 Hi, I'm Zor. Welcome to Unisor Education. Today we will continue talking about radio transmission. In particular, we will talk about one particular way to communicate through radio waves. It's called frequency modulation. Now, this lecture is part of the course called Physics 14 presented on Unisor.com. I suggest you to watch this lecture from the website rather than from some other source where you can find it, like YouTube for instance, because all the lectures are combined basically into course. But there are two courses actually. There is a prerequisite course, Math 14s, organized in exactly the same way. So you can always reference one lecture from another, plus every lecture has very detailed notes and sometimes with pictures, much better than whatever I can draw here obviously. And there are problems solving and there are exams for those who want. And the website is totally free. There are no ads, no strings attached. You don't even have to sign in if you don't want to. Okay, so let's start with frequency modulation. Now, we were talking about amplitude modulation before. This is one of the ways to transmit certain information, like sound. Let's talk about sound. To transmit sound through radio waves, because radio waves by themselves do not carry any information. It's just oscillations of electromagnetic field. Now, the source of these oscillations is something like LC circuit, which combines inductor capacitor and the electric current will just circulate back and forth, oscillate, and we're talking about why it happens with certain frequency. If this is capacitance C, this is capacitance L, the frequency, angular frequency is equal to, and it emits obviously radio waves if you can combine it with antenna through some kind of a transformer here. And this is the grounding. So this is basically a schema of transmitter, the first transmitter. Obviously, it's much more complex right now. So the oscillations by themselves do not carry any information, but if you would like to transmit voice, for example, you have to somehow modify these oscillations, something like to code information into it or to modulate as they're saying, modulation. Sound signal onto the oscillations of electromagnetic field produced by transmitter. So the first idea which we were talking about before was amplitude modulation, which is very, very natural kind of way. So whenever you have a sound, some kind of source of sound, obviously we are using microphone to transform it into oscillations of current in some circuit. And now we have to basically apply those oscillations, oscillations of sound onto the oscillations of this circuit. And then they will go, instead of this way, these are unmodulated oscillations of this particular frequency. Instead, if there is some kind of a sound which is much less frequently oscillating molecules of air and therefore current in some circuit produced by microphone. So we are modifying amplitude in sync with modification. So this is higher, so we will have a greater amplitude. This is lower, we will have lower amplitude. This is a higher gain. So the waves of the sound will be corresponding to waves of the amplitude. This is kind of a very first idea which came to people's mind. Now what's the problem with this? Well, the problem is that it's not very easy to basically get into every little detail of a sound. Now this is a very nice and smooth sound. Now a real sound, like if you for instance have an orchestra playing, you have many different instruments, every one of them has its own oscillations of air molecules. Now every oscillation is described by, let's say, something like a cosine omega t plus 5. Where a is amplitude, omega is the angular frequency of oscillations and phi is even some kind of a shift. Maybe one instrument starts earlier than another. So if you combine, let's say, 10 or 20 different sinusoidal oscillations with different a's, different omega's and different phi, you will get a really kind of chaotic graph here which represents the oscillations of air because everything is finally the oscillations of air which microphone is sensing and converts into oscillations of current which is supposed to be somehow modulating this constant frequency of signal produced by this LC circuit. So again, that was the first idea to use this type of amplitude modulation and it had certain problems. The problems are mostly related to the quality. Apparently the higher frequency of sound oscillation, the more difficult it is to inscribe somehow this higher frequency into every detail of the sound. Plus there is something which is called radio noise. So the devices which are built on amplitude modulation are very sensitive to noise. Now what it means is that we probably can successfully transmit certain types of sound but not all of them. The higher the pitch of the sound which means the higher frequency of oscillations, the higher the greater omega, the more difficult it is to inscribe our high frequency radio signal into every curve of the sound. So let me talk about numbers. The sound which our ear can actually sense is from 20 to 20 thousand hertz which means oscillations per second. Now let's talk about kilohertz. It's more convenient. So our ear can sense from 20 in kilohertz is 0.020 kilohertz to 20 kilohertz. So that's our ear. Now the musical instruments are not actually up to 20 kilohertz. 15 is considered to be relatively high for any musical instrument because the ear is more sensitive than the highest note produced by regular instruments. Now if we are talking about the amplitude modulation then the frequency of LC circuit produced, the frequency of carrier regular signal is from 540 to 1600 kilohertz. So this is significantly higher than this. Why? Because we would like to inscribe actually these high frequencies into lower frequencies to reflect every little detail of the sound wave. So that's why it's much higher. Now that apparently even with this particular standard of AM communication we can represent up to 4.4 kilohertz sound frequency. Not to 20, not even to 15 which is the highest musical note produced by musical instruments. And obviously the human voice is even lower than that. But this is the maximum which usually is represented with decent quality. Everything else will be distorted. So this actually puts some kind of upper limit to AM transmission. It's good for voice. So that's why for instance the news radio stations are mostly AM. And something about Hi-Fi. No, Hi-Fi is not really well transmitted through AM amplitude modulation. So we need another idea. And I was talking many times that it's probably much more difficult to come up with very first idea than to subsequently develop it into the real product for instance. So there was a person, I forgot his name, who invented a different type of changing the carrier signal by sound waves in such a way that it's still decipherable on another, demodulated on another side, on the receiver side. But it's a different kind of a communication which allows to represent a higher quality sound. Now the idea is instead of changing the amplitude of the base carrier, let's consider the base carrier always, that's not good, that it's always on the same frequency. That's the frequency which is produced by the corresponding LC circuit of that particular transmitter. It's tuned by L and C, by inductance and by capacitance of the components. And other components, obviously it's much more complex than just simple two parts. Now, what he suggested, this person, so whenever you have a higher sound, we will make this frequency a little bit tighter, a little bit, not by much. But whenever signal is low, the frequency will be lower, and then the frequency, when a gain sound goes up, the frequency gain will increase. So amplitude will be the same, but the frequency of oscillations will be slightly changed around the base frequency this particular transmitter is supposed to be transmitting information. So whenever you're saying that one particular radio station, FM frequency modulation radio station transmits uncertain frequency, it actually means that it deviates from this main frequency back and forth, up and down, a little bit, within certain boundaries. And these deviations are sufficient to basically represent sound much better, to add, I think, up to 15 kilohertz. So much higher, which basically is sufficient to represent all musical instruments in high-five quality. So this is a very important idea which came to mind somebody. Now, how can we accomplish this? Now, with amplitude oscillation, all we need is to change the amplitude of the current which circulates in the LC circuit. So whenever you have a higher sound, AM modulation just allows more current to go through. Whenever the sound is lower, we are probably using something like a variable resistor to change the current in the LC circuit. And that produce corresponding changes in the signal which is emitted by the antenna. In this particular case, we should not touch the amplitude, we should really touch the frequency. Now, the frequency is dependent on these things. So all we need to do is to change either C or L. So either we are using a variable capacitor or variable inductor, and slight modification of the values of capacitance or inductance will eventually change the frequency of transmission. Apparently, this allows a better quality. Now, in practice, in the United States, frequencies from 88,000 kilohertz to 108,000 kilohertz. This is the bandwidth of all the FM transmission, frequency modulation. It's divided, so it's 20,000 difference between them. So this 20,000 is divided into 100 channels. So each channel would be 200 kilohertz wide. So every station has the main frequency, for instance, like 88,100. And from 88,100 plus 100 and minus 100, so from 88,000 to 88,200, would be a channel for that particular radio station. Which means we can accommodate no more than 100 radio stations which are transmitting FM signal. Well, at least in the vicinity where this particular signal can be received. Now, since this is a higher frequency, this is 88,000 up to 108,000. This is up to 1600 kilohertz. So AM is significantly less frequent. So that's one way to explain why we cannot really transmit higher signals. So there are some historical considerations. Quite frankly, I don't know. Maybe if we will use this very, very high frequency of transmission and use amplitude modulation, maybe it would be fine as well. But anyway, historically, this is the range and this is much lower than this. So this allows, just because of the frequency, it allows to do much better quality. And also this principle of using frequency modulation rather than amplitude modulation makes this particular type more stable as far as radio noise is concerned. For some reason, which let's not actually get into this, this is probably for professionals, the amplitude modulation is more sensitive to noise than the frequency modulation. Okay, so we covered that. So you understand the graph. Now, if you will go to the website Unisor.com and look at the comments to this lecture, you will see better graphics than these two, obviously. Alright, and the last thing which I wanted to talk about is the implementation. Well, I did actually touch the implementation of the frequency transmission, should be arranged using variable capacitor or variable inductor. And now, what seems to be the result of this is that we can represent much better quality, up to 15 kHz frequencies will be correctly reproduced and interpreted on the receiver side using this methodology. Well, that's it. For AM modulation, I also had a lecture which describes AM modulation as basically an equation. Well, this type of equation. I mean, how it's actually looking mathematically. Now, I will have another lecture probably the next one, which will be about how FM modulation looks mathematically. I have to warn it a little bit more complex than for AM modulation. For AM modulation, we just added the sound wave equation, something like this, to amplitude. In this case, we have to add it to a frequency, but that's not as simple as this. So, I'm preparing this lecture, that would be our next one. And that would be an interesting lecture for people who are more familiar with mathematics, because there will be derivatives integrals, etc. Just to emphasize once more that for any kind of physics study, you do need mathematics. So, definitely calculus, vector algebra, something like this. Okay, that's it for today. Thank you very much and good luck.