 Myself, Mr. Aaliyar Sanjani, assistant professor from Department of Electronics, Walchen Institute of Technology, Sulapur. Today, we are going to see the topic Introduction to Frequency Modulation from the subject Analog Communication. So, basically what are the learning outcomes from this topic? So, at the end of this topic, students will come to know the concept of frequency modulation and its mathematical representation. Next, they can compare between AM, FM and PM techniques. Also they can compute power of the FM that is frequency modulated wave, modulation index, frequency deviation and bandwidth for FM signal. So, basically what is modulation? So, the definition is the it is a process in which some characteristics of low frequency signal that is modulating signal which is also known as main information signal are varied in accordance with the characteristics of high frequency signal which is known as the carrier signal. Here the characteristics generally deals with the amplitude, frequency and phase of that particular modulating signal. Next, there are types of analog modulation. So, basically there are three types of modulation. First one is the amplitude modulation, second one is the frequency modulation and third one is the phase modulation. So, frequency modulation here in this the modulating signal changes the frequency of the carrier signal that means here the main information signal changes its frequency with respect to the frequency of the carrier signal and hence the total bandwidth required for FM can be determined from the bandwidth of the audio signal which is given by bandwidth of FM is equal to twice of 1 plus beta into B where B is audio frequency and beta is usually considered as 4 where beta is nothing but the modulation index. And here you will see that here in this, this is the main information signal and there is a carrier and this is the AM modulated signal and this is the frequency modulated signal. Here you will see that here the amplitude varies in accordance with the modulating signal and here you will come to know that the frequency varies with respect to the frequency of the modulating signal. The frequency deviation here we are going to see the concept of frequency deviation here it is defined as maximum change in frequency that can occur in a carrier from its base value FC which is called as frequency deviation and which is denoted by delta FC. Here the modulation index can be defined as it is defined as the ratio of frequency deviation to the maximum information frequency that is Fi and which is denoted by beta and it is given by beta is equal to del F upon del FC upon Fi where del F is nothing but frequency deviation and Fi is the maximum frequency of the main information signal. So modulation index here you will come to know how a modulation index can vary or how it affects the frequency of a FM modulated signal. Here you are seeing this is the main information signal or modulating signal here is the carrier and here third is the waveform where the modulation index is of 3. Here you will come to know that these consecutive waveforms generally denote the high frequencies and the lagging waveforms which are away from each other generally these denote the low frequencies. Similarly, we are going to see the different changes in the FM modulated wave where the modulation index is of 5 and here it is of 7. Here you will come to know the clear cut idea that how the modulation affects the main frequency modulated wave. So this from this we can state two important points that as the modulation in modulation index increases the peaks of the high frequencies get closer that means this and for the low frequencies these get further apart or away from each other that means these represent the high frequency and these represent the low frequency. So determination of bandwidth for FM radio so bandwidth can be determined by using the modulation index here for example we are taking the modulation index which is to be greater than one which is high and generally this term is generally known as wide band FM signal. So for example if we can take if the national radio broadcast uses the FM frequency for a frequency deviation of del C which is up to 75 kHz and the bandwidth of the main information signal generally lies from 20 Hz to 15 kHz then the bandwidth is generally given or the modulation index is generally 5 and such broadcaster can determine the bandwidth of FM signal by using this equation bandwidth of FM radio is equal to twice of del F C plus F maximum as we know that del F before it is given as 75 which is the frequency deviation and F max is the maximum frequency which is of 15 kHz and hence the bandwidth comes up to be 150 kHz. So sideband generation in FM as we all know that sidebands are also generated in AM modulated signal in FM 2 we are getting the sidebands and these are generally given by using the equation as twice beta plus 1 where beta is nothing but the modulation index and these are represented in this format that is on the x axis we are taking frequency and y axis we are taking amplitude generally right hand side of the center frequency or the carrier frequency F C denotes the USB and the left side generally denotes the LSB so practically bandwidth is given by number of significant sidebands multiplied by the width of each sideband that is Fi and it is given by twice bandwidth twice of modulation index plus 1 into the maximum frequency but as we know that modulation index is given by the ratio of frequency deviation to the maximum frequency hence we are putting up the equation over here and by solving this equation we are getting the final equation as twice delta F C plus Fi. So from that equation you can solve some examples the here the maximum deviation of the carrier del F C is given as 50 kHz and the bandwidth or the range for modulating signal is given by 20 Hz to 15 kHz so calculate the bandwidth for such type of two signals which is given by using the formula of bandwidth hence find out the answer yes the answer comes up to be 130 kHz similarly solve the second example where the frequency deviation is of about 10 MHz and the baseband is of about 5 MHz again here use bandwidth equation formula and find out the bandwidth here you will come to know or the answer will be yes so the answer will be 30 MHz so these are some of the examples which for your practice where a carrier is of 10 MHz then it has frequency modulated signal of 8 kHz and then there is a deviation of 30 kHz similarly second suggest why it would not be sensible for long wave radio transmitters operating in a in the range of 110 kHz to 300 kHz to use FM so for the second question you have to revise all the previous shown PPTs and then find out the answer as well as give the reason for this question so these are some of the references which are used for the making of this PPT thank you for watching the video