Okay so we are continuing with the calculation
now the second stage starting from the circulator So main problem it comes from mixer so for
mixer T value is given that is the temperature ratio 1 point 5 so now then the temperature
output noise temperature under operating condition for an input temperature T 0 it is given T
n equal to 1 point 5 multiplied by 290 so it comes 435 Kelvin Now with this 45 Kelvin
we have to also consider the effect of conversion loss conversion loss is given as minus5 dB
so minus5 dB let us take ratio so you have to divide it by 10 we are considering all
power gain so minus0 point 5 then you take 10 to the power so T e then it becomes for
35 divided by this factor power gain 0 point 316 minus the reference value 290 so it is
equal to 1086 So you see I have calculated the gain of different
components of this receiver chain for example for the first component which is giving 1
dB insertion loss gain value is 0 point 79 what we did simply 10 to the power 0 point
1 Next we have LNA for which in the first slide gain is given 20 dB noise figure is
given as 4 dB so corresponding gain is 100 and noise factor (from law) to fraction if
we convert it is 2 point 51 Again 1 dB it is 0 point 79 and 1 point 22 so how we are
calculating uhh F this is equal to 1 plus T w by 290 Next we have the mixer for mixer
also we calculated T e 1086 again we have the next resistor so you see the 1 dB loss
is providing different noise temperature why because their physical temperatures are different
For the first one it is 180 Kelvin second one 250 Kelvin and the third one 400 Kelvin
and simply we are using these 2 formulas T e equal to T physical into L minus 1 and noise
factor F equal to 1 plus T e by 290 So that is how you can calculate these values
for all these components now once we have all these values then either one noise sector
equation Friis equation or temperature T e anyone of them can be used For example in
this calculation we are considering the Friis for noise equivalent noise temperature of
the receiver so if we go back so equivalent noise temperature T e this is equal to T e1
plus T e2 by G a1 plus T e3 by G a1 G a2 and it continues like this And if we use noise factor approach in that
case F that is equal to this is equivalent F F 1 plus F 2 minus 1 by G a1 For the next
component it would be F t minus 1 by G a1 into G a2 and it continues like that So using an equivalent noise temperature approach
we just put the values the first element is giving 47 plus 438 divided by G a1 which is
0 point 79 and you continue so equivalent noise temperature it comes 640 Kelvin So T
e is 640 Kelvin then T operating this is T e plus T s T s already we calculated here
source temperature this is 448 Kelvin so simply add them up it comes 888 Kelvin this is the
equivalent operating temperature of the receiver If you uhh look at here you see the main contribution
it comes from the first component and the second noisy component is mixer Next noise factor approach so we have the
values simply put the value in equation and then equivalent noise factor it comes 3 point
21 From this if I calculate T e using that previous formula F minus 1 into T 0 it is
equal to 640 Kelvin so F operating 1 plus T e by T s so put T e equal to 640 and T s
we calculated 248 so it comes 3 point 58 So F system for the given temperatures F minus
1 plus T s by T 0 it come 3 point 06 We have different forms of radar equations some of
them already be derived if we put the values noise contribution it comes k T operating
minus 199 point 1 dB for the second formulas when it comes minus199 point 1 for the third
one also same So all these equations you can verify individually by using their definition
in all the cases it is coming the same value it should be Now one application example passive imaging
so what is the difference between passive imaging and active imaging For imaging application
we have to use some source so consider simply imaging at specific wavelength using any video
camera so we if we daytime we have sunlight it is illuminated by Sunray but at night we
have to use some source right visible wavelength Similarly at millimetre wave frequencies also
if I want to image capture image or may be video we need to illuminate the object first
So if we use some transmitter some millimetre wave source and let us say after that one
antenna it is being (illu) it is being used for illumination we call it active imaging
where we use some source But noting down that we can also utilise the information due to
brightness where we do not use any power source millimetre wave uhh source we use simply whatever
radiation already available in nature we call it passive imaging Then what are the different sources for illumination
in this case So let me show you this picture we have dwelling radiation due to atmosphere
because atmospheric particles uhh they behave as secondary radiator and this radiation is
coming from all the direction Let us see we are going to image one runway without using
any millimetre wave source we are using whatever power already available in nature So this
uhh dwelling radiation it will be reflected by the object here it is runway and some of
this (ob) obviously this reflection it will be in all directions and some of this will
be collected by the receiving antenna here after some attenuation because it is a getting
through atmosphere And how much power is being reflected by the subject it depends on the
reflectivity of the surface which is given by Rho Now in addition to that we have blackbody
radiation so this a blackbody radiation is due to its temperature profile so if temperature
increases high frequency component increases so for example let me show you here If we
plot the spectral radiance per unit wavelength versus wavelength for 2 different temperatures
one blackbody its temperature let us say 6000 Kelvin then this is the curve So it peaks
in visible wavelength and the peak appears at yellow line if we keep on increasing the
frequency for this blackbody radiation decreases Now let us consider a second scenario where
the blackbody temperature is 300 Kelvin quite low In this case peak it appears in infrared
frequency range and if you look at millimetre wave frequency band you see we still have
some radiation Even though if I compare the values may be
it is 10 to the power 6 to 7 times lower than what available at infrared frequency So here
millimetre wave it starts from 30 gigahertz to 300 gigahertz after that we are calling
it sub millimetre or sometimes we can call terahertz frequency range So at terahertz
frequency we see the contribution is more for this uh temperature 300 Kelvin than compared
to what available at millimetre wave frequencies So now looking at this object which is runway
and immediately surrounded by some other ground objects so uhh the emission it depends on
temperature and as well as the dielectric constituents of this material so it is the
property of the material So for example if it is very close to blackbody for blackbody
emissivity is 1 but if we take something else which is not a pure blackbody which is not
a very good absorber as well as a very good emitter in that case the total emission will
be much less In previous example we considered emissivity
0 point 9 for example then the effective temperature it becomes 0 point 9 multiplied by the physical
temperature so Lower is the emissivity lower will be radiation from the object So we have
a chart actually for metal emissivity is very small whatever power falls on metal it simply
reflects back so reflectivity is very high for metal but emissivity is very small Now
if we consider (())(12:46) or any gravel surface or let us say a muddy surface for that emissivity
is very high almost close to 1 it is not a very good reflector or almost it behaves like
a blackbody with emissivity nearly equal to 1 So we have a chart here I am showing so you
see for bare metal these are the uhh measured effective emissivity now again emissivity
it not only depends on the type of material it also depends on the surface roughness where
you are placing the antenna if you and if you place your antenna immediately above that
material obviously it will receive maximum power If you go to horizon this power uhh
and emitted from this material it will decrease it depends on incident angle so we are considering
the maximum case when the antenna is receiving maximum power and it is just above that material
in right polarisation So this is this chart it shows the variation of effective emissivity
at different frequency For bare metal at 44 gigahertz 0 point 01
so almost it behaves as a very good reflector it does not emit much energy At 140 it increases
to 0 point 06 even then it is quite low now for painted metal it is little higher we have
also painted metal under cameras painted metal under camouflage dry gravel dry asphalt asphalt
dry concrete smooth water and rough or hard packed dirt So you see hard packed dirt emissivity
is one at all the frequencies so it behaves almost like a perfect blackbody and if any
power falls on it we do not have any reflection almost all of this power will be absorbed
by it and it will reemit all this power so now going back to the previous one So whatever power is being collected by this
antenna it then depends on the physical temperature of the surface emissivity of the surface and
also to reflectivity because it is also reflecting some of this dwelling down radiation Now practically
in practice uhh this radiation due to this cold sky is very small so mainly contribution
due to the emission or emissivity is higher Now we can scan this object and thus we can
form a two dimensional image and since we are not using any source so it is passive
imaging example of passive imaging Now why millimetre wave Already millimetre
wave components are very expensive already we have this type of imaging system available
at visible light even at infrared frequency then what is the need of millimetre wave imaging
So main thing millimetre wave imaging it can be used even under heavy foggy condition under
sun storm dust storm even under heavy rain this is the main advantage So we can design
all weather system even though uhh resolution of millimetre wave image is much lower compared
to infrared visible light image So when visibility is very low and uhh weather condition is bad
we cannot use any other system even then millimetre wave system will work so that is why it became
so popular So now let me give one example the significance
of millimetre wave imaging again going back to that plot you see uhh this is the radiation
coming from blackbody at 6000 Kelvin or 300 Kelvin this for these two different graphs
this is for this we did not consider any atmospheric attenuation Now let us consider this radiation
whatever receiving by antenna it is obviously going through atmosphere we have some atmospheric
loss so we are considering the effect of 1 kilometre fog Now now visibility in foggy
condition it varies with water content so here we are considering a foggy condition
where visibility is 50 meters in naked eye you can see at least 50 meter distance so
this is an example of light fog not even dense fog So in that case if I look at this spectrum
you see it has been redrawn under foggy condition So millimetre wave part it is attenuated how
much Maybe 10 to 20 times but if I look at sub millimetre wave or infrared range we have
nothing even till 10 to the power minus 10 so infrared or sub millimetre wave we can
say that it is attenuated more than 10 to the power 10 times whereas at millimetre wave
frequencies almost it is unaffected that is true also at microwave frequencies but at
microwave frequencies already the radiation value is smaller So this shows the significance
of millimetre wave imaging so that is why we call it all weather imaging system So now when we go for actual design we cannot
use any arbitrary frequency range we have some atmospheric windows we have to use those
frequency bands only So why let us say 60 gigahertz band so oxygen molecules it resonates
at 60 gigahertz band and it will reradiate or the brightness is already very high so
we will not have good contrast for imaging we need also good contrast So we have a effective
brightness variation versus frequency so this curve it shows the calculated brightness temperature
of the atmosphere for T 0 equal to 293 Kelvin and when water content in atmosphere 0 point
1 grams per meter cube so one curve for clear condition and the second curve of black dotted
cloudy condition for cloud is defined as 10 gram per cubic meter So you see the brightness the effective brightness
temperature is quite high at 60 gigahertz due to oxygen resonance and left hand side
we have a small attenuation band due to 22 gigahertz similarly again 118 100 so we have
in between some windows are available where we can use this radiometer for imaging purpose
or passive imaging so these windows are 30 to 50 gigahertz band 70 to 100 gigahertz band
and 130 to 150 gigahertz Now effective radiometric temperature so when
we are forming any image then the received the power it is expressed in terms of some
effective noise temperature T Now if the effective received power it varies accordingly effective
noise temperature will vary so you can form a two dimensional image and for good contrast
that temperature sensitivity is also very important So when we calculated radiometric
temperature T e we have two contributions in that same one that is due to reflection
and uhh the the second one that is due to emission So T s plus T sc so where T s this
is we call due to the surface brightness temperature that is equal to physical temperature multiplied
by emissivity epsilon so it represents due to emission And this scattered radiometric
temperature T sc this is due to reflection that is into equal to reflectivity Rho multiplied
by radiometric temperature T illuminator So this T eliminator it depends on whether
condition uhh under T r open sky T illuminator will be something but cloudy under cloudy
condition T illuminator will be something else Then the effective radiometric temperature
T e that is equal to if we put the value it comes Epsilon T physical plus Rho T illumination
So it depends on the physical temperature emissivity of that object reflectivity of
the object and T illumination So if I compare the contribution left hand side the first
component Epsilon T physical contribution is much more compared to the second one but
in practical system actually we need to calibrate the system first then only we go for imaging So this is one imaging skin left hand side
it shows object it simply follows the principle whatever we use for video camera at optical
frequency range So we have to use some focusing arrangement so this object is radiating millimetre
wave radiation all the directions so we are collecting some of them by using a focusing
lens it can be one dielectric lens antenna or simply a parabolic reflector antenna so
the whole parabola it will collect the power And then at the parabolic reflector at the
feed point feeder on point we have to place one detector array It can be one array antenna
and each antenna let us say connected to diode detector or we can use also single antenna
element so in that case we have to introduce some sort of scanning so in this example we
are considering detector array it can be an MMIC it can it can be actually fabricated
and already people are using it uhh millimetre wave integrated chip where antenna it is followed
immediately followed by detector So if we want so each and every antenna it
will give you 1 pixel If you want to improve resolution you have to improve pixel density
or number of antennas in the array so next is followed by signal processing and then
the display unit So this is a very simplified diagram of a PMMW imaging system and here
we did not consider SNR so what is the minimum power we need to sense so there will be many
calculations and signal processing part is little complicated So what are the applications
some of them already are in use for example in aircraft landing in guiding system and
we can use them at low visibility conditions for low visibility navigation both in let
us say harbour or for ground navigation as well for uhh (recon) reconnaissance and surveillance
applications for security applications For security applications how we can use it
so you see millimetre wave signal it can easily penetrate through clothes thin clothes or
even sweater jacket but it will be reflected by skin Now skin it appears to be one warm
object that means it will uhh its emissivity is high now if we place a metal on skin that
will block that radiation from skin and metals usually appears as a cold surface If any uhh
if we do not have any external source which is illuminating that metal then metal it appears
to be a cold surface because it is not its (emmis) its emissivity is very low Now uhh
if we use a millimetre wave source in addition to these in that case it becomes just opposite
so metal it will it looks like a one object Now depending on you are using active or passive
imaging obviously the image it looks completely different but the good thing is that millimetre
wave signal since it can penetrate through you can see concealed weapons you can uhh
so for security applications it can be used So next we will take a break after that we
will discuss on transceiver architecture