So next let us discuss about the mat material

properties at millimetre wave frequencies So first of all we need to measure these material

properties at different frequencies to characterise them there are some popular methods at microwave

millimetre or terahertz or infrared frequencies and these methods are different at different

frequencies For example at low RF or microwave frequencies we use parallel plate method We place dielectric material between two parallel

plates or characterisation or sometime we design some sort of resonators and then we

measure the resonance frequency and other effect to measure the dielectric constant

of any given material so we can still use that resonance method at millimetre wave frequency

also So other techniques are transmission line

methods so for transmission line methods what we do We fabricate different lanes of transmission

line it can be lets say micro strip line which uses umm which supportsTEM up to different

length and then we simply measure the S parameters or scattering parameters of this two different

lengths by using may be some vector network analyser So from the measurement of this complex scattering

parameters then we can determine what is the alpha or beta or that given transmission line

or what is the dielectric constant of the given substrate Actually if we further increase

the frequency to sub millimetre wave or to terahertz frequency this transmission line

method or that resonance method is not very accurate There are some other methods which we use

so that is terahertz time domain spectroscopy but unfortunately its not again very accurate

method so we can determine the material characteristics at lower frequencies as well as at higher

frequency For example infrared or optical wave length

very accurately but we have a problem from hundred gigahertz to ten terahertz we don’t

have any methods which can give us very accurate sigma tan delta and epsilon R values of any

given material so thats why sometimes we call it a terahertz cap So whatever values I am

going to show here these are approximate values thats why So lets take some popular substrate material

first for example the first substrate it is RT duroid six zero one zero so Roger suggest

its dielectric constant at ten gigahertz epsilon R is equal to six point two and loss tangent

that is equal to point zero zero two but some other groups already used the same material

at high frequency as high as hundred gigahertz And they report it that the measured dielectric

constant at hundred gigahertz of this same material is seven point four and they also

obtained similar loss tangent value point zero zero two now another popular material

RT duroid five eight eight zero so already we have seen the measured value given by Rogers

corporation at ten gigahertz epsilon R is two point two and tan delta is point triple

not nine so another group measured its performance at sixty gigahertz for that they got epsilon

R equal to two point two four So almost no difference and tan delta it actually

increases to point zero zero four So another popular material its quartz substrate so its

actually low loss substrate and very popular at millimetre wave frequencies but the only

problem is that its fragile At ten gigahertz epsilon R equal to three point eight even

at hundred gigahertz no change look at the loss tangent value its point triple not one

it increases to just point triple not two at hundred gigahertz So it shows why quartz is so umm less lossy

substrate Now we are doing a one experiment what we are doing We are fabricating lets

say one twenty millimetre long micro strip line which is basically a form of transmission

line on a thirty five NQ substrate and then what we are doing We are measuring is to one

and plotting it over the frequency range So look at the variation of loss at one gigahertz

this loss is just point one or point two DB And at lets say twenty gigahertz it increases

to one point two to one point three DB but for the same micro strip line at sixty gigahertz

loss increases to almost four DB What is the source of these losses Then as such umm whatever

material properties we have seen in comparison to ten and ten gigahertz and umm hundred gigahertz

that tan delta value or epsilon R its not changing as such but if I measure loss loss

is increasing very rapidly with frequency So at millimetre wave frequency you see if

the loss is three db that means half of the power is already wasted you are receiving

only half of the insuring power Then there might be some other sources of losses so that

we have to learn very carefully So the main point is at conductor loss it increases with

frequency not only that we will see there is one more type of loss which we call the

surface wave loss So before that lets go through some other

materials popular materials one of them is alumina so for alumina umm depending on its

purity epsilon R it can varies in between nine point six to nine point nine I will show

you the values of alumina even at terahertz its being used and typically its lon loss

tangent value is point triple not one this is most commonly used material for a low cost

fabrication at millimetre wave frequencies Sapphire typically at hundred gigahertz again

depending on its purity and composition epsilon R nine point three to eleven point seven loss

tangent point triple not four so its one type of anisrotropic material and not very popular

then the fused quartz so its main advantage it is excellent stability so quartz with different

cut its called Z cut quartz so for this one epsilon R is four point four And look at their loss tangent values its

very small in fact in this chart this quartz material they provide lowest loss then the

popular RT duroid substrate it is RT duroid five eight eight zero so typical epsilon R

two point two so this rexolite substrate two point five five and for this two types copper

clad substrates are available so that means the dielectric slap with top and bottom metallisation

then the PTFE substrate Teflon umm called typical dielectric constant two point zero

seven at hundred gigahertz Polythene polyethylene its dielectric constant

two point three and its a polymer we have also some other TPX so TPX material is flexible

material and polypropylene its dielectric constant two point two six it is again another

polymer so among there are many more Among these if you say which is the most popular

material at millimetre wave frequency it is alumina because its cost is very low Now in the previous one when we are going

through different dielectric so that means we were considering mainly circuit design

in printed circuit board technology but we can design also circuit on chip in that case

we have to use silicon germanium or group three group five material So then lets see

how this material they behave at millimetre wave frequency So first of all silicon or germanium and umm

typically when we consider N type or P type material its a semi conductor material So

it comes with a finite sigma value so its very lossy so we cant use this semiconductor

materials as metal or even we cant use this semiconductor material as dielectric Because

if we treat the semiconductor material as dielectric it will be very lossy already at

millimetre wave frequency umm We have many sources of loss we don’t want

to increase the loss further So then what is the option How we can utilize the silicon

germanium or other group three group five materials So one thing is that we can use

pure silicon intrinsic silicon or germanium so in that case we don’t have any doping

so its resistance will be high and we can use that type of silicon or germanium as umm

dielectric material to design our component umm how we do for PCB So with that silicon only thing is that we

have to act some metallisation so this silicon or germanium which is very close to intrinsic

material we call it high resistive silicon or high resistive germanium So lets see their

material properties So semi insulating silicon typical rho two

into ten to the power three to ten to the power five ohm centimetre so this value is

given umm ten gigahertz an its epsilon R is twelve Loss tangent is point zero zero one

not bad So if I consider a typical value for which measurement result is available rho

is eight into ten to the power three ohm centimetre and the measured value is at one hundred and

forty gigahertz epsilon R is eleven point seven And loss tangent point zero one three its

high but still we can use it for circuit realisation You can compare this point zero one three

three value with the previous table for all this dielectric its at least we have lets

say point zero zero three we have a point zero zero factor and here its point zero one

three Next semi insulating gallium arsenide so remember whenever we are using this word

semi insulating so that means it is more like intrinsic doping concentration is negligibly

small And we have to use special fabrication process

to fabricate them conventionalthey don’t support this fabrication So semi insulating

gallium arsenide rho typically ten to the power seven to ten to the power nine ohm centimetre

and epsilon R is quiet high sixteen and if I consider a typical value rho seven point

eight into ten to the power seven ohm centimetre for which the measured value is of epsilon

R is twelve point nine at one hundred and forty gigahertz And the loss tangent is point zero zero five

so if I compare the loss tangent value with silicon obviously its a very good substrate

almost like dielectric but the problem is that its very expensive compare to silicon

So we can use for monolithic circuit fabrication for both active and passive device fabrication

so you see dielectric constant lets say its already twelve or more than twelve now what

about the com passive component size Lets say antenna dimension and umm antenna

its length typically is lambda g by two So if I consider is sixty gigahertz design wavelength

free space wavelength is five millimetre at if I fabricate this antenna on gallium arsenide

so this is it cones then five millimetre five divided by root of twelve point something

divided by two because its lambda by two so their dimension of this resonating antenna

is so small that we can integrate this antenna on chip itself And we can think of on chip antenna not only

that on chip antennas arrays that is also possible at millimetre wave frequency Some

other passive components which we learnt later like couplers filters Which uses the properties

of transmission line and whose dimension again is determine by lambda g sometimes lambda

g by two sometimes lambda g by four so those passive components also we can design on chip Because size reduces it becomes fraction of

millimetre So in the same chip then we can design active components as well as those

passive components like filter couplers and we can integrate in a single chip So next lets see how the properties of alumina

is varies with frequency So alumina its being used noly not only at millimetre wave frequencies

as you see look at the frequency scale so starting from microwave to almost two point

five terahertz its being used And umm the refractive index which is related to dielectric

constant of this material so moral is it remains constant over this wide spectrum of frequency So we have their comparing two values one

umm for case one its almost very pure alumina ninety nine point six percent alumina and

the second one is ninety six percent alumina so if I look at the epsilon R values so it

is more or less constant over this frequency range and absorption coefficient which represent

actually the loss tangent so it increases but not that bad particularly if I typically

if I consider below one terahertz So thats why this alumina is very popular substrate

at millimetre wave frequency So now let us go back to the micro strip line

example So after studying this material properties at millimetre wave frequencies we see that

in comparison to microwave frequency range or a RF frequency range loss tangent value

or other properties is does not change umm they do not change drastically There is a

change there is an increment of loss tangent value but its really small So then if I look at the measured is to one

of transmission of a micro strip line but what we see We see that loss it increases

rapidly with frequencies so then there might be some other sources of losses And this loss

is a function of frequency which obviously is more at higher millimetre wave frequencies So sometimes this loss is so high lets say

at sub millimetre wave frequency umm that we even cant use printed lines For sub millimetre

wave frequency range near three hundred gigahertz so then what are these sources of losses We

will see one by one So the first one is conductor loss sorry here

it shows dielectric loss umm so umm the dielectric loss ohmic loss or conductor loss and then

the radiation and surface wave losses So if we design any wave guiding structure at millimetre

wave frequencies then obviously we have to use the complex propagation constant We cant use the approximation of lossless

line we have to consider both alpha and beta Alpha it represents the attenuation and beta

it is the phase constant So which is given by approximately twice pie by lambda g So

for a any given medium if we know the Mu epsilon and sigma value then we can easily calculate

what is the alpha value and beta value of any given medium Now the power flow along a lossy line lets

say around the line we don’t have any reflection P Z this is P not into E to the power minus

twice alpha Z We have a factor of two since we are considering a power and not the electric

field So uhh this alpha and beta we can actually measure it by fabricating two different lengths

of lines So the loss whatever we have it is then included

in alpha and if there is any phase variation umm for if there is any dispersion effect

that we can determine from the beta variation so then we see that alpha and beta both are

very important parameters for any wave guiding structures so how to measure them So you see

we have a relationship here the leakage constant alpha it can be represented in terms of this

catering parameter If we have a section of wave guiding structure

uhh then if we can measure the S parameters lets say the S one one and S two one then

from that S one one square plus S two one square this is equal to E to the power minus

twice alpha L So we can determine experimentally what is the alpha for any given guiding structure

similarly we can determine what is the phase constant beta by length difference method

So what we have to do We know that the theta due to a given physical

length L that is equal to theta equal to beta into L So now if we fabricate two diferent

length lets say Lone and L two and the length difference is delta L Then the angle difference

we can easily measure by S parameters because angle of S two one that is nothing but the

angle experienced by the signal from port one to port two So from that then experimentally

beta that is equal to delta theta by delta L So we see that we can measure experimentally

both alpha and beta and it will give you some idea about the alpha and beta Now obviously

for any design what we expect that alpha should be as small as possible and what should be

the variation of beta Beta is twice pie by lambda g So if I consider the frequency variation

of beta so this is twice Pie into C by F okay let us do in graph So beta this is equal to twice pie by lambda

g this is the guided wave length so twice pie we can write down the velocity of wave

inside the medium into F So then we see ideally if I plot beta versus frequency so it should

increase linearly and if there is any deviation from the straight line so that means we have

velocity as a function of frequency we have dispersion effect So practically we deal with

two important parameters We usually plot beta by K not instad instead

of beta so K not this is equal to twice pie by lambda not so it is nothing but beta in

free space And then we plot what is the value of beta by K not And what is the value of

alpha by k not So if I plot beta by k not versus frequency ideally it should be constant

But for any wave guiding structure it actually varies with frequency so already we know what

is fast wave What is slow wave So lets say we have a rectangular

wave guide filled with dielectric material and for that we are plotting beta by K not

versus frequency so I am considering one example uhh a rectangular wave guide with filled with

dielectric material of dielectric constant epsilon R So if I plot beta by K not for this given

material beta by K not plot is somewhat like this this dotted line it shows the value where

beta by K not equal to one0 this diagram beta by K not versus frequency is called the dispersiondispersion

diagram And it provides many important information for example you see at this particular frequency

lets say FC one its starting from lets say thirty gigahertz beta by K not equal to zero

that means we don’t have any propagation below this frequency this is the cut off frequency

of that wave guide Now as frequency increases beta by K not increases

now at a frequency point here we have a crossing where beta by K not is equal to one so below

this beta by K not is less than one What that means Beta by K not is less than one so that

means we have VP Phase velocity higher than C or we can call this left hand side part

this is the fast wave region and the right hand side part for which beta by K not is

more than one or phase velocity this is less than C we call it the slow wave region So in this region then my lambda g is smaller

compare to lambda not So componentis possible for the right hand side while for the left

hand side we can design on leaky wave antenna very easily So ideally it should be a straight

line but since it changing with frequency so that means it dispersive so how dispersive

this line is we can understand it from that beta by K not plot So you see then why this dispersion diagram

is so important we have so many information that what is the cut of frequency for this

given guiding structure Which range over umm what is the frequency range Over which it

behaves as the fast wave What is the frequency range over which it behaves as a slow wave

structure Then how dispersive this line is Similarly we may have another plot of alpha

by K not versus frequency from which we will have idea of how lossy the line is If for

a rectangular wave guide if I plot alpha by K not versus frequencies it will be highest

at cut off frequencies and actually its infinity and if I increase frequency alpha by K not

it decreases with frequency So today we will stop here So in next class we will discuss

the different sources of losses in details Thank you