 Now, let us see how amplitude modulation is actually done, you know, as in whatever we have done is a theoretical stuff, but practically how it is done, how it is produced, okay. So write down next heading, production of amplitude modulated wave, okay. Now, when you will be doing engineering, if you are planning to, then you will be seeing, you know, lot of, you know, such things which I am going to draw, you are going to see a block diagram here, so first let us draw all of you, this is a plus, so you can superimpose two waves here. What we will do? We will put here message signal m t, which is a m sin omega m t, okay. And then you put here carrier wave, this is c t, okay. This is a c sin omega c t. See, the way the amplitude modulation should done, should be done, will be in such a way that it should create three waves of frequency omega c minus omega m, omega c and omega c plus omega m. So if these three waves are present, no matter how you create am wave, you know, that it is fine. So it has, it should have these three frequencies, okay. So there can be multiple ways of creating these three frequencies. So this is what one of the ways is, okay, which we are going to discuss here. Then these two signals get added up, these two signals get added up and they become x t. So what is basically x t? x t is actually m t plus c t, okay. And then whatever x you are getting, you are putting it in a square law device. This is called square law device. So whatever goes in here, whatever goes in there will come out as a quadratic, okay. You will get y t, which is actually b times x t plus c times x t square, fine. So you are not directly squaring x t. What you are doing? You are doing b times x t plus c times x t square. This is the square law device, fine. And then you are putting under band pass filter, right down band pass filter centered at omega c. So what does it mean actually band pass filter? What it will do is, it will actually pass those frequencies which are near about omega c. It will not allow frequencies which are far different from omega c frequency, okay. It can only pass the frequency which are near about omega c, okay. So once you have this band pass filter, you will get the amplitude modulated wave, okay. So this is called am wave, fine. Now what I want all of you to do is, this is the value of m t and this is the value of c t. Now follow this procedure and tell me what is the equation of am wave you are getting on this side. All of you please try this. What is the equation of am wave you are getting at the end? So x t will be equal to m t which is am sin omega m t plus c t which is ac sin omega c t, okay. This is x t, okay. Now we have to follow the square law here. So this will be b times x t which is b times am sin omega m t plus ac sin omega c t plus c times this am sin. So guys this expression may look very big, okay. But then you have to try yourself until unless you try it yourself you will never be able to reproduce it when it is asked in the exam, okay. Now what I want you is to open up all the brackets and tell me how many frequencies you get. You get two frequencies, four frequencies, five frequencies or six frequencies. Quickly open up the brackets and tell me how many frequencies you have. Type in two, four, five or six. How many frequencies you have in this particular wave? I will just try and then I will wait. So this will be b am sin omega m t plus b times ac sin of omega c t, okay plus c into am square sin square omega m t, okay. Plus c times ac square sin square omega c t, okay. Then plus two times c times am into ac sin of omega c t into sin of omega m t, okay. Now if you look at this sin square omega m, sin square omega m can be written as one minus cos of two omega m t by two. Yes or no? This you can write down like that and this one, you can write down like one minus cos two omega c by two, okay. And when you open up this, when you open up this, you will get two frequencies omega c minus omega m and you will get what omega c plus omega m, okay. So this entire thing can be expanded as now I have to make some space over here. So y t will come out to be, all of you please write down b am minus b ac minus c ac square by two. See I can understand it is little overwhelming but then you know it flows. There is a connection from one step to the other step. So you can easily write down if you are sincerely doing it, you will get what I am writing here, okay. So you should actually do it with me here. Otherwise then you know before the exam you have to anyway do it and if you practice with me here then you will have to make lot less effort later on. Otherwise you have to do it from scratch once you start doing it. Okay this is what I will get. Now let's count how many you know frequencies we have, omega m we have, omega c we have, two omega m, two omega c, omega c plus omega m, omega c minus omega m. So there are how many frequencies? We have one, two, three, total six frequencies are there. Total six frequencies are there and if I write down the frequencies omega m, omega c, two omega m, all of you please write down this omega c minus omega m and omega c plus omega m. Okay now what I am doing here I am putting these six frequencies through a band pass filter which is centered at omega c. So since it is a band pass filter it will only send the signal which are closer to omega c. So omega c will go definitely, omega c will cross the band. This band will not allow frequency which is far away from omega c. Okay now tell me are these two frequencies, these one, one and two are these two frequencies they are near omega c or they are very far from omega c, far or near please message one and two these two frequencies they are far away from omega very far okay right so they are far. So band pass filter will not allow these two frequencies this is not allowed this is not allowed and even two times omega c is far even this is far away. So if omega c is 10 kilo hertz two omega c will be 20 kilo hertz so even two times omega c is very far now tell me omega c plus omega m and omega c minus omega m three and four are they very far or near they are near okay because omega m the message frequency is very less so you are subtracting or adding a very less frequency with a very high frequency which is omega c. So the band pass will only allow omega c omega c minus m and omega c plus omega m. So that's how you generate these bands okay so I hope you have understood this particular thing and this is what transmitter does transmitter will take the message signal do some sort of modulation okay amplify the power and then send it through the transmitting antenna. So if I draw a block diagram of the transmitter this is how transmitter will look like this is a block diagram of the transmitter it's a block diagram of transmitter so you have message signal this is message signal you have carrier wave okay and this is amplitude modulation that is going on here inside the transmitter okay so how much gap sir so how much gap is allowed see r n it depends on what bandwidth you want to occupy so you can like depending on you know your message and omega c the band will become fixed so if you want to occupy higher bandwidth then you know accordingly you will see what message signal you have to transmit okay so there is no fixed answer to it because the the gap is different for different thing but then it should be it should not be very large the gap should not be very large it will have the gap will have two times the frequency of the message right because you have omega c minus omega m and omega c plus omega m the difference in these two frequencies is two times omega m so this is what the gap is so two times the frequency of the message this is what the gap will be okay so coming back to this block diagram of the transmitter so this is amplitude modulation and here what you do you amplify you use that amplifier transistor amplifier that we have learned so you have power amplifier here which amplifies the power of this modulated signal and then this is transmitting antenna okay so such is the complicated communication that happens inside our phone transmitting antenna so transmitter inside our phone does all of this whatever you speak on your phone that get transmitted okay now this is with respect to transmitter now our focus is on the detection part of it so at the receiver end what happens this is what is our next focus so this is the last topic of this chapter so this is after this the part the chapter gets over write down detection of am waves fine now the way the amp see the thing is transmitter modulates the signal and this then it throws it through the channel okay now the modulated signal although it contains the message but modulated signal is not the message okay so receiver will receive the modulated signal okay and once the receiver receives the modulated signal it has to extract the message from the modulated signal then only it can play at the receiver end like when you speak on your phone the message whatever you speak it get transmitted and the person who receives it on his mobile phone on his or her mobile phone there will be receiver who will be demodulating the signal which it is receiving okay so the focus is on what happens at the receiver end now okay so we are talking about the amplitude modulated wave okay the way amplitude modulated wave is received so we have here a block what it will do it will amplify the received signal this is amplifier okay and this time in the receiver the antenna comes first in the transmitter the antenna comes the last because you have to do all the processing and then throw it through the channel fine so antenna comes the last in transmitter but in receiver it should first receive so that is why the antenna coming first when we talk about the receiver so this is the amplifier the message the modulated message goes to the amplifier and then you have this block is called if stage okay we will not discuss too much about how this if a stage is getting constructed or how the amplifier get constructed okay what is the antenna what is the construction of antenna all that is a very involved topic this you will learn in your engineering the basic construction of antenna itself will take couple of months to understand this is detector and then again we have amplifier okay this is amplifier and here is the output this is what you receive or this is what you hear through your speaker this is what you hear okay so before hearing the message gets amplified what detector that does it detects the message after if stage okay let's see all of it how it happens okay so you have suppose amplitude modulated wave which comes like this this is the amplitude modulated wave this amplitude modulated wave comes okay then what you do you put it through a rectifier there is a rectifier what rectifier will do it will convert this alternating signal into direct signal so you are using a full wave rectifier here so what you'll get is this this one remains the lower one is gone okay then what we are doing here this is envelope detector envelope detector will detect the variation of the amplitude and reject everything else okay so at the end only this will remain okay and this is the shape of the message signal fine so I hope you have understood this particular thing the if stage is actually rectifier and this envelope detector is this okay and before if and detect before if and after detector you have amplified okay so if you want to draw a block diagram on how it is done you can do that also so here we have rectifier and then it goes to envelope detector okay before the output comes in so in this block diagram we haven't drawn the amplifier but amplifier is required because the at times signals are very feeble all right so this is what the entire chapter is all about I hope you have you know understood the entire thing and in case you have any doubt please message me right away anything with respect to this chapter okay you have any doubt please message or if you don't have a doubt then also please message that no doubts so that I can proceed further okay so I'll take that answer for everyone no doubts