 Welcome to next lecture. So today we are going to see amplitude modulation and double sideband with suppressor carrier. These are the learning outcomes. At end of this session, students will be able to explain amplitude modulation and double sideband suppressor carrier modulation. Before starting to this session, recall modulation and the types of modulation technique what we have studied in the previous lecture. So let's start with the amplitude modulation. What is amplitude modulation? Amplitude of the carrier signal is changed in accordance to the instantaneous amplitude of the message signal. Message signal is the information signal. Though the amplitude of the carrier signal is changed with respect to modulating signal. Next, the carrier frequency must be relatively higher than the message frequency. If you want to calculate the modulation index, it is the ratio of Vm by Vc, where Vm is the amplitude of modulating signal and Vc is the amplitude of the carrier signal. In the same manner, if you want to calculate the modulation index in terms of percentage, we have to multiply by 100%. So you will get modulation index in terms of percentage. So now we will see the mathematical expression of an amplitude modulated signal in the time domain. So if we have the output result of an amplitude modulated signal, so we have Vam is equal to Vc sin omega ct plus m Vc by 2 cos omega c minus omega mt minus m omega vc 2 by 2 cos omega c plus omega mt. As this expression consists of a carrier signal as well as LSB and USB. LSB means the lower sideband and the USB means upper sideband. So this is an output of an envelope. So as we have seen in this graph, so this is a message signal which consists of an information and this is the carrier signal. So the output of these two signals is this that is known as an amplitude modulated wave. Here we have the carrier signal as well as LSB and USB. So as shown in this figure where there is no modulation means no information is there there is no output here. So no modulation will be there at the output side. So this is known as an frequency of an modulated modulating signal and this is the frequency of an carrier signal. So this is the Vmax and this is Vmin. So the modulation index lies always between 0 and 1. If it is more than 1, it is known as an over modulation. If it is less than 1, it is known as an under modulation. So after calculating this, how much bandwidth is required to transmit an AM signal? If we calculate the bandwidth that is USB minus LSB because the bandwidth is upper cutoff frequency minus lower cutoff frequency. So the bandwidth is given by fc plus fm minus fc minus fm. So that gives an 2 fm. So you require 2 fm bandwidth to transmit an AM signal. So from this mathematical expression, we conclude that so AM signal will consist of carrier signal LSB and USB. So if you want to represent AM signal in the frequency spectrum, so we have to represent in this manner. So this is an frequency and this is an voltage. So as shown in this figure, you have seen that f is USB and f LSB that is frequency of an LSB and frequency of an USB and this is an the carrier signal and this is an amplitude of these two signal. So it is being calculated m in 2 ec by 2 and m ec by 2 ec means the amplitude of an carrier signal. So this is an carrier signal. So now we will see the AM power distribution. The total power in AM signal will have three components that is PC, PLSB and PUSB. PC is nothing but the power in carrier LSB is the power in LSB and power in USB. So all these three things we require to transmit and the total AM signal. If we calculate individually, that is a carrier signal power that is PC is equal to V square C by 2 RL. So how it is coming? Because as a power is calculated in terms of three methods that is P is equal to V into I, P is equal to I square I, P is equal to V square by R. So we are going to take V square by R as these all signals are in varying quantity that is an AC signals. So we have to take an RMS value of that. So to calculate an RMS value, we require peak voltage upon under root. So we have to substitute that values into this PC. Then you will calculate carrier signal power that is PC is equal to V square C by 2 R. In the same manner, if you calculate the lower and upper sideband, so that is PLSB and PUSB, it comes out to be a M square by 4 into PC. So it will be same for LSB and USB and total sideband power if you calculate PLSB plus PUSB that comes to an M square by 2 into PC. Now we will see how much power is required to transmit and total AM signal that is PAM is equal to PC 1 plus M square by 2. So when the maximum power is required that is M equal to 1 because the modulation index lies between 0 and 1. So total AM power becomes 1.5 into PC. Next, if you calculate the efficiency of an AM signal, it comes to be an M square by 2 plus M square. So when the power efficiency is maximum, when M is equal to 1, if you calculate that, it comes to be 33.33 only. So the efficiency is very less in the AM signal. So we have to remember all this formula for solving the problems that is how much total power is required. It is being calculated according to the PC plus PLSB PUSB, carrier signal lower and upper sideband and total sidebands. And this is the total AM that is PC 1 plus M square by 2 and efficiency is M square by 2 plus M square. So these are the different AM systems that is now we have studied up till now the AM signal only. So these are the types of AM systems, double sideband with the suppressed carrier system, SSB that is known as a single sideband system, independent sideband system that is an ISB, vestigial sideband which is VSB which is used in the TV transmission. So now we are going to see the double sideband suppressed carrier modulation that is DSB SC. So it is modified from the AM technique in which the carrier signal is completely suppressed from an amplitude modulated signal and transmitting only two sideband upper and lower. Means if you want to transmit a DSB SC signal, we are going to suppress the carrier signal and we are going to send only two sidebands. So what is an advantage of doing that? So we can save a lot of power by suppressing the carrier and then DSB SC signal can be obtained by the multiplying the modulating signal with carrier. So there are two types of circuits are used to suppress the carrier which is ring modulator and second one is the fate modulator. So this is to represent the frequency spectrum of DSB SC wave. As we have seen in the AM modulated wave, the carrier signal was present here but in DSB SC signal the frequency that is the carrier frequency has been suppressed. Only two sidebands are being sent here. So one more thing, in the two sidebands the same information is there. So by suppressing the carrier signal, we have power saving that is up to two-third of the power is saved as more power is required to transmit an AM signal in which the carrier requires more power by which the 50% of efficiency goes on increasing. So we will study the circuits to suppress the carrier in the next lecture. So ring modulator and the fate modulator. So these are my references that is an analog communication AP Godse and UA Bakshi and analog communication by VA Chandra Shekhar. Thank you.