 Hello everyone. I am Mr. Praveen Kumar. Today we want to see system noise temperature and G by T ratio. The learning outcome of this topic is at the end of the session, student will be able to explain the concept of system noise temperature and G by 2 ratio in satellite communication. The contents of these topics are noise temperature, calculation of system noise temperature and noise model of receiver, noise temperature. Basically, in satellite communication there are two parts. One is a transmitter and second one is receiver. This noise temperature is calculated at receiver side. It determines generation of thermal noise by active and passive devices in the receiving system. At microwave frequency, a black body with a physical temperature Tp degrees Kelvin generates electrical noise over a wide bandwidth. For the calculation of noise temperature, here we want to calculate the thermal noise as well as the physical temperature Tp. The noise power is given by the equation Pn is equal to K into Tp into Bn. This K and Tp product is called as noise power spectral density and unit is watts per hertz, where K is Boltzmann constant is equal to 1.39 into 10 raised to minus 23 joule per Kelvin. Tp is physical temperature of source in Kelvin degrees. Bn is noise bandwidth in which the noise power is measured in hertz. Pn is available noise power in watts. Available noise power will be delivered only to a load when this impedance is matched to the noise source. The unit of the noise temperature is Kelvin. In satellite communication, we system work with the big signals because here in satellite communication, preferably we use for the large distance. The noise level as low as possible to meet the Cn ratio requirement. Noise temperature from 30 Kelvin to 200 Kelvin can be achieved without physical cooling if we use the device that is GAAS-FET means gallium arsenide field effect transistor amplifiers are employed. Now we see the noise temperature of 30 Kelvin at 4 gigahertz. Noise temperature of 100 Kelvin at 11 gigahertz means if we observe these two noise temperatures as the frequency increases this noise temperature will be increased. Therefore noise temperature increases with the frequency. Total thermal noise power is used to determine the performance of a receiving system. The noise power at the demodulator input is PnO is equal to K into Ts into Bn into Gr of X. The unit of that PnO is watts where Gr of X is gain of the receiver from RF input to demodulator input. Bn is narrowest bandwidth. The noise power referred to the input of the receiver is Pn. Pn is equal to K into Ts into Bn that is unit of Pn is watts. Carrier to noise ratio at the demodulator is given by C by n is equal to Pr into Gr of X divided by K into Ts into Bn into Gr of X is equal to after simplifying this equation we get Pr divided by K into Ts into Bn. This is equation number 4. From this equation number 4 we can calculate C by n ratio for the receiving terminal at the antenna output port. Calculation of a system noise temperature. This figure shows simplified earth station receiver. This figure is used for single frequency. Now in this diagram this LNA is used for low noise amplifier. Low noise amplifier followed by the band pass filter after that one this is a mixer, this is a local oscillator. Again it given to the band pass power and again it given to the IF amplifier. From this diagram we can conclude that it will convert the RF frequency into the IF frequency. Radio frequency is converted into the intermediate frequency. Most of the radio receiver is used this simplified earth station receiver. Here this diagram consists of mainly three parts. The first part is LNA which is low noise amplifier. Second part is mixer and local oscillator. And the third part is the demodulator. Here we convert this RF frequency into the intermediate frequency with the help of this mixer and local oscillator. This figure shows two stage demodulator frequency. Here double conversion earth station receiver we use. Here it will first down convert the shift signal in a 500 megahertz band to the first IF range that is 900 to 1400 megahertz. Means it will receive the signal from 5 megahertz satellite and it will convert into 900 to 1400 megahertz. Here we use two stages. This is what is called as first stage and this is what we called as the second stage. In the first stage this is a LNA means low noise amplifier is given to the band pass filter and again it will give to the local oscillator with the help of this local oscillator and mixer. We convert this RF frequency into the IF frequency. This is what is the first stage. After the first stage of a conversion of IF frequency it will give on to the receiver side with the help of the coaxial cable. Again with the help of this mixer and local oscillator we convert that one into the second IF amplifier and after that one we give to the demodulator. Number three shows the noise model of a receiver. This noisy amplifiers and down converts have been replaced by noiseless units with equivalent noise generation of their inputs. Here if you observe here the gain is called GRF. Again here we use a different gain that is a JM. Again here we use a different gain that is a gain GIF. This is a noiseless RF amplifier. This is a noiseless mixer and this is a noiseless IF amplifier. If you observe in the previous diagram that previous diagram is converted into this diagram with the simply replace that block with the this gain blocks. Here again this is a RF amplifier. This is a mixer and this is an IF amplifier and the corresponding temperature we have to provide that is a TIN and respective power output we have to calculate here PN. The total noise power at the output of the IF amplifier of the receiver is given by PN is equal to GIF into K into TIF into BN plus GIF GM into K into TM into BN plus GIF into GM into GRF into K into BN in bracket TRF plus TIN. This is equation number five where GIF GM and GRF are the gain of the IF amplifier mixer and RF amplifier and TIF, TM and TRF are the equivalent noise temperature. This equation five can be again simplified as PN is equal to GIF into GM into GRF in bracket K into TIF into BN divided by GM into GRF plus in bracket K into TM BN divided by GRF plus in bracket TRF plus TIN. Again this one is simplified and we get this equation number six. This figure shows noise model of the receiver. All the noise units have been replaced by one noiseless amplifier with a single noise receiver TS as the input. Now the noise source TS as the input, TIN is the temperature input is added and given to this gain. This is called as a noiseless receiver. This after this given to the noiseless receiver the output is a PN. The single source of a noise shown in figure four with noise temperature TS generates the same noise power PN at its output if PN is equal to GIF into GM into GRF into K into TS into BN. This equation number seven. This GIF, GM and GRF is the gain of that respective. If we compare the equation six and seven we get system noise temperature as follows. TS equal to TRF plus TIN plus TM divided by GRF plus TIF divided by GM into GRF. This is a represent equation number eight. That is a system noise temperature. Now figure five is a shows noise model for a lossy device. The lossy device has been replaced by lossless device with a single noise source that is TIN at its and output is noise source TNO and is a PN. The noise model for an equivalent output noise source as shown in figure five and produce a noise temperature TNO is given by TNO is equal to TP into one minus G1. That is equation number nine. Now the question is four gigahertz receiver with the following gains and noise temperature TIN is equal to 25 Kelvin, TRF is equal to 50 Kelvin, TIF is equal to 1000 Kelvin, TM is equal to 500 Kelvin, GRF is equal to 23 dB and GIF is equal to 30 dB. Now calculate the system noise temperature assuming that mixer has gain GM is equal to 0 dB. Now solving this mathematical equation. First of all you convert this decibel into the normalized function. This GRF and GIF you have to convert this decibel into the normalized function. Okay. Now we have to calculate here the system noise temperature. Now recall everyone the system noise temperature equation. Okay. Now TS that is the system noise temperature is equal to TRF plus TIN plus TM divided by GRF plus TIF divided by GM into GRF. Now before putting the values this temperature in Kelvin then no problem but this gain I want to convert into the normalized. This convert this dB into the normalized function. Now how we convert this gain in dB is equal to 10 log to the base 10 into normalized function. Okay. Now 23 is equal to 10 log to the base 10 into X. Now 23 divided by 10 you get 2.3 and that is and when you 10 raise to 2.3 that will convert into the normalized and you get the GRF and GIF into the normalized function and that put that values into this our equation and we get TS equal to TRF is a 50, TRF is a 50 Kelvin, TIN is equal to 25, 25, TM is equal to 500 that we put here. GRF after conversion of into dB we can get here 200 and after this product you get 200 and GRF we convert this GM. If you convert 0 dB into the normalized function we get 1 that is a 200 into 1 that is called 200. Now after solving this you get TS equal to 87.5 means extremize temperature for this solution is 87.5. The references for this topic is thank you.