still exist. It's all different frequencies. Certain frequencies we see with our eyes, other frequencies we don't. But we do have certain tools, certain devices which can feel it, measure it, react on these waves, etc. And the radio is one of those devices. So it somehow accepts the certain electromagnetic oscillations and converts it into oscillations of the air which we can hear with ear. Okay. Now, what's the most important problem? For instance, we know how to transmit certain radio frequency. And the question is how can we receive this particular frequency, considering we have so many different sources of electromagnetic oscillations. And somehow we have to select from all these different sources with all different frequencies, etc. One particular frequency where we would like to listen to a particular song. Okay. Now, to understand that concept, we really have to be very much familiar with the concept of forced oscillations. Now, what's interesting, and that was actually part of the previous lecture, I mentioned that equations of oscillations within a circuit which contains inductor and capacitor, these equations are exactly the same as oscillations of mechanical oscillations, like an object on the spring, for instance. The equations are exactly the same and principles are exactly the same. So, it's very important for you to understand whatever was started in mechanical oscillations, topic of this course, and in particular there are two different lectures, one of them is called force oscillations, one another is force oscillations, two. And in the force oscillation, two, I was talking about resonance, which is extremely important for the subject of this lecture. And also there is a problem following the force oscillations number two. This is a problem number four in that topic of mechanical oscillations. And that's basically about force oscillations when you have a capacitor, you have inductor, and you have a resistor in the RLC circuit, as we call it. So, everything in that particular problem, problem number four of mechanical oscillations topic, is exactly applicable to oscillations in the RLC circuit or L-C circuit as we will talk about today. So, it's very important that you understand all those equations, the solutions to these equations. I will use the basically whatever was there as given in this particular case. Because again, equations are exactly the same, just different letters. Next. So, we were talking about the space around us filled with different electromagnetic oscillations, waves of different amplitudes, different frequencies, different phases, etc. Okay, question is, how we can select from all these coagulant oscillations, excuse me, oscillations of particular frequency where we know used for transmission of specific signal which we are interested in. For example, you would like to tune on station such and such, 7.70 a.m. for instance. Well, that's basically the wavelengths or a frequency which characterizes a specific oscillations. And we would like to select it from all other frequencies of oscillations of different sources, including given those from far stars. They also, it's weak electromagnetic oscillations, but since we see the light from the star, we definitely understand that there is some electromagnetic oscillations because light is the electromagnetic oscillations. So, even from far stars we have electromagnetic waves. Okay, so now we will talk about how LC circuit, a circuit which contains inductor and capacitor, can help in selecting a specific signal out of these coagulant conglomerate of all other waves which are filling our space around us. Okay, so let's start with a very simple thing. For example, you have some kind of a conductor. Let's say it's just piece of wire and let's say we just connect it with the ground. So, whatever kind of current exists in this wire, it all goes down to the earth. So, this is how we will use the symbol we are using for this piece of wire. Now, why do I need a piece of wire? Why do I need a conductor? Well, you remember the Faraday's law of induction. Whenever you have oscillating magnetic field, it creates oscillating current, some kind of a current, in any conductor. So, I just use the piece of wire and all these coagulant oscillations of electromagnetic field around us will be reflected in this conductor. So, everything is based on this Faraday's law of induction. Electric current in this particular wire is inducted, is induced by the oscillations of electromagnetic field around it. Okay, so, from something which I don't really feel, don't really see the electromagnetic waves around us, we have made the first step. We have reflected all these coagulant oscillations in a piece of wire. Well, this is something tangible because if we have a current in the piece of wire, we can measure it, we can basically have some device working off it, etc. So, the first step we have done, we have captured the radio signals. Well, I'm using the word radio signals, but actually it's electromagnetic waves, oscillations of electromagnetic field. So, we have caught all these coagulant radio signals around us into something quite tangible which we can use. Okay, great. But inside of this wire we have exactly the same chaotic conglomerate result of superposition of all different oscillations with all different frequencies, phases, amplitudes, etc. How can we select one particular? Okay. Now, to help us with this particular process, we can use a concept called resonance. So, again, let me go back to mechanical oscillations. It was explained in the lecture related to forced oscillations. It's a second lecture for forced oscillations number two. So, the concept is if you have, well, let's say, let's go back to mechanical. If you have, let's say, a swing, okay, the swing goes back and forth, back and forth. It has its own natural frequency of oscillations. So, if I will not apply any forces, it will just go back and forth, back and forth. And if there is no friction, it will go indefinitely without stop with a particular frequency. And the frequency depends on the lengths and, I mean, the characteristics, basically, of this particular swing, right? So, it's a characteristic of swing. No matter how far we move our swing from the initial position and then let it go, it will still go with the same frequency, regardless of my initial condition. Frequency is inherent to the construction of this particular swing. Now, let's assume that you have the same swing and you're trying to apply force to basically swing it further and further. If your force is also periodic with a certain frequency, only in case your frequency is the same as the frequency of the swings, you will get a real result, you will basically, the swing will go to greater and greater amplitude. So, amplitude will be increasing. And graphically, you can devolve it with this. That will be the movement of the end of the swing of the initial, of the neutral position. It will be greater and greater if your force is in sync. So, it's increasing the oscillations of the swing. Same thing happens with LC circuit. So, if you have an LC circuit, which we were talking, we were talking about RLC with a resistor as well. But let's forget about the resistor, let's forget about friction in the mechanical oscillations and we will forget about the resistor in the electronic oscillations. This is an electronic oscillator without resistors, without basically resistance. So, we have only the capacity of the capacitor, capacitance and inductance of inductor. So, based on just this construction. Now, if you remember the previous lecture, I was charging the capacitor and let it go. And after this capacitor was discharging to this direction. But since there is an induction, the magnetic field would induce electric current. And not only it will go down to complete zero, it will go more and it will change the charge to the opposite. And then back and then again this direction and that direction. So, that was the last lecture. Now, that means that this particular device acts like our swing. It has its own frequency of oscillation, which it was derived as this. This is its own frequency of oscillation, which depends only on the parameters of this particular circuit. So, I'm thinking, well, not me, obviously. People who invented radio were thinking that out of all these chaotic oscillations, if we will be able to induce additional force, inducting force, induced force, if you wish, onto this circuit, which would exactly equal in frequency to the own frequency of the LC circuit, then these oscillations will start increasing. Well, of course, resistance, natural resistance will not allow it to go in infinitely high. But it will definitely be enhanced. So, the signal which comes here, if it comes here with the same frequency, will be enhanced. So, the oscillations with this particular frequency will be of a greater amplitude. Now, if we will have all these oscillations applied to this particular LC circuit, well, we will induce all these currents which are oscillating here in this wire. We will induce additional electromotive force onto, let's say, on this inductor. But some of those frequencies which we are inducing will not affect the amplitude. So, if they were weak, they will be weak, this thing will not increase their amplitude. But one particular frequency which is equal to this one, so out of this chaotic, one particular type of oscillations, those which have this frequency, they will actually be enhanced because they will work exactly like we were working with the swing. If our external force exactly equal in periodic movement to the movement of the swing, swing will be moving further and further from the center line. Same thing here. So, only one will be enhanced, the frequency which corresponds to this. Now, how can we transfer these oscillations to, let's say, to this inductor to generate a little bit more force? Well, we can do this. We can put some kind of a transformer here and connect it. So, the oscillations here of the current which are basically induced by electromagnetic oscillations of everything whatever happens in the whole space, they will all result in oscillating current here, oscillation current here. It's like a transformer basically. If there is some kind of a ferromagnetic connection between these two inductors. So, it will transfer here. So, the oscillations here with all the different frequencies, I mean result of superposition of all these waves. It looks really very chaotic, but it's actually a sum of sinusoidal oscillations with different amplitudes and frequencies and phases. So, it will be induced onto this. So, this thing will have basically two sources of energy. The energy of initial capacitor which goes back and forth, back and forth, and that's a concrete frequency. And also it will have some kind of a push from this connection. And the push will be a sum of all the pushes from all the different frequencies of all the different oscillations which are happening in this wire. Which reflect everything which happens in our space. So, everything will be reflected here. But only one particular frequency will fall on this one and only this one will be basically enhanced. So, after some time, well actually a very short time, the oscillations in this particular circuit, they will still contain lots of oscillations with different frequencies, different amplitudes, etc. But all those which do not correspond to this will have a smaller amplitude than the one particular oscillations with this particular frequency. Because it goes into resonance with the own frequency of oscillations of this LC circuit. So, the result of this will be a sum of one particular strong sinusoidal wave, like this one. And many more, many different oscillations with different amplitudes, different frequencies of different amplitudes and different phases, etc. But they all will be very small. So, as a result of the summing of this thing, I will have a signal which basically goes like this. So, it's still a useful thing. Because this is definitely something which we can use in some device which converts this particular frequency into some kind of oscillations of air around us so we can hear it with our ear. So, obviously, the better selection of one particular frequency is, the more difference we will have in the useful wave relative to all others which are actually in noise. And that's what actually defines the quality of the radio reception and there are different devices, etc. Now, do not think that this is it, that this is the solution. Because obviously, this is an idea. On the top of it, this idea was developed many times throughout the whatever hundred of years, well, 150 maybe years. Since invention of the radio and the quality is gradually increasing. So, basically, I wanted you to just familiarize yourself what is the main principle on which the radio actually reception is actually created. And that's the principle. The principle is a resonance between all the different chaotic electromagnetic waves which we can catch with an antenna. And one particular frequency which actually is a characteristic of our circuit. And only the frequency which corresponds would actually be selected. Now, the quality of selection is a different question, obviously. So, now, one particular circuit has one particular frequency of oscillation, own frequency. Which means that one particular circuit can actually select only one particular type of waves, waves which have this particular frequency. Now, how can we tune our radio to different stations with different frequencies of transmission? Well, here it is. Okay, this is a symbol for a variable capacitor. Now, what is a capacitor? Basically, it's two plates. You can just think about the simple capacitor. Two plates conducting plates on certain distance. Now, depending on the distance between the plates and their area, we have different capacitance of the capacitor. Now, what if I will be able to do it this way? So, I'm shifting one plate relative to another. Well, I'm basically changing the common area where electrons can actually act among themselves. So, I'm changing the capacitance. So, this will be a smaller capacitance than this one. So, whenever I'm shifting, I'm basically reducing the common area between these two plates. And that's the principle of variable capacitor. I mean, the first principle, again, any device has been transformed many times, but idea is exactly the same. My purpose is to introduce you to idea. So, idea is that there is a variable capacitor. Now, actually, you can also do the variable inductor because, for instance, you have some kind of a center ferromagnetic core inside the spiral. Well, by lifting and putting it up and down, you will change the inductance of the inductor. So, both inductance and capacitance can be variable. You just have to make a special device for this. If you have an inductor, you can obviously create a variable inductor. If you have a capacitor, you can create a variable capacitor. Okay. So, by using the variable capacitor, we can change one of these and change this. And that's how you tune to a specific frequency. Obviously, you can have some kind of a scale where you see exactly what's your particular frequency which you are trying to tune in. And based on that, you're changing your own frequency of oscillations of your LC circuit. And that's why you are selecting a different frequency of oscillations of electromagnetic field, which is a different radio station, for example. And that's basically what I wanted to talk about today. Again, two things very important. Go back to the lecture on mechanical oscillations. So, you go to Unisor.com, Physics 14, that's the name of the course. You go to Waves, that's part of the course which dedicated to Waves. And then the first topic is mechanical oscillation. And among the mechanical oscillations, you will see the particular lecture on forced oscillations, forced oscillations 1 and 2. And there are equations, there are solutions, differential equations, etc. Now, this lecture is without any kind of differential equations or anything like that, because I'm just referring you to those previously already delivered to you. And equations are exactly the same for mechanical oscillations as they are for this LC circuit. So that's very important. And another thing is, don't think that you understand completely how radio is working. This is just the beginning. This is the main idea from which something started. And then the whole development for 150 years or so have to be applied on the top of this idea to get something which you can use today and which delivers you a very clear high-quality, high-fidelity quality of the sound. So that's basically a very long history of development. If I will show you right now schema, which is significantly different than this one, schema of the real radio. Well, if you didn't see it yourself, obviously before, you'll be surprised how complex it is. Because you have to put lots of other different filters, different other devices which increase the amplitude, for instance, of the signal. Because even after it's enhanced by these oscillations, it has to be smoothed so you don't have these kind of tooth-like extensions to a regular signal. So you have to smooth the whole thing, etc. It's a lot of thought in the contemporary radio, a lot of very ingenuity and engineering solutions. And what's important is, again, the principle. My purpose right now is to introduce it to a principle. And that's the beginning. That's how the first inventors of radio, whether it's, you know, I don't want to get involved in who actually did it first, doesn't really matter. But whoever did it, they were using something like this to start and then the whole development actually started. It's always more difficult to come up with a principle than to develop very gradually, step by step. You see, the very first principle is a huge jump. But then when this jump is made and people understood how the whole thing can be made, then they started to increase, to improve, to develop, etc., etc. And then there is a gradual improvement throughout the time. So after the first jump, after the first invention, so to speak, then it's much easier and smoother and then many people are involved. Jump is usually related to one particular person or a group of people. And then it's spread around and people take over basically the whole concept and develop it to whatever the quality of, in this case, radio. We have right now. Okay, that's it. Thank you very much and good luck.