WEBVTT
Kind: captions
Language: en
00:00:19.070 --> 00:00:31.210
Welcome to this 6 lecture of this lecture
series that today we will see in insertion
00:00:31.210 --> 00:00:52.329
loss based insertion loss based microwave
filter design Now already we have seen the
00:00:52.329 --> 00:01:00.649
motivation for going for this design in the
previous lecture Now today let me first define
00:01:00.649 --> 00:01:21.590
what is insertion loss? Insertion loss
is its symbol is PLR and this is ratio of
00:01:21.590 --> 00:01:44.909
power available from source to power delivered
to load by any subsystem Suppose I have any
00:01:44.909 --> 00:01:49.700
subsystem in this particular case it will
be filtered but insertion loss is a generalize
00:01:49.700 --> 00:02:00.659
concept that is why let me call it a electronic
network It is a black box it is 2 port black
00:02:00.659 --> 00:02:14.900
box now this side it will be connected
maybe to some other block but for this network
00:02:14.900 --> 00:02:20.590
this is the source side that so it will be
connected with this source Similarly it may
00:02:20.590 --> 00:02:30.390
be connected to some other block but to this
2 port network that is the load so it will
00:02:30.390 --> 00:02:43.380
be connected to another box which is called
load Now let the power source is delivering
00:02:43.380 --> 00:02:59.100
Pin and the load is taking PL So insertion
loss power available from source what is the
00:02:59.100 --> 00:03:07.720
power available from the source to these electronic
network that is Pin and so I can write this
00:03:07.720 --> 00:03:24.229
as Pin and power delivered to load is PL Obviously
you know that I do not know the impedance
00:03:24.229 --> 00:03:32.880
level of this so and I am assuming that in
general this is there will be some loss here
00:03:32.880 --> 00:03:42.389
also but in this particular case particularly
our filter case so this filter case there
00:03:42.389 --> 00:03:48.449
is no inside there is no power dissipation
because we will use only the reactive components
00:03:48.449 --> 00:03:56.479
and so the power is not dissipated inside
so it is a lossless part here internally But
00:03:56.479 --> 00:04:02.920
you know that due to that impedance mismatch
there can be reflections here so the wave
00:04:02.920 --> 00:04:10.240
is going and then the wave can come back so
there are reflections so all the power may
00:04:10.240 --> 00:04:19.320
not go here obviously the power that is reflected
that will go back here so here it will be
00:04:19.320 --> 00:04:25.729
something less power similarly here also due
to the impedance mismatch the wave is going
00:04:25.729 --> 00:04:40.200
like this but there may be reflections So
can I see that all this PN PL so overall reflection
00:04:40.200 --> 00:04:52.260
coefficient so can I say that this is equal
to 1 minus gamma which is a function of Omega
00:04:52.260 --> 00:05:02.480
This gamma is the reflection Coefficient over
all reflection coefficient which comprises
00:05:02.480 --> 00:05:11.230
of reflection here reflection coefficient
here so by that I can define an overall coefficient
00:05:11.230 --> 00:05:19.080
between this and that is gamma it is the function
of gam gamma and I know that the this ratio
00:05:19.080 --> 00:05:25.960
will be nothing but 1 minus this that means
1 minus reflected power this gamma please
00:05:25.960 --> 00:05:30.880
remember we have earlier discussed that this
gamma is a voltage reflection co efficient
00:05:30.880 --> 00:05:46.500
that is why we are taking this square thing
because we are taking of power now a if there
00:05:46.500 --> 00:05:52.640
is no mismatch here that means already impedance
matching has taken place between source and
00:05:52.640 --> 00:05:59.910
this our filter network and also between load
and our filter work then it will be like these
00:05:59.910 --> 00:06:06.010
so there wont be this reflection co-efficient
is zero there but remember there is one more
00:06:06.010 --> 00:06:13.430
thing that is this network what about the
power I gave yesterday also I said depending
00:06:13.430 --> 00:06:20.410
on the propagation constant in the pass band
it will flow but in general a portion of that
00:06:20.410 --> 00:06:27.420
will go here In high frequency or microwave
what is that suppose if I give some voltage
00:06:27.420 --> 00:06:37.790
how much voltage comes here that I can express
by a ratio called S parameter S21 S21 So I
00:06:37.790 --> 00:06:49.670
can see that under matched condition so this
is one and also I should then say that this
00:06:49.670 --> 00:06:59.050
is S21 square this S21 is this is port sec
2 of the electronic network this is port 1
00:06:59.050 --> 00:07:10.139
So actually insertion loss is 1 by this into
S21 Square So under matched condition both
00:07:10.139 --> 00:07:22.310
source and load matched then PLR is nothing
but S21 square here no there is a pit fall
00:07:22.310 --> 00:07:32.520
in measurements many times I see that in indian
engineer they say that what is insertion loss
00:07:32.520 --> 00:07:41.440
it is a S21 square Please remember that if
you have enforced the matching then only it
00:07:41.440 --> 00:07:48.090
is true otherwise you should also consider
the reflection taking place both here and
00:07:48.090 --> 00:07:54.320
here Many times when the measurement takes
place this impedance mismatch is not taken
00:07:54.320 --> 00:08:02.750
care and people forget to in incorporate this
part the reflection co efficient part ok so
00:08:02.750 --> 00:08:08.750
now I can say that I have define insertion
loss that means physically what is this it
00:08:08.750 --> 00:08:18.690
says that if this network was not there some
power was flowing to the load if I inin If
00:08:18.690 --> 00:08:25.940
i include this in the circuit the power will
change so this difference is basically the
00:08:25.940 --> 00:08:31.250
insertion loss So due to the insertion of
the this particular electronic network how
00:08:31.250 --> 00:08:45.260
much loss am getting in the circuit so in
general . this insertion loss in IL this is
00:08:45.260 --> 00:09:01.320
expressed in db so is remember that 10 log
10 PLR is the insertion loss in db now here
00:09:01.320 --> 00:09:13.460
I will haah take a property of any microwave
network you may not be familiar with this
00:09:13.460 --> 00:09:20.760
in graduate level we do not teach that but
in post graduate the microwave technology
00:09:20.760 --> 00:09:33.290
courses there we prove one point that gamma
omega for any two port network that should
00:09:33.290 --> 00:09:45.130
be always an even function of omega So what
does that mean that means always this is a
00:09:45.130 --> 00:09:50.779
property believe me or if you want to see
this is proved in any microwave engineering
00:09:50.779 --> 00:10:01.800
course so in any book particularly the our
recommended book this book microwave Engineering
00:10:01.800 --> 00:10:10.170
by David Pozar it is already recommended in
your course So in this book this is derived
00:10:10.170 --> 00:10:18.070
that always gamma is event function of Omega
that means gamma omega is equal to gamma of
00:10:18.070 --> 00:10:24.620
minus Omega we will utilize this property
now let me write what is gamma omega Gamma
00:10:24.620 --> 00:10:39.330
Omega is the impedance of the network either
this side or this side looking at input impedance
00:10:39.330 --> 00:10:53.170
or output impedance here minus Z0 by Z0 plus
if the characteristic impedance of the this
00:10:53.170 --> 00:11:03.460
filter section is Z0 then source then this
Z omega is the source impedance if I am talking
00:11:03.460 --> 00:11:10.000
of this reflection if I am talking of this
reflection then this Z omega is the load impedance
00:11:10.000 --> 00:11:20.630
and here also there is another property that
any impedance source load etc or the input
00:11:20.630 --> 00:11:35.410
impedance there the Z omega it can be retained
as r omega plus jx omega that is the part
00:11:35.410 --> 00:11:45.380
of this impedance and reactive part of impedance
and r omega is always again is an event function
00:11:45.380 --> 00:11:56.410
of omega and x omega is odd function of omega
This property are also true as I said that
00:11:56.410 --> 00:12:04.590
gamma omega is event function similarly this
is also true so we will write that ok this
00:12:04.590 --> 00:12:19.600
will break into that r omega minus Z0 minus
jx omega and r omega plus Z0 plus J omega
00:12:19.600 --> 00:12:28.060
now what is gamma of minus omega because I
want to test what is the nature of this PLR
00:12:28.060 --> 00:12:35.740
So we are going there that is insertion loss
has some specific functional characteristics
00:12:35.740 --> 00:12:41.840
with respective omega So that we are trying
to see so let me see what is this this is
00:12:41.840 --> 00:12:56.770
utilizing this properties that r Omega minus
Z omega sorry minus jz omega by r omega plus
00:12:56.770 --> 00:13:09.370
Z omega minus jx omega but we know that this
two should be equal So if I say that then
00:13:09.370 --> 00:13:18.860
basically basically what is this right side
can also retain as the complex conjugate of
00:13:18.860 --> 00:13:28.950
gamma omega You see that this is real so at
this minus this by this minus this so we saw
00:13:28.950 --> 00:13:38.670
that minus gamma minus omega is nothing but
gamma conjugate omega if we have this so we
00:13:38.670 --> 00:13:45.860
can say that what happens to this term.13:40)
gamma omega square because this is there in
00:13:45.860 --> 00:13:54.600
the insertion loss expression so gamma omega
square is gamma omega into gamma this is equal
00:13:54.600 --> 00:14:03.290
to gamma mega is equal to gamma minus omega
this is by definition and then we have just
00:14:03.290 --> 00:14:10.310
seen that this is nothing but gamma minus
omega So I can write it as gamma minus omega
00:14:10.310 --> 00:14:19.890
whole square because I can replace this with
or I can write like this gamma of minus omega
00:14:19.890 --> 00:14:28.720
and gamma of minus omega so that is gamma
minus omega whole square So I can say you
00:14:28.720 --> 00:14:46.529
see the property that gamma omega whole square
can I say is an event function of Omega so
00:14:46.529 --> 00:14:54.370
what does it mean that gamma omega square
when I will synthesizes as I said from the
00:14:54.370 --> 00:15:02.310
start that actually ee in this insertion loss
base method we specify the insertion loss
00:15:02.310 --> 00:15:08.899
we specify the insertion loss which is nothing
but attenuation part that how it will go that
00:15:08.899 --> 00:15:17.721
in pass band stop band etc For that we require
to have this but these says that this can
00:15:17.721 --> 00:15:26.170
be of that I event function of omega means
allot function components odd components are
00:15:26.170 --> 00:15:36.030
0 that means it can have only this a plus
b omega square plus c omega 4 plus d omega
00:15:36.030 --> 00:15:52.329
6 etc no omega 1 omega 3 like that terms So
we can say that this gamma omega square can
00:15:52.329 --> 00:16:20.209
be represented by two polynomials where m
and n are real polynomials in omega square
00:16:20.209 --> 00:16:25.620
m and n are real polynomial You see this is
reflection coefficient so all obviously this
00:16:25.620 --> 00:16:32.769
will be m omega square plus n omega square
because this is this plus something so what
00:16:32.769 --> 00:16:51.019
is then PLR PLR is 1 by 1minus m omega square
by m omega square plus n omega square and
00:16:51.019 --> 00:17:04.220
that this 1 plus m omega square by n omega
square So it is says that you can specify
00:17:04.220 --> 00:17:16.860
anything but I will be able to realize a filter
only this insertion loss is specified in this
00:17:16.860 --> 00:17:26.539
given form that means if you specify something
with omega etc then it won’t be realizable
00:17:26.539 --> 00:17:39.980
Now based on this specification there are
various choices So already I the student to
00:17:39.980 --> 00:17:52.820
refer to another NPTEL course basic building
blocks of Microwave Engineering
00:17:52.820 --> 00:18:14.039
in lecture 9 basic . building blocks no no
no basic basic tools of Microwave Engineering
00:18:14.039 --> 00:18:28.009
my course there in lecture 9 actually that
was in respective impedance matching and there
00:18:28.009 --> 00:18:35.359
we have seen in details the properties of
various polynomials which was used for synthesis
00:18:35.359 --> 00:18:41.989
that time it was impedance transformers but
those are also valid for filters so please
00:18:41.989 --> 00:18:50.489
brush up your knowledge of basic polynomial
functions like butterwork polynomial Chebyshav
00:18:50.489 --> 00:18:59.529
polynomial elliptic polynomial maximally flat
which is nothing but butterworth etc etc so
00:18:59.529 --> 00:19:09.119
here we start with butterworth polynomial
so if insertion loss is specified in the form
00:19:09.119 --> 00:19:19.450
of butterworth polynomial you know butterworth
is also called as maximally flat because given
00:19:19.450 --> 00:19:27.110
the order compare to any other polynomial
function it as suppose if it is ordered in
00:19:27.110 --> 00:19:38.210
upto N derivatives are all zero so that is
why called as derivative flat response So
00:19:38.210 --> 00:19:47.330
butterworth polynomial so this is the flattest
possible pass band so that means if we specify
00:19:47.330 --> 00:19:56.429
the insertion loss in the pass band by butterworth
filter Then we can say that we will get a
00:19:56.429 --> 00:20:02.690
very flat response which is desirable in the
pass band Obviously always zero cannot be
00:20:02.690 --> 00:20:08.360
achieved that attenuation constant zero but
will achieve a very flat pass band and by
00:20:08.360 --> 00:20:16.659
specifying a level we can say that ok my pass
band is I am not attenuating this all the
00:20:16.659 --> 00:20:24.139
frequency components in this band not more
than this amount So for a low pass filter
00:20:24.139 --> 00:20:32.679
the specification so low pass filter the specification
if we follow butterworth you know butterworth
00:20:32.679 --> 00:20:44.480
polynomial is given like this So already omega
square it is a function so you see that it
00:20:44.480 --> 00:20:51.360
is a function only omega square so it is realizable
from this property of M and N that ok I can
00:20:51.360 --> 00:20:58.419
realize it so let us try to realize this and
N is the order of filter that you know sorry
00:20:58.419 --> 00:21:12.409
I can make it capital N So N is the order
of the filter
00:21:12.409 --> 00:21:20.229
omega C is the cut of frequency low pass filter
cut of frequency will be lo low pass filter
00:21:20.229 --> 00:21:36.200
angler given by omega C Now pass band if you
see this pass band pass band extends from
00:21:36.200 --> 00:21:47.080
omega is equal to zero to omega is equal to
C and at the bandage that means suppose I
00:21:47.080 --> 00:21:59.489
am plotting omega and PLR oh sorry P L R then
zero this is omega C now from here it will
00:21:59.489 --> 00:22:10.470
be having some stop band so PLR will change
but what is the baah PLR at this point we
00:22:10.470 --> 00:22:25.030
can find from here so at omega is equal omega
C PLR is equal to 1 plus K square So I can
00:22:25.030 --> 00:22:31.169
specify now you know butter worth response
since we have taken like butterworth response
00:22:31.169 --> 00:22:39.039
is like this its maximally flat very flat
But in pass band I will have some attenuation
00:22:39.039 --> 00:22:43.989
But this the maximally flat one but I should
know that what is the maximum attenuation
00:22:43.989 --> 00:22:55.580
I am having so this value is what 1 plus K
square So suppose I want that ok no more than
00:22:55.580 --> 00:23:03.580
3 db attenuation or no more than 1 db attenuation
So I will put that at I know that at at omega
00:23:03.580 --> 00:23:09.320
is equal to omega C at cut off in the pass
band the maximum attenuation takes place here
00:23:09.320 --> 00:23:15.259
in the butterworth polynomial and that value
is K square from that I can always find K
00:23:15.259 --> 00:23:29.159
so for a example if we choose that this our
insertion loss maximum value is the PLR maximum
00:23:29.159 --> 00:23:39.499
at pass band I wont tolerate more than 3 db
so if this is 3 db what happens to K that
00:23:39.499 --> 00:23:48.779
1 plus k square ten log of this is 3 so from
that you can find out K is equal to 1 under
00:23:48.779 --> 00:24:04.739
this condition . So we can plot this PLR versus
omega by omega c normalize with respective
00:24:04.739 --> 00:24:15.529
omega C so I know the values will be like
this by 5 1 15 etc so this is point where
00:24:15.529 --> 00:24:29.590
cut off will takes place and
so what is the value at zero let us also see
00:24:29.590 --> 00:24:44.470
the at zero what is PLR ? this is 1 so PLR
is 1 here and PLR this value is 1 plus K square
00:24:44.470 --> 00:24:52.259
also what happens to this polynomial when
omega is . . into to the stop band that means
00:24:52.259 --> 00:25:00.389
Omega by omega C is the large number then
can I say that for omega greater than omega
00:25:00.389 --> 00:25:14.450
C I can say PLR is approximately K square
omega by omega C whole to the power 2n So
00:25:14.450 --> 00:25:24.489
what is the rate of increase of PLR in the
stop band from this I can say that rate of
00:25:24.489 --> 00:25:41.629
increase of PLR is how much it is 20 n db
part decade This is well known if you have
00:25:41.629 --> 00:25:48.029
this expression you can always say this so
we see that here at attenuation that alpha
00:25:48.029 --> 00:25:59.620
increase monotonically with frequency But
we know that it is at lower side of the pass
00:25:59.620 --> 00:26:07.450
band it is not much but at bandage that means
near cut off it is increasing but I can always
00:26:07.450 --> 00:26:15.150
specify that where it will be level fixed
lamp and this rate of interest is 20n db per
00:26:15.150 --> 00:26:23.099
decade so how much you want to achieve this
rate so that basically by that you select
00:26:23.099 --> 00:26:31.980
what is the order of this filter order means
you will have to find how many sections you
00:26:31.980 --> 00:26:41.130
need to put ok So third order fourth order
means you will have this now let us got to
00:26:41.130 --> 00:26:50.870
the another design that instead of this if
I say that in the low pass filter unlike this
00:26:50.870 --> 00:26:58.519
Chebyshav ok I want this rate to increase
further that I want this should be sharper
00:26:58.519 --> 00:27:06.379
than this I do not mind obviously you cannot
choose everything so I will say I want a very
00:27:06.379 --> 00:27:13.289
sharp price compare to butterworth here I
do not mind if instead of monotonically increasing
00:27:13.289 --> 00:27:22.570
the in pass band the insertion loss repels
that means I can have high low but do not
00:27:22.570 --> 00:27:33.269
cross this limit so that is possible Chebyshav
is sharpest one . or much sharper than our
00:27:33.269 --> 00:27:48.380
butter worth so I have this PLR here omega
by omega C let we fix my 1plus k square this
00:27:48.380 --> 00:28:00.659
is designer will choose and this is my omega
C so a butterworth polynomial it can be so
00:28:00.659 --> 00:28:19.729
let me first draw the maximally flat one this
is my butterworth maximally flat or butter
00:28:19.729 --> 00:28:34.570
worth now this is Chebyshav Chebyshav as various
depending on the order that chebyshav various
00:28:34.570 --> 00:28:41.090
but it repels whether there will be one repel
1 cycle or 2 cycle 3 cycle that depends on
00:28:41.090 --> 00:28:48.509
order but you see always they are confined
between this and this but so what is the advantage
00:28:48.509 --> 00:28:54.389
you see that here it was at monotonically
increasing here I have repel but I can specify
00:28:54.389 --> 00:29:00.249
that ok B within this limit so in pass band
it is never crossing the limit Once it is
00:29:00.249 --> 00:29:07.090
going away from pass brand it is much sharper
than butterworth that’s it is advantage
00:29:07.090 --> 00:29:13.249
so if you want your prime concern is after
pass band when I entering stop band I will
00:29:13.249 --> 00:29:21.690
have a very good cut off and very sharp cut
off You opt for this chebyshav shape polynomial
00:29:21.690 --> 00:29:32.649
so again you can determine the polynomial
by this K square and what is this rate of
00:29:32.649 --> 00:29:39.679
increase if we see the so in this case first
me let me write down the chebyshav polynomial
00:29:39.679 --> 00:29:52.399
from 1+ksquare Tn square omega by omega C
Now Tn is the Chebyshav polynomial of . . and
00:29:52.399 --> 00:30:00.830
we choose like this so for large N again I
can say that when omega is greater than omega
00:30:00.830 --> 00:30:25.720
C PLR is K square Tn square omega by omega
C Now at high value of omega by omega C Tn
00:30:25.720 --> 00:30:37.220
chebyshav polynomial it is approximated very
good approximation is this so this becomes
00:30:37.220 --> 00:31:01.419
K square Tn sorry K square into half 2x
y to the power N so this is K square by 4
00:31:01.419 --> 00:31:21.529
2 this is Tnx here I will write 2 omega by
omega C So 2 omega by omega C e to the power
00:31:21.529 --> 00:31:30.519
N This is Tnx so Tnx square . . so here you
now tell what is the slope I have came here
00:31:30.519 --> 00:31:45.599
because I want it is sharper slope so slope
is 20 db by decade 20 ndb so same as butterworth
00:31:45.599 --> 00:31:53.479
then you can say that how I am getting it
and what is the advantage at advantage is
00:31:53.479 --> 00:32:09.879
that always this value of Tn it is always
2 to the power 2N by 4 times insertion loss
00:32:09.879 --> 00:32:28.961
of any chebyshav filter is 2 to the power
2N by 4 times larger than butterworth Now
00:32:28.961 --> 00:32:37.460
obviously if you go for N is equal to 1 that
means the single section chebyshav then you
00:32:37.460 --> 00:32:45.110
do not have any advantage but the moment you
go for N is equal to 2 or N is equal to 3
00:32:45.110 --> 00:32:55.259
etc so N is equal to 2 means you have 2 to
the power 4 sixteen by 4 that means 4 times
00:32:55.259 --> 00:33:02.749
larger the butterworth always you will have
the value so even if the slope are not much
00:33:02.749 --> 00:33:11.149
different but you are getting more value of
insertion loss so your alpha is increased
00:33:11.149 --> 00:33:19.789
So then we will see there is another filter
called another very popular filter . particularly
00:33:19.789 --> 00:33:33.279
in CD ROM etc this is used this called elliptic
filter Now if you want you have seen that
00:33:33.279 --> 00:33:42.539
butter worth and chebyshav same rate of price
but elliptic is the maximum rate of price
00:33:42.539 --> 00:33:51.320
it can give but what it will you will suffer
that it has repel both in pass band and stop
00:33:51.320 --> 00:34:00.140
band so checbyshav you see it monotonically
increases once it is in the pass band it had
00:34:00.140 --> 00:34:06.849
repel in once it is ahh at attenuation of
stop band here it is in pass band it is repel
00:34:06.849 --> 00:34:14.940
but it does not have any repel elliptic have
repel in both so that means here it will be
00:34:14.940 --> 00:34:24.480
something like these how many it depends on
the order so it goes and then here again it
00:34:24.480 --> 00:34:35.930
repels but no problem if you specify that
ok atleast everywhere I want this attenuation
00:34:35.930 --> 00:34:43.280
in the stop band this is your stop band this
is your pass band So here as before you can
00:34:43.280 --> 00:34:50.409
specify that ok instead of pass band it is
beyond this and stop band attenuation should
00:34:50.409 --> 00:35:00.770
be like this then you go for elliptic and
there is another one sometimes in a filter
00:35:00.770 --> 00:35:08.120
if you have if your bass band signal or if
you want to possess the signal any bass band
00:35:08.120 --> 00:35:15.830
signal is not a single tone it as a sprayed
of frequency suppose when am talking talking
00:35:15.830 --> 00:35:25.360
up to 20 Kilohertz or roughly from 4 kilohertz
to 20 kilohertz there will be the voice sorry
00:35:25.360 --> 00:35:34.580
20 hertz to 20 kilohertz So you see this differ
different frequency if they are attenuated
00:35:34.580 --> 00:35:41.300
differently then there is problem in the reconstruction
So sometimes that means a linear system I
00:35:41.300 --> 00:35:47.800
want filter should act as a linear system
sometimes sometimes I can tolerate that is
00:35:47.800 --> 00:35:54.690
not a problem but in some application I cannot
tolerate that that time I want that linear
00:35:54.690 --> 00:36:06.730
phase filter Sorry this is linear phase filter
so linear phase means what that my phase should
00:36:06.730 --> 00:36:19.170
be specified like this 1plus P omega by omega
c whole to the power 2N so if we specify that
00:36:19.170 --> 00:36:26.020
P is a constant but I should have this type
of variation so this is a as you can guess
00:36:26.020 --> 00:36:31.000
but in phase am specifying a butterworth type
polynomial this is nothing but a butterworth
00:36:31.000 --> 00:36:37.390
type polynomial so this is the phase of the
voltage transfer function of the filter that
00:36:37.390 --> 00:36:43.140
should satisfy these under this condition
the group delay because that is the measure
00:36:43.140 --> 00:36:50.080
of whether I can tolerate or not As a group
when the bass band signal is moving so bass
00:36:50.080 --> 00:36:57.960
band signal or any RF signal with a frequency
spread that what is the group delay that means
00:36:57.960 --> 00:37:04.310
what is the maximum id id what is the maximum
delay between the maximum phasing delay and
00:37:04.310 --> 00:37:11.880
minimum phasing delay so that is given by
D pie by D omega and you see it trans out
00:37:11.880 --> 00:37:23.100
to be 1 plus b 2n plus1 omega by omega C whole
to the power 2N So this is a again you it
00:37:23.100 --> 00:37:29.920
is a maximally flat response so that may be
tolerable so if you use the linear phase filter
00:37:29.920 --> 00:37:35.190
you have this Like that there can be other
specification other polynomial still this
00:37:35.190 --> 00:37:40.640
is search is going on people are using various
newer newer functions from mathematics taking
00:37:40.640 --> 00:37:46.380
new functions and implementing that to get
a more desired attenuation characteristic
00:37:46.380 --> 00:37:55.960
etc So we have seen that how to do it so now
we will try to see how a microwave engineer
00:37:55.960 --> 00:38:01.710
will implement this because this mathematics
or this specifications is one thing but finally
00:38:01.710 --> 00:38:07.830
as a engineer we should implement that for
that we need to have some mechanism there
00:38:07.830 --> 00:38:15.070
is nothing fundamentally new this is all about
filters but unless and until we engineers
00:38:15.070 --> 00:38:23.090
plan how to design how to implement it we
do not consider our job finished scientist
00:38:23.090 --> 00:38:28.940
upto this they stop but we engineer will always
go on and try to make that ok if I want to
00:38:28.940 --> 00:38:35.420
make it and taste it I should know after this
what will happen that will see in the next
00:38:35.420 --> 00:38:38.569
class the implementation of this filters thank
you