 Hello friends, myself Ilya Arsandane, Assistant Professor from Department of Electronics, Vulture Institute of Technology, Sallapur. Today, we are going to see the further part for noise calculation part 2. So, these are the learning outcomes at the end of this topic. We can compute noise calculations and signal to noise ratio. Also we have seen effect of noise and different types of noises. So, noise calculations as we have seen in the first part of noise calculations. Noise calculation can be done by considering these four different methods. In the first part we have seen resistance in series and parallel noise calculation. Noise calculation can be done by reactance and equivalent noise bandwidth. Today in this lecture we are going to see the third and the fourth part or the fourth method third and the fourth method which includes noise calculation due to equivalent noise resistance and noise calculation due to the several amplifiers when connected in cascade. So, equivalent noise calculation can be done by considering a tuned circuit. So, this is the third method which we are going to see. In this as you can see there is a RLC tuned circuit which is given by this circuit. There is a resistance inductor and capacitance and then there is a supply given. Hence, consider the noise generating component in is the resistor which is in series with the coil. Here what we are considering is there is a resistor which is generating a noise and this resistance is corrected in series with the capacitor and the inductor. Hence, noise bandwidth is restricted to bandwidth of resonance of coil. So, the bandwidth for this circuit basically it is equivalent to the bandwidth of resonance of the coil. In series circuit the voltage across the capacitance is Q times the applied voltage. Hence, it is given by E c square is equal to Q Q square into E n square. So, E c square that is the voltage across the capacitance is given by Q square by putting up the value of E n square that is RMS noise voltage value which we have calculated in the first part which is given by 4 R k T bandwidth. Hence, it is given by the final equation as V n square is equal to 4 Q square R into k T bandwidth. So, Q is the Q is the quality factor R is the total resistance of the circuit of the RLC circuit. K is Boltzmann constant, T is again the temperature and B is the effective bandwidth. By further simplifying by taking the square root we can see that the all other all the terms come under the square root. As the circuit is tuned to the dynamic resistance as the as the circuit is tuned hence the dynamic resistance is given by Q square into R where Q is very much higher. So, the dynamic resistance equation can be given as R d is equal to Q square into R. Further by putting up the resistance value as the dynamic resistance in the RMS noise voltage we are putting up the resistance value as dynamic resistance. So, it is given by E n square is equal to R d we are replacing the total resistance by the dynamic resistance k T bandwidth. The fourth part or the fourth method by which we can calculate noise by which we can calculate noise is noise calculation done due to the several amplifiers connected in cascade. So, as you can see there are two amplifiers A1 and A2 where A1 basically denotes the first gain for the first amplifier A2 denotes the gain of second amplifier R1, R2 and R3 are the resistance which are connected in parallel. So as the supply gain of first amplifier is given by A1 gain of second amplifier by default it is given by A2. The first stage has a total input noise resistance as R1 which is given as here. Second stage has R2 which is given as here. The RMS noise voltage at the output due to R3 so we are going to calculate the RMS noise voltage at the output resistance which is nothing but R3 at this point it is given by En square is equal to root of 4 k T bandwidth into R as we are taking the voltage across R3 resistance. If R3 is replaced by R3 dash at the input of second stage then RMS at the input of second stage can be given by En3 dash is equal to En3 divided by A2 where En3 we are having the value or equation of En3 as root of 4 k T bandwidth into R3 divided by A2 where A2 is the gain of the second amplifier. Hence the final equation for the RMS noise voltage due to the R3 dash resistance is given by En3 dash is equal to root of 4 k T bandwidth into R3 dash so R3 dash can be given as R3 dash is equal to R3 that is the output resistance divided by A2 square that is gain of square of the gain of second amplifier. The equivalent output resistance of the circuit is given by Req is equal to R2 plus R3 dash hence by putting up the value of R3 dash we are having R2 plus R3 divided by A2 square R equivalent is given by R1 plus R2 dash hence the R equivalent for the total circuit is given by R1 plus R2 divided by A1 square plus R3 A1 square into A2 square where A1 and A2 are the gain of amplifier 1 and amplifier 2 signal to noise ratio basically it is termed it is a term which is used to check the performance of communication system and the receiver signal to noise ratio is simply a number which basically indicates the strength of signal and noise when signal is strong noise will be weak and the signal to noise ratio is high when signal to noise ratio is low the reception of the signal is very less at the receiving side so how signal to noise ratio is defined it is defined as the ratio of signal to signal power to noise power at the same point and is basically given by the equation as S by n ratio E2 square by R EN square by R hence the final equation is given by ES upon EN total bracket square so in terms of log it is given by twice it is given by in terms of decibels it is given by S by N dB is equal to 20 log ES by EN so effect of amplification on signal to noise ratio so there are certain considerations which have to be done for the signal to noise ratio in that first one is the effect of amplification when the signal is amplified how it will affect the signal to noise ratio noise resistance of mixer stage at a super heterodyne receiver is very much high hence strong signal is required to maintain SNR for weak signals first the signals are amplified by an RF amplifier and then the signal is given as input to the mixer stage but the RF amplifier has to be a low noise amplifier otherwise the signal to noise ratio will not be improved so signal to noise ratio here when the signals are received by the antenna and then given as input to the RF amplifier stage the output of this stage is then applied to the input to the mixer which is shown at this point so let RNM be the equivalent resistance of the mixer at the at its input the mean square noise voltage across RNM is given by VNM square similarly RNM be the equivalent noise resistance of the amplifier hence the voltage across the resistance is given by VNA square the circuit is then replaced as the Thevenin circuit which has the two components VTH and RTH the mixer noise voltage VNM square at the output of the amplifier is basically given by VNM square by A square where A is the gain of the amplifier hence the at the input of amplifier where A is gain of amplifier the total noise resistance the the total noise for the amplifier is given by VN square is equal to VNA square that is square of the voltage across the amplifier as well as the mixer stage is given by VNM square by A square and the signal to noise ratio for this is given by S by N is equal to V square TH by 4 RTH plus RNA plus RNM by A square into kT bandwidth so this is the equation for the amplified signal effect of amplification are done for the SNR so effect of cascade connection on SNR in communication system networks are connected in cascade hence overall SNR of the cascade is always less than that of one in the network hence considering the communication network connected in cascade let PS be the signal power hence the noise power of the links are given by PN1, PN2 and so on hence the overall SNR at the output is given by 10 log PS upon PN1 plus PN2 and so on if the links are identical hence all the power becomes identical which is shown in this equation overall SNR for this particular condition is given by P upon M plus N hence further it is further it is given by S by N dB is equal to 10 to the log 10 log to the M hence if we consider that three identical links each of them are having the SNR as 60 dB are connected in cascade by considering this equation we are having the value of 55.22 dB hence if the SNR of any one link is much less than that of other connected in cascade the overall SNR of the links is nearly equal to SNR of links smaller values so these are the references for you people for the further study thank you for watching the video.