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