 Hello friends, myself, Mr. Alia Arsandari, Assistant Professor from Department of Electronics, Walsh and Institute of Technology, Solapur. Today, we are going to see the second chapter, Noise Calculation Part 1. So, what are the learning outcomes from this chapter? In this chapter, when we study, we will study the effect of noise and analyze different types of noise. Good noise calculations and signal to noise ratio. So, noise calculations, so whenever a noise gets affected, gets introduced in a signal, we need to find out how much percentage of the noise has affected the main information signal. So, for that we need to calculate the noise. Hence, this can be done by using below method. Resistors in series and parallel. Second is reactance and equivalent noise bandwidth method. Equivalent noise resistance and fourth one is noise due to several amplifiers connected in cascade. So, these are the four different types of noise calculation methods. So, first one is registers when these registers are connected in series and parallel. So the total resistance Rs is basically given by Rs is equal to R1 plus R2. So this is the basic equation for the resistance when the resistance are connected in series. Hence, the total noise voltage produced due to each and every resistance is given by En square is equal to 4 kT bandwidth into R where k is Boltzmann constant, T is temperature, Bw is bandwidth and R is the total resistance of the circuit. Hence, it can be further given as 4 kT just putting up the value of Rs which is nothing but addition of two resistance R1 plus R2 and the bandwidth. So simplifying the equation, we have the third equation as En square is equal to En1 square plus En2 square. So basically what we can conclude from the third equation is the total noise voltage produced due to the resistance connected in series it can be given as the sum of the noise voltage produced due to the first resistance that is R1 and the second noise voltage which is produced due to the second resistor and addition of these two noise voltages gives us the total noise voltage across the resistance connected in series. Hence, the total noise voltage is obtained by just adding En1 and En2. Similarly, when two resistors are connected in parallel it can be given as En square 4 kT bandwidth into RP where RP is nothing but the total resistance connected in parallel. So it is given by 1 upon R1 plus 1 upon R2. We have to just put up the value of RP into the above equation of total noise voltage. We reactance and equivalent noise bandwidth. So this is the second method for noise calculation. So it can be given as by the below block diagram. So as you can see there is a block diagram which basically denotes a passive filter and there is an input noise density at the output of the passive filter we are getting an output noise spectrum. This Sn is the noise input noise density which is given by Sn is equal to kT where k is Boltzmann constant and T is the temperature, secondly the output is denoted by Sn0 which is given by H of omega square into kT where H of omega is the real and imaginary part for the passive kind of filter. So inductance and capacitance do not generate thermal noise. So as we have seen whenever we are considering a passive network we have to consider two different components inductance as well as the capacitance. These two components basically do not generate any thermal noise but as we consider the reactance, the reactance plays an important role for the noise calculation and noise generation as these are reactive components that is inductance and capacitance are reactive components but reactance can affect noise spectrum. So the above equation of the passive filter having voltage transfer function which is denoted by H of omega hence the noise spectrum density is given by Sn is equal to kT is equal to PN by BW so kT we are further simplifying that and we are getting the noise spectrum density as PN by BW. Hence output noise spectrum density of the passive filter is given by Sn0 is equal to k into T where k into T gives us the Boltzmann constant product of Boltzmann constant and the temperature and H of omega square is nothing but the voltage transfer function of the passive filter. Consider the passive RC low pass filter here H of s is the output which is given by V out by V in which is basically given by 1 upon s into R divided by R plus 1 divided by s into C where H of s is again further by simplifying the above equation which is this the equation is given by 1 upon 1 plus s into R and the passive filter output is basically given by H of j omega is equal to 1 divided by root of 1 plus omega C R square where omega stands for the angular velocity and C is the capacitance of the capacitor and R is the resistance of the capacitor. Hence further the output noise spectrum density which is denoted by s of n0 it is given by H of j omega square into kT just put up the value of H of j omega square which is nothing but this value into the above equation of output spectrum density we are getting 1 upon 1 plus omega C square into k of t. Hence the output noise spectrum density basically we can say that or we can conclude that the output noise spectrum density it is inversely proportional to the angular velocity of the noise signal also the capacitance of the circuit also the total resistance of the circuit and also the product of Boltzmann constant and the total temperature of the circuit. The output spectrum decreases as frequency goes on increasing so as this is inversely proportional from this equation what we can conclude the second point is the output spectrum density the output spectrum density s n0 it will go on decreasing as the frequency goes on increasing so as we know frequency f is equal to 1 by t if frequency goes on increasing this will go on decreasing as it is inversely proportional. Hence the total noise power output is obtained by integrating s n0 over the entire frequency spectrum which starts from 0 to infinity. So this is the these are the conclusions from the from the equation third so by by summing up or by integrating the terms we have pn0 is equal to s n0 into df and is equal to k of t into 1 plus omega square into dt hence by integrating further we are having the equation as pn0 that is output noise power basically it is given by integration of 0 to infinity 1 upon 1 plus u square du upon 2 pi fc into kt so this is the value for the j omega in terms of power output noise power so the total noise power is given by pn0 and hence by taking out the constant term and by keeping the integrating terms we are having the final equation as kt upon 2 pi cr tan inverse of u and the final equation is basically given by kt upon 4rc hence the total output noise power can be given by kt upon 4rc also we can conclude from the equation as the total output noise power is directly proportional to the product of Boltzmann constant and the total temperature as well as it is inversely proportional to the product of resistance 4 times the product of resistance and capacitance the total noise power at output is given by we have seen the equation as kt upon 4rc where by simplifying the term we can write it as 4ktb where 1 upon rc basically it denotes the effective bandwidth and hence rms noise voltage en is given by en square is equal to 4rkt where effective bandwidth is 1 upon r and hence it is given by en square is equal to 4rkt into 1 upon rc so rms noise voltage from this equation we can conclude as en square is equal to kt by rc from this equation we can conclude as the rms noise voltage en square it is directly proportional to the product of Boltzmann constant and the total temperature also it is inversely proportional to the capacitance of the capacitor which is connected in the low pass filter so these are the references for you people for the further study thank you for watching the video.