WEBVTT
Kind: captions
Language: en
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Welcome to this lecture series today will
be starting the RF microwave and amplifier
00:00:29.340 --> 00:00:37.040
design we have in the previous ten lecture
we have seen have Seen the microwave filter
00:00:37.040 --> 00:00:45.510
design today will start amplifier design you
know the signal amplification is one of the
00:00:45.510 --> 00:00:54.850
most basic needs of the any electronic circuits
and at microwave region we are mainly concernt
00:00:54.850 --> 00:01:03.950
with power amplification we do not we generally
not so bothered about the voltage amplification
00:01:03.950 --> 00:01:12.250
as happens in low frequency or baseband cases
Here we are bothered about the power amplification
00:01:12.250 --> 00:01:18.820
because microwave power is at premium It is
very costly to produce microwave power also
00:01:18.820 --> 00:01:26.490
we generally wirelessly transmit the power
So we want sufficient power to receive get
00:01:26.490 --> 00:01:32.130
received at the receiver That is why we take
special care for microwave amplifier design
00:01:32.130 --> 00:01:39.910
also you know that after world War II when
microwave Sources like Guyton travelling webtube
00:01:39.910 --> 00:01:47.410
Mecatrons etc were invented that time the
amplifier microwave amplifier were based on
00:01:47.410 --> 00:01:57.599
tubes but with the advances in semiconductor
technology now a days many transistor amplifiers
00:01:57.599 --> 00:02:05.539
transistor based amplifiers are used in Microwave
region and already NPTEL courses we have seen
00:02:05.539 --> 00:02:12.640
the microwave sources how those transistors
particularly the fade transistors gas fades
00:02:12.640 --> 00:02:21.970
then HBT HEMT etc are used what are the design
principles please refer there now in this
00:02:21.970 --> 00:02:28.500
course we will consider the transistor based
amplifier as a block box again as a 2 port
00:02:28.500 --> 00:02:37.280
network and we wont see the inner mechanism
or the device mechanism of the transistors
00:02:37.280 --> 00:02:45.000
that we already seen earlier Now we will see
a S parameter based description of that amp
00:02:45.000 --> 00:02:55.230
a transistor So we care 2 port S parameterii
S parameterized transistor we will try to
00:02:55.230 --> 00:03:06.750
design an amplifier and will try to get power
amplification by that . Now if we compare
00:03:06.750 --> 00:03:23.569
the low frequency and high frequency power
gains we will see that at low frequency you
00:03:23.569 --> 00:03:35.010
know that the generally describe the transistor
at low frequency with generally describe with
00:03:35.010 --> 00:03:46.270
a H parameter and most important parameter
of that is hfe So the generally that power
00:03:46.270 --> 00:04:02.520
gain at low frequency something like this
this is generally hfe square so the this hfe
00:04:02.520 --> 00:04:16.430
is the short circuit current gain now generally
it the power gain becomes the if we express
00:04:16.430 --> 00:04:26.570
this in dB scale then at 0dB that means 1
value of 1 power gain so it is 10 So this
00:04:26.570 --> 00:04:36.210
frequency at which the SC short circuit current
gain hfe that falls to 1 hfe square that is
00:04:36.210 --> 00:04:48.000
called the beta cutoff the maximum usable
frequency of the transistor and there is also
00:04:48.000 --> 00:04:57.100
relevant parameter called F beta which is
the frequency at which DC short circuit current
00:04:57.100 --> 00:05:08.380
gain beta of the transistor falls to 1 FT
is much higher than f beta But if we go higher
00:05:08.380 --> 00:05:17.440
we see that in microwave region This H parameter
description is not adequate There as I said
00:05:17.440 --> 00:05:27.020
that a whole transistor Transistor we represent
by s parameter with an impedance level Z0
00:05:27.020 --> 00:05:33.470
characteristic impedance level Z0 and if we
see the typical power variation in the dB
00:05:33.470 --> 00:05:52.000
scale That takes the form of this that generally
this S 21 If we take the pure transistor and
00:05:52.000 --> 00:05:57.940
if we try to find out that if we give some
signal and out without any loading or proper
00:05:57.940 --> 00:06:07.130
matching Then this S 21 square that for certain
region it is flat in dB scale and then after
00:06:07.130 --> 00:06:15.410
that it generally falls off generally with
a roll off factor And this frequency where
00:06:15.410 --> 00:06:27.990
the power gain becomes 1 that is called FS
the frequency at which this power gain of
00:06:27.990 --> 00:06:40.120
the transistor alone that falls to 1 However
by proper design we can have a we can improve
00:06:40.120 --> 00:06:49.940
this we can add some extra gain and that actually
will be the topic of this lecture series That
00:06:49.940 --> 00:07:00.050
we can improve this part and make it go upto
a more higher or upto a higher frequency F
00:07:00.050 --> 00:07:11.860
max Now this one we give a new name called
GT max the this G T is called transducer power
00:07:11.860 --> 00:07:19.650
gain and this maximum achievable thing is
somewhat higher than is S 21 square so this
00:07:19.650 --> 00:07:28.080
is the play that a microwave engineer or an
RF engineer who carefully designs an amplifier
00:07:28.080 --> 00:07:35.680
he can get this much extra gain by proper
designing and also he can extend the frequency
00:07:35.680 --> 00:07:44.600
a bit to F max So this difference between
f S and f max that allows or RF engineer should
00:07:44.600 --> 00:07:50.290
know how to exploit this gap And so he can
extend or push the amplifier design to higher
00:07:50.290 --> 00:07:57.150
value Obviously below above this frequency
no will be willing to use this Because the
00:07:57.150 --> 00:08:04.320
power gain that is falling to 1 so these transducer
power gain is a new quantity or I will say
00:08:04.320 --> 00:08:13.669
that in microwave region we need to look carefully
at various gain definitions I am saying from
00:08:13.669 --> 00:08:19.110
the beginning of this course and all NPTEL
courses that at high frequency or at microwave
00:08:19.110 --> 00:08:25.570
region we are very careful of the maximum
power transfer and we are very careful of
00:08:25.570 --> 00:08:32.210
the impedance matching in one of the first
NPTEL lectures for this microwave technology
00:08:32.210 --> 00:08:42.299
we have elaborately said about impedance matching
Now it when impedance matching is given its
00:08:42.299 --> 00:08:52.670
. . importance The in a microwave based amplifier
there are many as power gains that are possible
00:08:52.670 --> 00:09:05.350
so we will going into that now and for that
. we again assume that the transistor is represented
00:09:05.350 --> 00:09:18.119
by a 2 port network This is a transistor block
obviously this is a microwave transistor Generally
00:09:18.119 --> 00:09:25.740
you know that HEMT or HBT this transistors
we can use upto 100GHz people also trying
00:09:25.740 --> 00:09:31.149
to push it further Now this transistor for
our purposes will be represented by its 2
00:09:31.149 --> 00:09:38.350
port is S parameter and also will assume that
the character impedance level of this transistor
00:09:38.350 --> 00:09:49.120
is Z0 Now obviously this one will be connecting
with the a source and a load So let us put
00:09:49.120 --> 00:10:02.329
SC source is here And let us that source will
have typically an source resistance similarly
00:10:02.329 --> 00:10:15.189
we will be connecting in this side is to the
load
00:10:15.189 --> 00:10:27.689
of load impedance is ZL Now you see that there
are what happens to the waves here so we can
00:10:27.689 --> 00:10:38.189
say that actually the terminal voltage here
is V1 Actually we know that the at high frequency
00:10:38.189 --> 00:10:41.329
at actually at all frequency but at high
frequency actually at all frequency but at
00:10:41.329 --> 00:10:48.389
high frequency we generally cannot neglect
that actual signal propagation is in the form
00:10:48.389 --> 00:10:56.029
of waves So there will be you know for scattering
parameter is define in terms of that voltage
00:10:56.029 --> 00:11:03.649
waves So we have an incidence voltage wave
going to here that will call V1 plus also
00:11:03.649 --> 00:11:12.050
depending on the mismatch we know there will
be a V1 minus here And V1 the sum of these
00:11:12.050 --> 00:11:22.319
at this port port 1 V1 plus and V1 minus that
will be calling V1 Also we know that here
00:11:22.319 --> 00:11:35.679
the something will happen That from this port
there will be a incident voltage V2 plus that
00:11:35.679 --> 00:11:41.779
will be entering Because of this in general
there will be mismatch here So this V2plus
00:11:41.779 --> 00:11:47.930
will come and also there will the V2 minus
Again the port voltage is nothing but V2 plus
00:11:47.930 --> 00:11:59.739
plus and V2 minus And also will see that there
will be various reflections So if we look
00:11:59.739 --> 00:12:07.829
at the source side we know if we look at here
we can see that there will be some source
00:12:07.829 --> 00:12:17.970
reflection Similarly if we look at here there
will be some input reflection because input
00:12:17.970 --> 00:12:23.879
impedance will be seen here and depending
on the impedance level there will be input
00:12:23.879 --> 00:12:33.000
reflections similarly from here if we look
we can say that there will be a output reflection
00:12:33.000 --> 00:12:43.369
coefficient also from here if we look there
will be a load reflection coefficient Now
00:12:43.369 --> 00:12:53.540
we know what are this value of this reflection
coefficient Let us see that this gamma S the
00:12:53.540 --> 00:13:05.990
source reflection coefficient that we know
that will be given by ZS – Z0 by ZS + Z0
00:13:05.990 --> 00:13:20.589
and ZS ZS is a complex number Z0 is generally
is a real number So gamma s is a complex reflection
00:13:20.589 --> 00:13:26.439
coefficient because this is a complex number
similarly at the load side due to mismatch
00:13:26.439 --> 00:13:39.459
between ZL and Z0There will be ZL minus Z0
by ZL Z0 Now you see that I have certain power
00:13:39.459 --> 00:13:48.049
depending on what is the input impedance I
am seeing here This ZS will be able to transfer
00:13:48.049 --> 00:13:56.959
a part of that power We know that if ZS is
chosen as Zin conjugate then maximum power
00:13:56.959 --> 00:14:06.541
can be transferred to this transistor Again
here the this transistor which is has impedance
00:14:06.541 --> 00:14:13.239
level Z0 It is seen some output impedance
so depending on that it will transfer a part
00:14:13.239 --> 00:14:21.499
of that power if we can have a conjugate match
here Then we know that it will able to deliver
00:14:21.499 --> 00:14:28.929
that power And then again depending on the
this output impedance and ZL We can have a
00:14:28.929 --> 00:14:34.999
maximum power transfer here But also we won’t
be able to do maximum power transfer So that
00:14:34.999 --> 00:14:44.540
time some amount of power transfer will be
there So we define three definitions of power
00:14:44.540 --> 00:14:52.259
you see here with respect to this figure We
will say now three definitions of the power
00:14:52.259 --> 00:15:16.699
. One is that Power avs this is actually power
available from source That means the power
00:15:16.699 --> 00:15:24.499
that source can deliver that we are calling
power available from source Similarly we have
00:15:24.499 --> 00:15:34.069
here actually we are calling this transistor
it is a 2 port network So it is in the symbols
00:15:34.069 --> 00:15:54.230
this will call as network so Pavn this is
power available from the output of network
00:15:54.230 --> 00:16:04.649
which actually for the amplifier is this transistor
part Then also we have P or before this I
00:16:04.649 --> 00:16:28.989
will say Pin Where Pin is power delivered
at the input of the network S Similarly I
00:16:28.989 --> 00:16:52.129
will have PL which is power delivered to load
ZL So you see that I can now write four things
00:16:52.129 --> 00:17:01.819
That means the power Input power is what power
is going from here Then here it is taking
00:17:01.819 --> 00:17:09.370
P some of this power because all power depending
on the mismatch All power cannot come So P
00:17:09.370 --> 00:17:17.559
avs is the power that is available here Then
again P avn is the power that is available
00:17:17.559 --> 00:17:24.870
at the output And again depending on the impedance
level the power that gets delivered is P L
00:17:24.870 --> 00:17:32.190
so there are this four different power things
Which if everything is properly matched then
00:17:32.190 --> 00:17:38.210
I know that means if I do conjugate matching
from maximum transfer theorem view point Then
00:17:38.210 --> 00:17:44.390
I know whatever Pin it is supplying that maximum
power will come here That means generally
00:17:44.390 --> 00:17:51.500
that is for resistive loads half of this power
Then again here due to this impedance level
00:17:51.500 --> 00:17:56.710
some of that will come here From that again
if I can do maximum power will be transfer
00:17:56.710 --> 00:18:03.950
maximum power will be transferred here now
based on these I have 3 definitions of power
00:18:03.950 --> 00:18:12.981
gain You see that there are three definitions
of power gain the first one is Simple Power
00:18:12.981 --> 00:18:40.580
Gain But is it it is PL by Pin so PL we know
power to load and Pin is the power delivered
00:18:40.580 --> 00:19:05.930
at
00:19:05.930 --> 00:19:42.630
the input of
00:19:42.630 --> 00:20:22.010
the network S similarly I can have the next
one is called available Power Gain It is generally
00:20:22.010 --> 00:20:36.150
denoted as GA and this is Pavn by Pavs Where
avn and avs are there that means what I am
00:20:36.150 --> 00:20:47.310
seeing here Pavn by Pavs here you see that
I am considering power available here divided
00:20:47.310 --> 00:20:52.390
by this power that means here I have been
incorporate ZS But I have not incorporated
00:20:52.390 --> 00:21:12.230
ZL this loading I have not considered So I
can say that GA is independent of ZL So obviously
00:21:12.230 --> 00:21:24.110
this G is dependent on ZL independent on ZS
this G A is dependent on ZS independent on
00:21:24.110 --> 00:21:30.220
ZL So in both this definition you can see
I am keeping this open that in 1 case I am
00:21:30.220 --> 00:21:37.080
not keeping considering the effect of Z s
In another case I am not considering the effect
00:21:37.080 --> 00:21:43.111
of Z L So obviously I need another because
finally my job is how much power I have in
00:21:43.111 --> 00:21:49.300
the source and how much power I am delivering
in the load there will be a final one Which
00:21:49.300 --> 00:21:55.610
generally in low frequency we consider that
but here this powers depending on the impedance
00:21:55.610 --> 00:22:03.110
level they are not all equal that why we are
doing this This final power calculation is
00:22:03.110 --> 00:22:19.880
called Transducer
power gain GT The very important one and it
00:22:19.880 --> 00:22:36.600
is defined as PL by Pavs From the final PL
by P avs I got this so this is the most important
00:22:36.600 --> 00:22:57.030
one and it is defined as you see I can write
that GT is dependent on both ZS and ZL So
00:22:57.030 --> 00:23:03.710
when I complete loading is their both in the
load side and also the source impendency is
00:23:03.710 --> 00:23:11.800
considered Then what is my power gain that
is called Transducer Power Gain So G T is
00:23:11.800 --> 00:23:19.120
the most important factor but you know that
out of this three obviously GT that will be
00:23:19.120 --> 00:23:26.030
the least because after taking everything
into account this value will be reduced from
00:23:26.030 --> 00:23:35.460
any of this values this various parameter
help us to have various separately consider
00:23:35.460 --> 00:23:44.310
various size suppose if I want find out that
what is the effect on the gain of GL then
00:23:44.310 --> 00:23:53.720
I use this what is the effect separately if
I want what is the effect on gain of GS I
00:23:53.720 --> 00:24:02.880
use this when everything together the final
output is this one now Obviously if everywhere
00:24:02.880 --> 00:24:08.620
the power the conjugate matching is there
that means the input is conjugate matched
00:24:08.620 --> 00:24:17.601
that means ZS = Z in star also ZL = Z out
star Then I know that maximum power transfer
00:24:17.601 --> 00:24:24.410
is taking place so whatever is available that
I can delivery here has Pin and whatever P
00:24:24.410 --> 00:24:36.980
avn is giving that I can delivery to P L under
that condition so we can write that . When
00:24:36.980 --> 00:24:58.950
input and output are conjugately matched all
this definition are same G is equal to G A
00:24:58.950 --> 00:25:08.451
is equal to G T But otherwise not because
for a G T is the function of Z S and Z L So
00:25:08.451 --> 00:25:16.310
for a particular selection of Z S and Z L
only I get GT a particular selection of Z
00:25:16.310 --> 00:25:32.050
S and Z L only I get G
00:25:32.050 --> 00:25:48.700
and GA etc now we want to find out what are
the powers because we have written this expression
00:25:48.700 --> 00:25:58.220
but we need to make it u know gain etc finally
we need to convert to the devices parameters
00:25:58.220 --> 00:26:09.160
So here I can have any excitation VS But I
need to find out an expression of this GA
00:26:09.160 --> 00:26:19.030
GA G GAGT in terms of the parameters S parameters
of the transistor and also the load coordination
00:26:19.030 --> 00:26:26.020
and source coordination it should be independent
of the excitation of that I give because any
00:26:26.020 --> 00:26:33.080
volt source that I can change voltage source
gain etc they should not get changed so we
00:26:33.080 --> 00:26:41.050
will now need to manipulate and get some expression
of powers in terms of the source voltage VS
00:26:41.050 --> 00:26:48.660
so that I will do So before that first letter
write what is our input impedance if you lo
00:26:48.660 --> 00:26:56.740
I input reflection coefficient I have input
reflection coefficient here simply this reflection
00:26:56.740 --> 00:27:06.960
coefficient is nothing but V1minus by V1 plus
so I can write V1 minus V1 plus but B1 this
00:27:06.960 --> 00:27:15.310
side is loaded so this V1 plus is entering
going from here as V2 minus then coming back
00:27:15.310 --> 00:28:02.300
as V2 plus again coming here as V1 minus also
please remember this generally students beginners
00:28:02.300 --> 00:28:07.860
they make mistakes that they think that input
reflection coefficient that is always S11
00:28:07.860 --> 00:28:19.450
no its S 11 we have this term goes to zero
that means gamma L is zero when gamma L is
00:28:19.450 --> 00:28:27.840
zero gamma L zero means out is match so if
port 2 is match then only I can say that input
00:28:27.840 --> 00:28:34.240
reflection coefficient = S 11 Otherwise let
I will have to consider that what is mismatched
00:28:34.240 --> 00:28:41.581
here what is the reflection coefficient also
S12 and S21 and S22 they matter so this we
00:28:41.581 --> 00:28:49.360
have earlier derived and we know that this
what is gamma in from impedance perspective
00:28:49.360 --> 00:29:01.580
this is nothing but Zin minus Z0 by Zin plus
Z0 Now also we know what is relation because
00:29:01.580 --> 00:29:08.040
ultimately will have to relate to source voltage
VS so what is the relation between V1 and
00:29:08.040 --> 00:29:22.980
VS V1 is the terminal voltage so I can write
it that V1 is Vs into Zin by Zin plus ZS simple
00:29:22.980 --> 00:29:32.960
voltage division so from this you just since
our actual quantities are V1 plus and V1 minus
00:29:32.960 --> 00:29:43.140
you express this V1 as V1 plus V1 minus and
will do simple manipulation that I can find
00:29:43.140 --> 00:29:52.680
out expressions V1 plus in terms of VS as
this also incorporate what is gamma S I have
00:29:52.680 --> 00:30:07.559
already written gamma S here So in terms of
VS and gamma S we can do very simple manipulation
00:30:07.559 --> 00:30:17.330
So if I have these then what is the input
power you see what is my Pin P in is whatever
00:30:17.330 --> 00:30:28.400
V1 plus this voltage have getting how much
power average power if we assume the Pi I
00:30:28.400 --> 00:30:47.550
can write as half Z0 V1 plus square into 1
minus gamma In square this we have earlier
00:30:47.550 --> 00:30:55.900
seen how to do this Pin is this we know Impedance
level is Z0 and there is a reflection here
00:30:55.900 --> 00:31:02.870
so if we subtract that value reflected power
we know how much power is being inputed to
00:31:02.870 --> 00:31:15.150
this network so Pin is this now withmmV1 finally
we want to because V1plus it will change from
00:31:15.150 --> 00:31:22.420
various loading condition but VS it is the
source voltage that is independence of all
00:31:22.420 --> 00:31:28.610
let us relate it there And if we do that means
if you put that expression of V1plus value
00:31:28.610 --> 00:31:46.490
We get expression of VS square by 8 Z0 1 minus
gamma S square by 1 minus gamma S gamma In
00:31:46.490 --> 00:32:08.690
square
00:32:08.690 --> 00:32:36.520
to 1minus gamma in square now also . what
will be PL let us see PL so PL can I write
00:32:36.520 --> 00:32:59.320
from this What will be PL you see what V2
minus square by 2 Z0 1 minus gamma L square
00:32:59.320 --> 00:33:08.110
and then I can V2 minus here I have done for
V1minus V2 minus also we can relate with this
00:33:08.110 --> 00:33:17.020
gamma S and gamma L So this finally if we
do we can write that this will also turn out
00:33:17.020 --> 00:33:36.059
to be BS square by 8 Z0 S21 square into 1
minus gamma L square into 1 minus gamma S
00:33:36.059 --> 00:33:57.309
square divided by 1 minus S22 gamma L square
1 minus gamma S gamma in square so we got
00:33:57.309 --> 00:34:04.490
PL in terms of VS square and all these are
S parameters and gamma S and gamma L and gamma
00:34:04.490 --> 00:34:13.129
in Similarly now let us see the other two
available things what is P available S? that
00:34:13.129 --> 00:34:21.500
is the power that the source can make available
so this is source can make available maximum
00:34:21.500 --> 00:34:31.289
power under when this input side is conjugate
match That means P avs is power is that power
00:34:31.289 --> 00:34:32.490
so I can say Pavs is power Pin when Z in is
equal to Z S star So already have P in expressions
00:34:32.490 --> 00:34:36.319
i should enforced this condition Z in is equal
to Z S star It means gamma in is equal to
00:34:36.319 --> 00:34:39.859
gamma S st Put it here So I have the expression
of the P avs Similary P avn is the maximum
00:34:39.859 --> 00:34:40.859
power transferred to the load So available
from the network and that can be transferred
00:34:40.859 --> 00:34:43.429
to the load when this side is conjugately
match I have P L expressions So I can say
00:34:43.429 --> 00:34:53.069
P avn when Zin is chosen as ZS star So I already
have Pin expression you see already have Pin
00:34:53.069 --> 00:34:59.309
expression there I should enforce this condition
that Zin is equal to Zs star Zin is equal
00:34:59.309 --> 00:35:08.130
to Zs star means gamma in is equal to gamma
S star so if I put it here I get the expression
00:35:08.130 --> 00:35:31.910
of Pavs that is VS square 1 minus gamma S
Square by 8 Z0 1 minus gamma S square similarly
00:35:31.910 --> 00:35:42.039
what is P avn pavn is the maximum power that
can be transferred to the load So available
00:35:42.039 --> 00:35:48.200
from that network and that can be transferred
to the load when this side when this side
00:35:48.200 --> 00:35:56.089
is conjugatly matched so again I have PL expression
there I will have to put the conjugate matching
00:35:56.089 --> 00:36:14.520
so I can say Pavn is power PL when ZL is equal
to Z out start that means this implies that
00:36:14.520 --> 00:36:23.769
gamma out is equal to gamma L star So I can
if I do that then I get the expression of
00:36:23.769 --> 00:36:49.800
Pavn and that becomes Vs square by 8 Z0 S21
square 1 minus gamma out square into 1 minus
00:36:49.800 --> 00:37:17.059
gamma S square divided by 1 minus S22 gamma
out star square 2 1- gamma S gamma in square
00:37:17.059 --> 00:37:27.680
So I have these expressions So all 4 power
quantities we have expressed in terms of source
00:37:27.680 --> 00:37:38.400
voltage the impedance level of the active
device that means transistor then S parameter
00:37:38.400 --> 00:37:48.910
of transistor and various reflection coefficients
depending on the load and source conditions
00:37:48.910 --> 00:37:56.859
So we can we are in a position to find out
analytical expressions for a various gain
00:37:56.859 --> 00:38:00.140
quantity that we will see in a next lecture