WEBVTT
Kind: captions
Language: en
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Welcome to this sixteenth lecture of tis lecture
series today we have already seen the RF amplifier
00:00:31.840 --> 00:00:42.360
design for maximum gain and for specified
gains Now today we will see one amplifier
00:00:42.360 --> 00:00:50.190
where gain is not so important but noise performance
is important you know that that amplifier
00:00:50.190 --> 00:00:59.489
is called low noise amplifier it is a integral
part of any RF receiver You know in any RF
00:00:59.489 --> 00:01:06.590
receiver we have very small signal because
in when we transmits the signal and receive
00:01:06.590 --> 00:01:15.240
the signal in wireless path due to large path
losses we get very week signal so there ahhh
00:01:15.240 --> 00:01:22.350
you know any amplifier in its input there
are noises also the amplifier or any electronic
00:01:22.350 --> 00:01:31.730
device it produces its own noise So the signal
and noise both gets amplified by the any amplifier
00:01:31.730 --> 00:01:41.280
now if the its own noise is very high of any
amplifier because of active devices there
00:01:41.280 --> 00:01:47.420
is chance of quite good amount of noise the
amplifier itself adding up now now if that
00:01:47.420 --> 00:01:54.780
is not content then you may have the whole
signal gets buried in noise So it is very
00:01:54.780 --> 00:02:04.970
important to design for low noise amplifiers
and this amplifier is generally the first
00:02:04.970 --> 00:02:11.620
block after the antenna antenna receives the
signal antenna as we already seen that antenna
00:02:11.620 --> 00:02:17.730
is basically a narrow band filter So it gets
one RF frequency to which it is supposed to
00:02:17.730 --> 00:02:24.530
be tuned because its a narrow band device
so that RF signal is first fit to an amplifier
00:02:24.530 --> 00:02:29.200
because you need to amplify the signal for
further processing and giving to the other
00:02:29.200 --> 00:02:37.469
subsystems of.. subsequent blocks of receiver
Now their the first one that if it is adding
00:02:37.469 --> 00:02:44.989
noise then the whole strategy of deduction
may get disturbed that is why we take high
00:02:44.989 --> 00:02:51.889
precaution for this and this LNAs is are not
supposed to have maximum gain but they are
00:02:51.889 --> 00:02:58.200
supposed to minimize the noise that is why
the design is separately seen so let us see
00:02:58.200 --> 00:03:09.370
that in todays lecture. so you see suppose
I have an RF block 1 this LA LNA after that
00:03:09.370 --> 00:03:17.510
there will be mixture after that I will be
amplifiers etc then will be detectors So there
00:03:17.510 --> 00:03:22.830
are various blocks so if there are various
Rf blocks let us say that we have the first
00:03:22.830 --> 00:03:31.639
RF block 1 with the gain 1either gain or attenuation
both we are calling hmmm gain So if it is
00:03:31.639 --> 00:03:36.209
attenuation it will be a ahhh ho gain so if
it is attenuation it will be a less than 1
00:03:36.209 --> 00:03:45.599
absolute value of db scale it will be minus
and let us say that it has the the power is
00:03:45.599 --> 00:03:55.110
given by pp P1 and the noise figure that is
coming to be F1 All of you know noise figure
00:03:55.110 --> 00:04:03.200
it is basically the output noise power divided
by the input noise power map to the output
00:04:03.200 --> 00:04:09.170
and we all know that if we do simple those
mathematics which all of you done in BTech
00:04:09.170 --> 00:04:17.090
that it is basically the SNR at the input
divided by SNR at the output the input is
00:04:17.090 --> 00:04:22.751
kept at a fixed temperature generally that
is to ninety degree kelvin and there is no
00:04:22.751 --> 00:04:31.810
mismatch in the between the source or the
input and input side So under that it is the
00:04:31.810 --> 00:04:39.050
SNR ratios so let us have that noise figure
which is also a characterization of noise
00:04:39.050 --> 00:04:46.370
Instead of noise temperature we can have noise
figure anyone is will do but when we have
00:04:46.370 --> 00:04:51.530
amplifier blocks it is more convenient to
work with noise figure that is why are saying
00:04:51.530 --> 00:04:57.210
that this block as a noise figure of F1 now
it is connected to a another block suppose
00:04:57.210 --> 00:05:07.840
RF block 2 with the corresponding gain 2 the
signal power P2 and F2 and we know this you
00:05:07.840 --> 00:05:16.720
all know from your basic ahhh B Tech classes
that over all this whole 2 blocks together
00:05:16.720 --> 00:05:24.970
the overall noise figure that is given by
F1 plus F2 minus 1 by G1 You see that this
00:05:24.970 --> 00:05:35.260
F2 etc that means the second blocks noise
figure even if that is quite high that means
00:05:35.260 --> 00:05:42.220
you have good amount of noise still it is
being divided by G1 the gain of this amplifier
00:05:42.220 --> 00:05:49.310
or gain of this block so that becomes low
but this F1 it is not divided by anything
00:05:49.310 --> 00:05:55.950
So whatever the noise figure of first block
that will be always will be dominant factor
00:05:55.950 --> 00:06:02.870
in the overall noise figure whole visible
system So it is very important that this F1
00:06:02.870 --> 00:06:10.510
is quite kept low because this F1 is high
is no chance of hmmm mmmm making this overall
00:06:10.510 --> 00:06:18.600
noise figure low that is why the design for
this if it is become an amplifier LNA then
00:06:18.600 --> 00:06:24.840
it is important because I will have to keep
this F1 low low noise as I said crucial for
00:06:24.840 --> 00:06:31.830
LNA moderate gain required to suppress higher
noise obviously if I want to have low noise
00:06:31.830 --> 00:06:38.370
I cannot get moderate gain because you see
that When we do that for conjugate matching
00:06:38.370 --> 00:06:45.730
etc the maximum gain that time we make the
amplifiers operate with the full activeness
00:06:45.730 --> 00:06:53.150
and time we will have full noises When we
try to make low noise amplifier the gain may
00:06:53.150 --> 00:07:01.400
not be very high but moderate gain is required
because some gain is required for any amplifier
00:07:01.400 --> 00:07:11.280
type of thing and as of subsequent blocks
so this gain is because it will suppress the
00:07:11.280 --> 00:07:18.460
subsequent blocks noise so some gain is required
it may not be very high gain of this block
00:07:18.460 --> 00:07:24.740
it should be substantial . So this is the
challenge so noise figure is related to source
00:07:24.740 --> 00:07:32.110
admittance you see that this has been shown
by people that this as been shown by people
00:07:32.110 --> 00:07:38.810
that this noise figure of any amplifier that
is related to his source admittance source
00:07:38.810 --> 00:07:46.490
admittance we are calling Ys and you know
with any impedances we have the ba corresponding
00:07:46.490 --> 00:07:51.050
reflection coefficient similarly with this
source admittance means obviously we have
00:07:51.050 --> 00:07:58.700
a source impedance So we have corresponding
reflection coefficient of source and people
00:07:58.700 --> 00:08:07.090
have shown that this relationship that any
F of this amplifier that is given by this
00:08:07.090 --> 00:08:15.530
F min + RN by GS by YS minus Y opt Square
so ys we have already seen it is a source
00:08:15.530 --> 00:08:25.060
admittance so what are this F min RN Gs and
Y opt so Ys this Ys is nothing but g source
00:08:25.060 --> 00:08:31.110
admittance seen by the RF amplifier Source
admittance the real part is called the source
00:08:31.110 --> 00:08:37.769
conductance and this part is called source
susceptance Bs that you all know Y opt is
00:08:37.769 --> 00:08:43.140
an optimum source admittance that results
in the minimum noise figure for the amplifier
00:08:43.140 --> 00:08:50.730
Fmin It is a specification given by the amplifier
manufacturer that optimum source admittance
00:08:50.730 --> 00:09:00.310
if I make that then the noise will be minimum
and RN is the equivalent noise resistance
00:09:00.310 --> 00:09:07.980
of the amplifier as we are saying that this
amplifier has a its own noise it adds that
00:09:07.980 --> 00:09:13.670
equivalent noise resistance Any electronic
circuit has a noise resistance that we are
00:09:13.670 --> 00:09:20.590
calling resistance That we are calling RN
that also specified by manufacturer and . so
00:09:20.590 --> 00:09:33.880
you see that RN GS Fmin and Yopt there are
this thing Gs obviously the source admittance
00:09:33.880 --> 00:09:42.571
part so this is excitation part but this three
parameters the Fmin then RN and Yopt they
00:09:42.571 --> 00:09:47.800
are characteristic of the amplifier This are
called the noise characteristic of the amplifier
00:09:47.800 --> 00:09:55.430
so for transistors Fmin tower opt plus RN
they are specified by manufacturer and also
00:09:55.430 --> 00:10:01.510
you can sometimes measure it measurement posib
procedure for measuring this So let us say
00:10:01.510 --> 00:10:11.400
that this is known so then we define a noise
figure parameter out of this things and also
00:10:11.400 --> 00:10:18.630
the characteristic impedance So let the noise
figure parameter is called N N is given by
00:10:18.630 --> 00:10:28.260
this formula F minus Fmin by 4RN by Z0 1 plus
Tow opt Square sorry there are two vertical
00:10:28.260 --> 00:10:34.900
buds actually there should be one only so
also this is not T this is actually tow or
00:10:34.900 --> 00:10:42.400
gamma gamma of of capital gamma for specified
F and noise parameters N is fixed You see
00:10:42.400 --> 00:10:52.040
that suppose we are asked to design LNA for
a specified noise figure then once that is
00:10:52.040 --> 00:11:01.690
fixed and Fmin RN and Tow opt are the parameters
of naa noise parameters of transistors and
00:11:01.690 --> 00:11:08.680
Z0 it is the characteristic impedance of the
character So for the specified F and this
00:11:08.680 --> 00:11:14.440
three noise parameters we can see that N is
fixed for particular characteristic impedance
00:11:14.440 --> 00:11:25.880
. now you see this formula this formula that
in terms of admittance we know how to convert
00:11:25.880 --> 00:11:33.480
the reflection coefficient we know Ys given
by this formula Y opt is given by this formula
00:11:33.480 --> 00:11:41.310
and Gs is the real part of Ys So in terms
of this from this Ys I can write this so this
00:11:41.310 --> 00:11:49.790
is finally this so with this we will have
to change this Ys and Y all this Y things
00:11:49.790 --> 00:11:57.880
to gamma things so that can be done so that
conversion if you just do the manipulation
00:11:57.880 --> 00:12:05.339
this conversion is this you see this formula
here I do not have any source admittance part
00:12:05.339 --> 00:12:13.870
but I have this in terms of reflection coefficient
we have written and we know that so already
00:12:13.870 --> 00:12:19.610
we have found that value of N what is the
value of N this is the value of N SO if we
00:12:19.610 --> 00:12:31.370
put that then we get that this equation N
is this Now for a specified noise figure N
00:12:31.370 --> 00:12:40.830
is fixed so now you see also gamma opt Gamma
option optimum that is also a parameter for
00:12:40.830 --> 00:12:48.060
transistor so you see this is a one equation
in one unknown that is gamma S so we can then
00:12:48.060 --> 00:12:56.420
solve for Gamma S from this equation consideration
N and gamma opt as given constant so that
00:12:56.420 --> 00:13:04.270
will be doing next . and that is the the manipulation
always we do So from that equation we can
00:13:04.270 --> 00:13:12.840
write like this then we can this is the next
step of this you see and that means I have
00:13:12.840 --> 00:13:21.730
already got Gamma S gamma S star so that if
I just I am making the whole square thing
00:13:21.730 --> 00:13:31.360
as we do always so finally the solution is
this gamma S minus some complex quantity because
00:13:31.360 --> 00:13:38.380
this gamma optimum is a complex quantity N
is a real number So and this side is fully
00:13:38.380 --> 00:13:47.089
a real number so by now you know that this
is locus of the circle This is the in the
00:13:47.089 --> 00:13:58.990
smith chart in this smith chart if I now locate
gamma S for a given N that means given noise
00:13:58.990 --> 00:14:07.180
parameters then I know that this will represent
a circle . what is the center of the circle
00:14:07.180 --> 00:14:13.190
we are calling C with the Subscript F to show
that for a given noise figure this value is
00:14:13.190 --> 00:14:22.040
this center is this and radius is this So
obviously here if F is equal to Fmin you can
00:14:22.040 --> 00:14:32.899
check that If F F is equal to Fmin let us
see the N value so where is N so if F is
00:14:32.899 --> 00:14:51.960
Fmin N becomes 0 So if N becomes 0 you see
the radius becomes 0 and the center is at
00:14:51.960 --> 00:15:04.260
gamma opt so basically the F is Fmin that
means specified noise figure is same as minimum
00:15:04.260 --> 00:15:11.110
possible noise figure from the amplifier then
that represents a point which is equal to
00:15:11.110 --> 00:15:18.740
then gamma source resistance just equals the
gamma opt obviously that is also the definition
00:15:18.740 --> 00:15:25.820
of gamma opt so circle degenerates to point
that part is easy That means if we always
00:15:25.820 --> 00:15:32.779
design for Fmin we get it but sometimes we
do not because if so much noise stringent
00:15:32.779 --> 00:15:38.750
noise figure is not require then we try to
design for a bit higher noise figure which
00:15:38.750 --> 00:15:44.460
will serve our purpose but that will give
us some more gain because we know gain in
00:15:44.460 --> 00:15:51.620
also important though we are not maximizing
it for LNA but some gain if you get then subsequent
00:15:51.620 --> 00:15:59.070
stages they are noise figure will be improved
. So that we do so let us take an example
00:15:59.070 --> 00:16:06.450
of this whole thing suppose I want to find
noise performance of Galiya marshan FET You
00:16:06.450 --> 00:16:16.330
know gas FET their FET is always superior
to BJT because in BJT ther are actually current
00:16:16.330 --> 00:16:24.500
is controlled Current means flow off charges
so that will add noise whether in any FAT
00:16:24.500 --> 00:16:31.860
it is basically field operated so not much
so much charge carrier they cause that is
00:16:31.860 --> 00:16:37.690
why their noise is less so noise performance
of GAS FET is generally superior to BJT that
00:16:37.690 --> 00:16:44.709
is why if LNA is generally designed with FAT’s
not with BJT’s Now let us say for that particular
00:16:44.709 --> 00:16:50.769
transistor FAT we have the parameters given
that means this are all S parameters You see
00:16:50.769 --> 00:16:59.310
S parameters S11 is magnitude of S11 is less
than 1 Magnitude of S22 is also less than
00:16:59.310 --> 00:17:07.490
1 So you know that we can we have unconditional
stability extra also the minimum noise figure
00:17:07.490 --> 00:17:15.120
for this particular transistor is given as
25 db it typical value gamma optimum that
00:17:15.120 --> 00:17:23.459
means optimum source resistance for which
I can achieve this is given by this 475 angle
00:17:23.459 --> 00:17:31.890
166 degree So you know that that optimum source
resistance will be somewhere here because
00:17:31.890 --> 00:17:40.850
here it is 166 degree and point something
So something is one so half of that roughly
00:17:40.850 --> 00:17:49.060
and RN the real part of the source or admittaaaah
real part of source baah impedance that is
00:17:49.060 --> 00:17:58.330
35 db ohm So design a LNA for minimum noise
figure here so that is RM here they are saying
00:17:58.330 --> 00:18:06.350
minimum noise figure means we will try to
design for 25 db itself . so we know first
00:18:06.350 --> 00:18:12.410
will any amplifier we need to do the amplifier
analysis you know rollest criteria so check
00:18:12.410 --> 00:18:22.059
for amplifier stability to find out this values
K rollest stability factor that is you see
00:18:22.059 --> 00:18:32.371
1 greater than 1 so no problem also you check
that delta it magnitude is 419 Delta is a
00:18:32.371 --> 00:18:41.230
complex quantity we should have written the
delta magnitude of delta that is 419 so that
00:18:41.230 --> 00:18:49.140
is also less than 1 ok so we have passed the
K delta test or rollest test so we can say
00:18:49.140 --> 00:18:54.501
that device is unconditionally stable so you
need not worry we can proceed for LNA design
00:18:54.501 --> 00:19:01.780
. so LNA design you see for minimum noise
figure already gamma opt is given so that
00:19:01.780 --> 00:19:11.730
gives us the source reflection coefficient
Now minimum noise figure of 2 db 25 db now
00:19:11.730 --> 00:19:19.030
we plot constant noise figure circles from
25 db to 3 db actually if you want to have
00:19:19.030 --> 00:19:24.630
minimum noise no problem but for any general
design we are showing that ok we are starting
00:19:24.630 --> 00:19:33.230
from 25 db so at whatever step you want you
find out those circles . that can be done
00:19:33.230 --> 00:19:41.730
let us say we have taken that instead of minimum
noise will take 28 db noise figure so then
00:19:41.730 --> 00:19:47.299
we can calculate the value of NI that will
turn out to be remember this is that absolute
00:19:47.299 --> 00:19:55.799
thing so I need to convert this db’s to
the actual figure and that is like here so
00:19:55.799 --> 00:20:05.000
you see the NI which is the noise parameter
for the 28 db noise figure that subscript
00:20:05.000 --> 00:20:14.100
using I that means we are specifying I noise
figure So noise parameter that will be become
00:20:14.100 --> 00:20:23.299
this point 378 center of the constant noise
figure circle we can easily plot because that
00:20:23.299 --> 00:20:31.650
Cf expression we have so by putting I here
you get this is the values you get radius
00:20:31.650 --> 00:20:39.820
of the circle that will be here that you can
calculate that is 312 so that means center
00:20:39.820 --> 00:20:48.540
is as I said somewhere here and it is having
a circle of radius not much . so that we have
00:20:48.540 --> 00:21:06.580
done you see this is 25 db 26 db 27 db 28
db 29 db We see that you see the circles are
00:21:06.580 --> 00:21:13.630
closely spaced so we can say for this transistor
the noise figure is not sensitive to small
00:21:13.630 --> 00:21:24.610
variation of tow s and tow opt gamma opt So
no it is upto us to choose where from this
00:21:24.610 --> 00:21:30.480
circles on the circle somewhere you choose
so that will determine your noise figure if
00:21:30.480 --> 00:21:37.799
you decide that I will choose from 27 ok you
can choose it and advice is to try to make
00:21:37.799 --> 00:21:46.820
it as near to center as possible So if you
are on this you come down here as much as
00:21:46.820 --> 00:21:55.600
possible so that you get a goo less mismatch
etc It is no unique it is upto you now whatever
00:21:55.600 --> 00:22:03.040
noise figure you choose that will determine
your noise performance as well as gain you
00:22:03.040 --> 00:22:13.510
see though it was said you can do for 25 db
we are lets taking it 28 db and doing it . Now
00:22:13.510 --> 00:22:23.460
the question of you will have to now match
design the any amplifier finally the input
00:22:23.460 --> 00:22:29.890
input haaaah matching network gain and output
matching network gain that you will have to
00:22:29.890 --> 00:22:36.670
do so you see it is better to find out that
since you have already choosen gamma S you
00:22:36.670 --> 00:22:44.919
can find out gamma L from this formula last
lecture we have extensively used this so that
00:22:44.919 --> 00:22:51.200
already makes that you are makes that load
reflection coefficient is this for gamma S
00:22:51.200 --> 00:22:59.020
is equal to gamma star db If other gamma S
is chosen that means we chosen a particular
00:22:59.020 --> 00:23:05.850
gamma S but if you choose something else then
you remember that you will have to choose
00:23:05.850 --> 00:23:12.750
the gamma L also accordingly then determine
gain in our case once this is there you know
00:23:12.750 --> 00:23:20.260
how to find the gain Because once you have
this gamma S gamma L value we know that what
00:23:20.260 --> 00:23:26.400
is the maximum gain or what is the specified
gain let us say the determine our gain is
00:23:26.400 --> 00:23:33.820
11 db though we could have got 127 db upto
to that it goes we will decide 11 db will
00:23:33.820 --> 00:23:41.400
be sufficient So design means you see there
is no harden first thing in practice will
00:23:41.400 --> 00:23:48.190
see that what value will choose etc It is
a guideline you should not go beyond this
00:23:48.190 --> 00:23:55.720
range You see that we are going from 25 db
noise figure to 3 db if that is the whole
00:23:55.720 --> 00:24:01.530
application can sustain that we will go there
and we will get this gain similarly we could
00:24:01.530 --> 00:24:09.940
have got by proper input and output matching
this 127 db but we say 11 db sufficient to
00:24:09.940 --> 00:24:15.710
a choosing that . Now another example let
us take that transistor is this another parameter
00:24:15.710 --> 00:24:22.320
thing Fmin is this here it is saying ok design
for a noise figure of 2 db You know noise
00:24:22.320 --> 00:24:30.370
figure the unit is kelvin sorry noise figure
is unit less it is wrongly here written . we
00:24:30.370 --> 00:24:36.210
should design for maximum gain at this fixed
noise figure because we since noise figure
00:24:36.210 --> 00:24:42.200
is specified we keep upto that what we should
design for maximum gain So first we find out
00:24:42.200 --> 00:24:49.090
the noise figure parameter N that turns out
to the points this so immediately we got constant
00:24:49.090 --> 00:24:58.870
noise figure circle for that 2 db noise figure
that is here RF is here So now input gain
00:24:58.870 --> 00:25:05.990
on the smith chart we plot input section constant
gain circles for input section gain let us
00:25:05.990 --> 00:25:13.070
say we are trying to make from 1 db to 17
db these are the things once I have GS like
00:25:13.070 --> 00:25:22.740
this then I know that normalize GS will be
these Then we can find out what is the specified
00:25:22.740 --> 00:25:33.210
value of gain what is this that we have already
seen so CS and RS input matching circles maximum
00:25:33.210 --> 00:25:40.799
gain circle 17 db out of which intersects
2 db constant noise figure circle at this
00:25:40.799 --> 00:25:49.090
point so we will take gamma S to be that point
also . we assume unilateral device and we
00:25:49.090 --> 00:25:54.250
make conjugate match because we are trying
to maximize whatever we have in that we are
00:25:54.250 --> 00:26:02.160
trying to maximize the gain so here the you
this all we saw so it determines the load
00:26:02.160 --> 00:26:09.850
impedance also S22 is given value from that
we can always find gamma L it is this will
00:26:09.850 --> 00:26:20.290
be your gamma L then the gain from the load
side that you can get as 125 db . so conjugate
00:26:20.290 --> 00:26:28.340
matching already the transistor Its own gain
is 585 we have seen that input we are taking
00:26:28.340 --> 00:26:36.470
17 just now we have decided that output side
we will take 125 db So you see that we are
00:26:36.470 --> 00:26:46.150
getting 853 db so by conjugate matching this
LNA which is designed for 2 db noise figure
00:26:46.150 --> 00:26:56.820
it will give you the gain 853 db 53 that is
ok for LNA this type of gain is possible if
00:26:56.820 --> 00:27:02.720
not LNA in other cases generally it should
be a double digit factor but here since we
00:27:02.720 --> 00:27:10.870
are enforcing that ok we will be keeping our
noise figure low we are satisfied with this
00:27:10.870 --> 00:27:18.059
85 db gain . now also when since we are made
unilateral assumption we need to give the
00:27:18.059 --> 00:27:24.590
error or upper bound or lower bound of our
answer So yesterday in the last lecture we
00:27:24.590 --> 00:27:31.809
have discussed that how we can have find this
parameter that unilateral assumption parameter
00:27:31.809 --> 00:27:38.370
U that is this so note this is the formula
and you put this value of you you know that
00:27:38.370 --> 00:27:45.980
GT by GTU that this is the error in unilateral
assumption that various from this in db terms
00:27:45.980 --> 00:27:56.990
various from minus 05 db to 05 db 053 SO we
know that it is the assumption can be made
00:27:56.990 --> 00:28:04.000
And we have made that so our matching section
that becomes simpler than a classical conjugate
00:28:04.000 --> 00:28:15.169
match thing so 5 plus minus 5 db error will
be there in gain calculation so we know we
00:28:15.169 --> 00:28:23.820
have calculated 85 we may it may be 9 db may
be 8 db its not more than that that is important
00:28:23.820 --> 00:28:30.860
with this we have seen an low noise amplifier
design now this is basically extension of
00:28:30.860 --> 00:28:36.289
the earlier that constant gain circle part
but here we have given special attention to
00:28:36.289 --> 00:28:41.490
noise figure so we have introduced noise parameter
noise figure parameter and with respect to
00:28:41.490 --> 00:28:48.610
that basically that specify we design and
then we match to get some gain out of it that
00:28:48.610 --> 00:28:49.809
follows the whole procedure thank you