So let us take one numerical example we will

be calculateing link budget for a given system for a millimetre wave system We are considering

a simplified transmitter and receiver circuit where the transmitter is shown here we have

a millimetre wave source followed by one antenna and in between we have antenna feed network

antenna feed network is lossy it can attenuate more than 50 percent power Next at the receiver

side we have to receive antenna then antenna feed network followed by band pass filter

we typically use a band pass filter just after the antenna to minimise the thermal noise

contribution as well as to minimise any undesired interference from other sources And immediately

after that we use a low noise amplifier for which noise figure is very small We will discuss

later that why we need to use a LNA as soon as possible just after antenna Because in chain of any given receiver the

first component determines the overall noise figure of this receiver so if I use a smaller

value of noise figure for the first component then the overall noise figure of the receiver

it will decrease Next is channel selection filter it can be a switch also followed by

high gain amplifier and then the demodulator So some typical values are given for a 60

gigahertz system transmit power to antenna is 15 dBm loss in transmit antenna feed network

is 5 dB it is quite high 3 dB represents 50 percent loss even it is more than that Transmit

antenna gain : 12 dBi free space loss at 5 meter considering N equal to 2 81 point 98

dB and reflection loss due to multipath so due to multipath we are subtracting some power

which is given by 15 dB So input signal level at the receive antenna

in dBm we can calculate so the positive contribution is due to transmit power and the gain of transmit

antenna so 15 minus 5 plus 12 minus path loss minus reflection loss it comes minus approximately

minus 75 dBm so this is the power signal level at receive antenna Now at the receive side let us say these are

some typical values given here Feed network loss 5 dB so that means gain is minus 5 dB

we can say or cumulative again just after antenna due to feed network minus 5 and for

any passive components which for which gain is less than one or lossy network noise figure

again noise figure is the ratio of SNR at the input to SNR at the output it is equal

to simply gain of the device So if any uhh device provides 5 dB insertion loss its noise

figure will be 5 dB It is followed by a BPF for which the loss is 1 dB cumulative gain

minus 6 dB next we have a LNA then LNA again is given 20 dB and cumulative gain then 5

plus 6 minus 20 it comes 14 dB Channel selection switch it has loss 5 dB and then it is followed

by one amplifier and cumulative gain is 39 dB But when we are considering total gain of

this chain we did not calculate the total noise contribution due to this chain and also

what happens for the noise what is coming with the signal Some noise again will be collected

by the receive antenna due to the radiation blackbody radiation so we did not consider

all those effects because we do not know till now how to calculate that so after this we

will concentrate on that topic how to calculate the overall noise contribution and hence overall

SNR for the receiver So let us start the next topic there are many

different sources of noise thermal noise flicker noise short noise 1 by f noise but here mainly

we are going to consider the effect of hormone noise So it happens because of random vibration

of molecule this is due to thermal agitation and as the temperature increases then their

thermal agitation increases and noise contribution also increases And we can model a thermal

noise by a by by all the frequency components by a random variable which has all the frequency

components so that is why sometimes we call it white noise which has all the frequency

components Now since our receiver it will have a finite bandwidth it cannot pick up

all the thermal noise components it will pick up the components whatever we have inside

bandwidth So for now we will consider ideal band pass

type response so the bandwidth whatever the receiver has it will be represent we will

represent it by a rectangular window function and below that below or above that frequency

range the contribution of thermal noise is simply 0 but actual noise bandwidth is different

that we will discuss later So then from a resistor if we have a resistance R which is

let us say at temperature t the noise power generated by the resistor we can write down

that is equal to k T into B R where B is that bandwidth of that rectangular window function So in general then let us represent one resistor

R then the noise power this is given by k T where T is the temperature of the resistor

into B into R Then if we represent this noise by a noiseless ideal resistor in series with

a noise source let us say the voltage RMS value it is e n in that case e n this is equal

to it is 4 k T B R

It can be shown that the noise contribution it depends only on the temperature of the

resistor not the resistance value okay let us consider one scenario If we have any component

it can be a passive component it can be an active component now we are using it in the

system let us say one source is connected to this component source resistance is given

by R and it is meshed to a load that is also given by R We are considering a meshed scenario

so this input size is meshed to resistance R and output side of this two port component

that is also meshed to R and this resistor it is at a temperature T s So now whatever noise generated by the resistor

at left hand side it will be the input to this 2 port device and depending on gain or

loss it will be attenuated or it will be amplified that ( nof) that noise contribution from left

hand side and it will be delivered to right hand side So in addition to that this 2 port

component itself it will produce some noise so total noise contribution at the output

side n 0 this is equal to let us say gain gain of this 2 port network is given as G

then n 0 this is equal to N internal which is being added by this device itself plus

gain of the device multiplied by whatever noise being delivered by this uhh device at

the left hand side let us say that is given by n incident so G into n i Now from this

n 0 how much power can be delivered to R a given resistor So let us model this whole source by an equivalent

resistor R and an equivalent noise source which is given by e n it is connected to a

load meshed load R from maximum power transfer theorem we know that maximum power from a

source that can be delivered to a load only when this load resistance is equal to source

resistance So in that case if we calculate what is the maximum noise power delivered

to the load it is given by let us say (noid) noise voltage is en then the current component

is e n by twice R so I square multiplied by R this is equal to

e n if I put the value this is k 4 k T B R multiplied by 4 R square into R so it comes

k T B So you see one interesting thing that the maximum power that maximum noise power

that can be which can be delivered to a mesh load it is k T B so it depends on Boltzmanns

constant k temperature of the device this is the noise temperature of the device and

bandwidth it does not depend on any resistor value so this is one important observation Now let us go back let us say we have a resonator

a tank circuit made of L and C then noise power stored in one particular component inductor

or capacitor it can be shown that it is half of the total noise total available noise power

so total available noise power if I consider per unit hertz it is k T per hertz The noise

power stored in inductor it will be k T by 2 similarly it will be k T by 2 inside the

capacitor we can also prove it here Let us consider this circuit it is connected to this

noise source and which is represented by an ideal noiseless resistor R and the noise source

e n then now we calculate E c the average energy stored energy in the capacitor this

is half C v square so we can calculate this half C v square as C by 2 integration 0 to

infinity then the transfer function square H (f ) is the transfer function of the circuit

into N (f) df So N (f) this is the noise power spectral

density due to e n because e n it is a function of frequency and we are considering N (f)

as the one sided power spectral density of this e n and h f since L and C is given we

can calculate what is the transfer function H (f) equal to simply 1 by 1 plus j Omega

R C plus R by j Omega L this is the system transfer function then take magnitude square

and put it in the equation then we calculate Now we are considering the normalised value

k T per unit hertz but we have a finite bandwidth here So what we can do we can arbitrarily

narrow down this transfer function around a mid band frequency let us say f 0 So integration

limit we will choose from f 0 minus to f 0 plus and we will consider the frequency bandwidth

is very narrow so that this H (f) more or less is constant so in that case you put the

values here H(f) and N(f) is represented by constant value at f 0 N (f 0) and it comes

out And if we put the values here and solve it

then it can be shown it is equal to N (f 0) by 8 R so put the value of N (f 0) it comes

k T by 2 so k T by 2 noise power is stored in capacitor similarly another half is stored

in inductor N (f) this is 4 k T R So whenever we use the expression noise power that is

equal to 4 k T R it is actually a simplified form We have a more accurate form which is

given here N (f) noise power thermal noise power you remember that is equal to 4 k T

R h f by k T actually it is divided by this exponential function it is shown here by to

the power minus 1 so exponential h f by k T minus 1 this is the general form for thermal

noise And under a special condition when h f by k T is much less than 1 it is called

Rayleigh Jeans approximation and you see if I put h f by k T much less than 1 that means

you are considering low frequency high temperature case So for lower millimetre wave frequencies we

do not have any problem we can use this approximation but if we go to higher frequency let us say

near to 300 gigahertz and go for space application where uhh (the nega) temperature is negative

in that case we cannot use this we have to use this whole form but for indoor channel

modelling or whatever we are doing on earth surface where (room) we use room temperature

290 Kelvin in most of the cases this formulation is valid below 100 gigahertz and we can write

down then N (f) this is equal to 4 k T R watt per Hertz Then the corresponding noise voltage

RMS value so already we discussed previously we used another parameter e n so that is square

root of 4 k T R volt per hertz then power delivered to a mesh load already we have seen

this is equal to k T it does not depend on R this is watt per hertz So available noise power is independent of

any resistor now let us say we have a receive antenna so antenna it will generate some noise

so whatever noise coming to antenna it will be attenuated by the antenna loss In addition

to that antenna will add some extra thermal noise so we can represent then antenna by

an equivalent noise resistance which can be given by R ant and let us say noise equivalent

noise temperature is given by T e over a bandwidth B hertz Then we define the equivalent noise

temperature of the antenna as T e equal to N a by k B so this is the definition of any

equivalent noise temperature So not just for antenna we can also define this equivalent

noise temperature of any amplifier also so let us say the previous example or let me

draw it again We have one amplifier which is a 2 port network

At the input side I am representing the source resistance by R which is at a temperature

T s Now amplifier amplification factor is given by G then the effective noise temperature

is given as T e We have a mesh load here then noise power coming out from the amplifier

is n 0 Now if I consider left hand side we do not have any noise source then whatever

noise power absorbed in this mesh load it is due to the internal noise power generated

inside this amplifier So in that case that means we are considering T s equal to 0 and

we do not have any noise contribution from left hand side so whatever noise we are having

at the output side it is due to antenna only sorry due to the amplifier only Now we are

representing this amplifier by one noiseless amplifier G and the noise produced by the

amplifier we are representing by a resistor equivalent register So in the antenna example we designated it

by R ant here since we are considering mesh scenario let us consider it as R So in between

these 2 R we have a noiseless amplifier and whatever noise actually coming from this practical

amplifier we are representing by a noise source on left hand side Then the effective noise

temperature it is given let us say by T e then noise power this is equal to k T so noise

power generated by the left hand side noisy source is k T E it is passing through the

amplifier so it will be multiplied by G and then if we consider a bandwidth of B we have

to further multiply it by B and that is equal to the output noise n 0 So effective noise

temperature of this amplifier T e we can write down this is equal to noise power at the output

divided by this is k B into G And if I consider per unit hertz we have to

just put B equal to 1 so this represents the effective noise temperature of this amplifier

Similarly we can do it for any lossy device also in general

Now we already have seen what is the effect of noise for any 2 port network or for any

antenna now receive antenna it can collect also radiation blackbody radiation so what

is blackbody radiation let me first discuss it So let us consider earth surface or any

object it can be human body it can be any uhh home furniture any building anything Now

from uhh Black Planks law we know that it will continuously radiate and that radiation

it is a function of temperature and frequency So if I plot radiation intensity coming from

any blackbody it varies with frequency f and we are plotting the radiation intensity or

sometimes we call simply uhh radiance L so this peak value it depends on the temperature

of that object For example some its temperature is approximately 6500 Kelvin and for which

this peak value is at optical frequency yellow line Now if I consider Brown earth surface

and temperature let us say 300 Kelvin then in that case this peak value it corresponds

to infrared frequency range IR range And if we go further down sorry this is not versus

frequency this is versus wavelength So if we go further down that means if we decrease

the frequency further so we have this (freq) spectral component it decreases but it is

not negligibly small at millimetre wave frequencies Now if we have any antenna let us say it is

focusing towards Earth from satellite then it will collect this radiation which is coming

out from Earth surface and we have a degrading effect on the antenna performance Similarly any Earth Station antenna it can

point towards sky and it can pick up the radiation due to Sun it can pick up radiation due to

atmosphere atmosphere also as secondary radiation dwelling radiation and also it can pick up

radiation from other galactic sources and all these are sources of noise This noise

is (seper) superimposed with the signal power and it will degrade SNR of the antenna and

receiver system as a whole So next day we will see that the brightness or this black

body radiation how it affects any SNR or the receiver performance and then we will combine

the noise figure (com) noise figure contribution of all other components in the receiver chain

and combining this all the effect due to the blackbody radiation and noise contribution

of uhh the receiver chain as a whole we will calculate the SNR of the receiver Okay so

let us finish here thank you