 Hello friends, myself, Mr. Alia Arjandane, assistant professor from Department of Electronics, Walshan Institute of Technology, Singapore. Today we are going to see the further chapter noise factor and noise temperature. So what are the learning outcomes from this chapter? So that when the chapter is studied, you will be able to compute signal to noise ratio also compute noise figure and noise temperature. So what exactly is meant by noise factor? So noise factor basically it is considered for the amplifier and it is defined as defined as noise factor is available power, available SNR power at the input to the available SNR power at the output. That means it is the ratio of signal power at the input and the signal power signal to noise ratio power at the output. Hence it is denoted by noise factor is denoted by capital F and it is given by these equations. So the numerator basically this equation denotes the SNR power at the input and this basically denotes the SNR power at the output. So further by doing the further analysis we have PSI by PNI and into PN0 by PS0. As the circuit is in ideal state, hence noise gets added to the signal the SNR will always be less than that of the input. That means whenever we are considering a circuit in ideal state noise gets interfered to that circuit or the signal and hence when we calculate the SNR it is always less when compared to the input. The noise factor F will always be greater than that of unity at the input. Noise factor gives the indication of noise added by the circuit for which noise factor has been calculated. In many cases noise factor basically depends upon frequency and is calculated at signal frequency where it is known as spot noise factor. Hence the average noise factor is calculated for a given frequency range as here we are going to consider the power gain also which is denoted by G. Hence G is equal to signal power at output to the signal power at input. Hence it is given by PS0 PS0 is the signal power at the output PSI is the signal power at the input. Further the initial equation for the noise factor which is this one here what we are going to do is we are going to replace we are going to replace the terms as PSI by PNI is replaced by PS0 and PN0 and PS0 is replaced by PNI. Hence further doing the analysis we have PN0 by PNI into 1 by G. So 1 by G is nothing but the power gain of the circuit. Hence whenever we have to calculate noise factor we have to consider the power gain of the circuit and it is considered and it is given by this equation noise factor is equal to output noise power divided by input noise power into 1 by G where G is the available power gain of the circuit. Hence further it is given by as such and when we when we do the analysis it is given by PN0 that is output noise power is equal to PNI that is input noise power into F into G which is FG PNI. So the output noise power basically it is directly proportional to the noise factor power gain also to the input noise power but the noise power at the input is given by we have seen this equation we have seen this equation in the first chapter itself that is at the start of the noise chapter PNI input noise power is given by kTB where kT is the k is Boltzmann constant T is the temperature absolute temperature and B is the bandwidth. Hence noise power at the output is given by PN0 is equal to just replace PNI by this term we have output noise power at the output is given by FG kT bandwidth. Hence noise factor in terms of Rn so here we have to consider a resistance amplifier which is having a noise resistance Rn and which is having a input resistance and this circuit we have to consider for the noise factor when it is to be calculated for noise equivalent noise resistance for the amplifier. So consider an amplifier with equivalent resistance Rn and the actual input resistance as R in the above amplifier can be replaced by a noiseless amplifier with equivalent noise resistance as Rn at the input side at the input side and this is the circuit for the noiseless amplifier for the consideration purpose the signal circuit can be replaced by Thevenin's equivalent circuit as Vth and Rth. So the supply here we are giving as Vth the Rth is nothing but the Thevenin's resistance equivalent and Rn is the equivalent noise resistance. So for this circuit we are going we are going to find out the Vth and Rth. The as the amplifier is noiseless the SNR at the input will be the same as SNR at the input terminal. So E and F, B and C these are the points E and F and B and C these are the points. So these are the input points and E and F are the output points. So SNR at these points will be the same. So SNR at the output will be given by SNR output is equal to Vth square divided by 4Rth plus Rn into kT bandwidth. The SNR at the input between A and D will be given by so A and D are the points at the input side. So A and D these are the two points at these points the SNR input is calculated as Vth square is equal to 4Rth kT bandwidth by considering the noise factor equation. So it is given by F is equal to SNR input divided by SNR output. So just placing up so just putting up the value of SNR input which is this equation into the noise factor equation and the SNR output equation into the noise factor equation we have the final equation as F is equal to 1 plus Rn upon Rth. Hence from this we can conclude that the noise factor basically it depends upon the sum of it basically depends upon the sum of 1 plus directly proportional to the equivalent resistance also it is inversely proportional to the equivalent resistance which is given by Rth. Second term which is considered as noise factor hence noise sorry noise figure. So noise factor which is expressed or when noise factor that is capital F when it is expressed in decibels it is called as a noise figure. So noise figure is given by 10 log of F where Rn when Rn is equal to 0 then F is equal to 1 hence noise figure for noise factor 1 it is 0 decibel. So amplifier input noise in terms of noise factor F noise output power is given by Pn 0 is equal to F g kT bandwidth which we have seen in the previous slides where g is the gain or the power gain. The total noise power at the input is Pn 0 by g is equal to F kT bandwidth as source contributes kT bandwidth hence amplifier noise power is given by Pn 0 is equal to total Pni minus Pn due to the source. Hence total input power input noise power is given by F kTB and the equivalent noise power due to the source it is given by kT bandwidth. So simplifying these equations we by subtracting these two equations we have F minus 1 bracket into kTB. The fraction of total available noise is contributed by the amplifier as F minus 1 kT bandwidth by F kTB is equal to F minus 1 divided by capital F. So this is the noise factor when it is considered for the amplifier input. So Fritz formula when amplifiers are connected in cascade we have to consider the Fritz formula here as you can see amplifier A1 is having gain G1 also it is having a noise factor as F1. Similarly, amplifier A2 is having gain G2 and noise factor F2. So the total noise factor F for the amplifiers connected in cascade is given by F is equal to F1 plus F2 minus 1 divided by G1. Further the equation can be given as F1 plus F2 minus 1 by G1 where G1 is the power gain for the first amplifier F3 minus 1 G1 G2 is the power gain for amplifier first and amplifier 2. Hence it is called as Fritz formula. So noise temperature here noise can be can also be represented as equivalent noise temperature as the noise power due to the power amplifier with the noise factor is given by PNA is equal to F minus 1 kT bandwidth where T if we suppose consider that T is the equivalent noise temperature hence PNA is represented as F minus 1 kT bandwidth further it is given by TE is equal to when further simplified it is given by simplifying these two LHS and RHS equation we have TE is equal to F minus 1 into T where equivalent noise temperature is an alternative method to represent noise factor also equivalent noise temperature can be given by using Fritz formula as this TE is equal to TE1 plus TE2 by G1 TE3 by G1 G2 where G1 and G2 are the power gain for respective power gain for amplifier 1 and amplifier 2. So these are the references for you people for the further study. Thank you for watching the video.