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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

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