WEBVTT
Kind: captions
Language: en
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Welcome to this lecture haaa we have already
seen the RF amplifier design for conjugate
00:00:31.210 --> 00:00:39.640
maximum gain specified gain then low noise
amplifier design then broad band amplifier
00:00:39.640 --> 00:00:48.030
design now we will another very important
part because you know in any transmitter finally
00:00:48.030 --> 00:00:55.430
before sending the signal RF signal to free
space we have a power amplifier where we try
00:00:55.430 --> 00:01:03.760
to give as much power we can as much is possible
to give power so that is a power amplifier
00:01:03.760 --> 00:01:15.710
and that power amplifier generally has a very
high isss signal level but over till now whatever
00:01:15.710 --> 00:01:21.900
amplifier design we have seen in their we
assume small signal model but in power amplifier
00:01:21.900 --> 00:01:30.030
it is not small signal it is quite large amplitude
of signal and you know that in power amplifiers
00:01:30.030 --> 00:01:37.840
many time operate it at class C etc so generally
non linearity may come in power amplifier
00:01:37.840 --> 00:01:44.920
so if non linearity comes how do you go about
in RF power amplifiers so we will have to
00:01:44.920 --> 00:01:52.180
see power amplifier design actually amplifier
design we have already seen but in power amplifier
00:01:52.180 --> 00:01:59.270
there are certain haaa characteristics which
are not baah weeee we do not pay any attention
00:01:59.270 --> 00:02:09.679
to them in low small signal amplifiers but
in power amplifiers or large signal cases
00:02:09.679 --> 00:02:17.310
we need to pay attention to them because if
we do not put that haaa if we do not restrict
00:02:17.310 --> 00:02:25.390
ourselves to within those constants then what
happens due to non-linearity haaa we generate
00:02:25.390 --> 00:02:32.349
some other spurious frequencies etc also saturate
the amplifier so its gain etc that falls so
00:02:32.349 --> 00:02:41.519
it is essential to understand this power amplifier
non linearity so that will see In this first
00:02:41.519 --> 00:02:48.080
lecture there will be thaa baaa the next two
three lecture will be on this so first one
00:02:48.080 --> 00:02:53.659
will be power amplifier design first we will
discuss about the non-linearity at large signal
00:02:53.659 --> 00:03:01.379
values I already said that at power amplifier
which is the final stage of before antenna
00:03:01.379 --> 00:03:07.769
the final stage of any transmitter wireless
transmitter they are this due to large signal
00:03:07.769 --> 00:03:17.889
the non-linearity may come so we let us see
those non-linearity . so at small signal levels
00:03:17.889 --> 00:03:24.999
linearity will maintain but due to interconnect
joint etc at large signal values non linearity
00:03:24.999 --> 00:03:37.890
appears how to characterize the non-linearity
of any amplifier . now you see that S parameters
00:03:37.890 --> 00:03:47.249
characterization for large signal is an absurdity
why because S parameters for large signal
00:03:47.249 --> 00:03:53.900
do not depend on power label there we have
seen that any voltage any current a reflector
00:03:53.900 --> 00:04:01.579
incident that ratio that we take but for larger
signal due to non-linearity S parameters also
00:04:01.579 --> 00:04:06.999
becomes level dependent we have already seen
their frequency dependent but now that time
00:04:06.999 --> 00:04:12.870
also you said that they are bias dependent
at large signal they are highly on signal
00:04:12.870 --> 00:04:21.199
dependent so if it becomes as signal dependent
then suppose am writing . that S11 is equal
00:04:21.199 --> 00:04:35.010
to V1 by V1 plus when I have the V2 plus is
0 now if this ratio is again a function of
00:04:35.010 --> 00:04:42.870
this is the ratio but if it is a function
of let us say V1 plus then it is very difficult
00:04:42.870 --> 00:04:49.060
to have this parameter because for every level
then i will have to define this that is why
00:04:49.060 --> 00:04:55.730
for the large signal people do not use S parameters
to characterize power amplifiers or characterize
00:04:55.730 --> 00:05:04.170
any block which is using any large signal
levels . So what will do will see there are
00:05:04.170 --> 00:05:12.070
various figures of merit parameters for characterizing
non linearity one them is 1 db gain compression
00:05:12.070 --> 00:05:19.840
point another is called dynamic range another
is called spurious free dynamic range another
00:05:19.840 --> 00:05:27.470
is called third order intercept point so this
four are very important characteristic that
00:05:27.470 --> 00:05:35.000
is why we will see that power amplifiers generally
they haaa are specified in terms of this not
00:05:35.000 --> 00:05:48.020
in terms of our usual S parameters or other
those gain and other values . now let us first
00:05:48.020 --> 00:05:55.280
see what is gain compression we know that
in a linear thing if we plot the transfer
00:05:55.280 --> 00:06:01.340
characteristics the power transfer characteristic
of any two port network particularly amplifier
00:06:01.340 --> 00:06:10.620
So let us say that in the X axis we are putting
intput power in dbm in aaam Y axis we are
00:06:10.620 --> 00:06:20.810
putting output power in dbm now in the linear
zone it is slope of 1 we know we have a linear
00:06:20.810 --> 00:06:28.030
thing so as we are increasing the power in
the input output is following that after certain
00:06:28.030 --> 00:06:35.120
point to a C that it starts falling now why
its starts falling we will later explain but
00:06:35.120 --> 00:06:42.970
all systems are these that this it would have
gone infinitely with the dotted line but in
00:06:42.970 --> 00:06:50.250
all practical systems we see that this curve
instead going like this linearly it starts
00:06:50.250 --> 00:06:57.970
this So this is when it starts deviating from
this normal we can say that it become non-linear
00:06:57.970 --> 00:07:06.400
so that transfer is no more non-linear now
where I will say that it as become non-linear
00:07:06.400 --> 00:07:13.080
here or here here or here here or here here
or here obviously when it is flat I know that
00:07:13.080 --> 00:07:22.280
it is a non-linear thing it is saturated but
here where so people made this that we will
00:07:22.280 --> 00:07:28.850
not say that it is here we will say that here
that it has become clearly non-linear This
00:07:28.850 --> 00:07:34.580
point is called 1 db compression point so
what is this definition now it can be in terms
00:07:34.580 --> 00:07:41.480
of input power or output power because this
point if I say this point as an X coordinate
00:07:41.480 --> 00:07:47.630
as well as this point as Y coordinate that
mean this can be reference to input power
00:07:47.630 --> 00:07:54.320
level or output power level now that is why
am saying that input or output power point
00:07:54.320 --> 00:08:01.590
is1 db compression point if it is input side
we call it 1 db gain compression point if
00:08:01.590 --> 00:08:08.600
it is output side we call it output 1 db compression
point now what is the definition of this point
00:08:08.600 --> 00:08:14.150
because this point need to be precisely defined
to say that ok I have already entered the
00:08:14.150 --> 00:08:22.770
non-linear region where this is the point
where the gain as fallen 1 db from linear
00:08:22.770 --> 00:08:29.840
small signal gain you see I was having some
gain here because P out by P in was my power
00:08:29.840 --> 00:08:37.360
gain now that would have been something in
the linear case but here you see I have got
00:08:37.360 --> 00:08:45.310
it please remember this is a db scale that
is why we are writing slow one that does not
00:08:45.310 --> 00:08:51.339
mean the gain is not here In the db scale
if I have the slope of 1 that means it is
00:08:51.339 --> 00:08:58.270
linear but what it says that there is some
gain Now the linear gain is something but
00:08:58.270 --> 00:09:05.190
here it is fallen by 1db from that you see
that is why this is called gain as fallen
00:09:05.190 --> 00:09:15.940
1 db from linear small signal gain So in mathematical
terms we can write that G at 1 db gain compression
00:09:15.940 --> 00:09:28.700
point that means here G In db scale is 1 db
less than this points power gain so this point
00:09:28.700 --> 00:09:35.020
power gain is linear one so from that it has
fallen to 1 db so I know always this point
00:09:35.020 --> 00:09:41.380
that where it is and I check that whether
this is 1 db because had I checked it here
00:09:41.380 --> 00:09:46.980
I would have seen that ok still this difference
between the linear thing and actual thing
00:09:46.980 --> 00:09:52.920
that is not 1 db but the moment it becomes
1 db this point we characterize that ok in
00:09:52.920 --> 00:10:00.850
the actual graph this point represents the
1 db compression point this points also represents
00:10:00.850 --> 00:10:06.570
1 db compression point this is the input 1
db compression point this is the output 1
00:10:06.570 --> 00:10:11.590
db compression point now you can ask that
why it is compression it could have been that
00:10:11.590 --> 00:10:17.900
non linearity could have been gain could have
been increased yes it may increase also but
00:10:17.900 --> 00:10:26.730
we see that generally this is compression
not the expansion but theatrically it is possible
00:10:26.730 --> 00:10:33.360
and in some system it may comp expand also
generally we do not encounters the systems
00:10:33.360 --> 00:10:46.160
but obviously with newer applications one
day sometimes we may see expansion also ok
00:10:46.160 --> 00:10:57.150
so now
if we see this that means now I can say that
00:10:57.150 --> 00:11:05.980
from here to here I can use the system because
I want to have in amplifiers we need to have
00:11:05.980 --> 00:11:13.470
linear things so if the transfer characteristic
is not linear then amplifier will have problem
00:11:13.470 --> 00:11:23.250
So we need define a range of input or output
power labels where the amplifier will be behaving
00:11:23.250 --> 00:11:30.200
as linear so we say that this is the onsite
of non-linearity so from this 1 db gain compression
00:11:30.200 --> 00:11:37.660
point to maximum minimum usable level I will
say range that is called dynamic range of
00:11:37.660 --> 00:11:48.120
any amplifier or any 2 port network now it
is a very useful thing it is the range of
00:11:48.120 --> 00:11:54.540
output power here am saying in terms of out
power dynamic range is also defined in terms
00:11:54.540 --> 00:12:01.930
of output power so range of output power where
amplifier range is linear now upper is fixed
00:12:01.930 --> 00:12:16.300
by range compression we are not express to
shown what is the lower range now . lower
00:12:16.300 --> 00:12:27.490
range is fixed by noise floor even if you
do not give any input to any 2 port network
00:12:27.490 --> 00:12:36.540
here suppose I have a 2 port network and I
am not giving any input here but suppose output
00:12:36.540 --> 00:12:44.440
these output I have no input here but output
I have connected to any oscilloscope or spectrum
00:12:44.440 --> 00:12:52.890
analyzer or something a measuring device so
there will see always without signal a also
00:12:52.890 --> 00:13:00.720
I have this if I have a signal then I get
somewhere here suppose I am looking at a spectrum
00:13:00.720 --> 00:13:07.560
analyzer then you will see there is a signal
but in other places where no signals are there
00:13:07.560 --> 00:13:13.050
still this what is this because there are
actually noise is always present particularly
00:13:13.050 --> 00:13:22.050
these particular block it is adding some noise
that is the noise floor of the device oscilloscope
00:13:22.050 --> 00:13:29.120
in multimeter spectrum analyzer everywhere
you have noise in multi meter you have a visual
00:13:29.120 --> 00:13:34.860
display of that but in oscilloscope or spectrum
analyzer you will see that there are noises
00:13:34.860 --> 00:13:42.560
now that noise float so my signal should be
sufficient care of that noise float Actually
00:13:42.560 --> 00:13:53.080
several db up from that noise float so minimum
usable range is always that noise float plus
00:13:53.080 --> 00:14:00.330
some extra db so that I can recognize at signal
because if my signal is such that instead
00:14:00.330 --> 00:14:08.000
of this the signal was also this i think you
understand this red one that instead of this
00:14:08.000 --> 00:14:13.779
if I have signal like these I would be able
to recognize as a signal even though it is
00:14:13.779 --> 00:14:21.930
as a signal so minimum level of input signal
should be sufficiently have a noise float
00:14:21.930 --> 00:14:29.680
typically it is depending on what you prefer
that you may call these as signal I may say
00:14:29.680 --> 00:14:36.490
no no unless and until it becomes like this
this green one I wont say so that green one
00:14:36.490 --> 00:14:44.990
is saying that his definition of signal is
so much a bit higher db then the red ones
00:14:44.990 --> 00:14:51.870
thing but whatever you decide that ok this
is signal so that means there is above noise
00:14:51.870 --> 00:15:01.730
float you have something so lower range of
the dynamic range is fixed by noise floor
00:15:01.730 --> 00:15:10.110
now let us see noise model of an amplifier
. you see I have a I think the picture is
00:15:10.110 --> 00:15:26.450
not visible . so I have a amplifier the amplifier
has its gain also it has some noise equivalent
00:15:26.450 --> 00:15:32.760
bandwidth this terms I think you are familiar
noise equivalent bandwidth it is not the actual
00:15:32.760 --> 00:15:40.510
bandwidth but that means a rectangular haa
gain function that whatever bandwidth is . . then
00:15:40.510 --> 00:15:52.360
it has some temperature and equivalent temperature
noise equivalent temperature and also it has
00:15:52.360 --> 00:16:07.810
the some noise figure now when you have the
input obviously what we do the source that
00:16:07.810 --> 00:16:15.810
will have some resistance and we assume that
source is a pure thing it does not have resistance
00:16:15.810 --> 00:16:21.790
whatever source resistance we have whatever
noise it produces because this will also produce
00:16:21.790 --> 00:16:29.170
noise that we in abstract we say the temperature
here resistance here whose this temperature
00:16:29.170 --> 00:16:40.720
is haaa at two ninety degree kelvin and the
noise this whole signal part aaahay source
00:16:40.720 --> 00:16:48.570
part that is producing that is giving NI I
think then the amplifier will be adding noise
00:16:48.570 --> 00:17:00.160
now output of the amplifier is typically on
a load it is good so if I write what is the
00:17:00.160 --> 00:17:09.399
to this amplifier what is the input noise
sorry input noise let us call this NI and
00:17:09.399 --> 00:17:26.520
output noise is No so I can say that PI which
is the input power to this amplifier that
00:17:26.520 --> 00:17:34.600
will comprise of one is the signal power another
is the noise power because I will get in the
00:17:34.600 --> 00:17:41.799
input side both of this generally they are
additive so PI is SI plusNI Similarly at the
00:17:41.799 --> 00:17:49.610
output I will get PO which is SO which is
the signal power though actually always it
00:17:49.610 --> 00:17:58.200
is added so we cannot separately recognize
it But in mathematics we say that SO is the
00:17:58.200 --> 00:18:06.430
signal powers level and N0 is the noise powers
level You know this is a deterministic level
00:18:06.430 --> 00:18:13.811
this is a random signal so but when they are
mixed we cannot separately say but for the
00:18:13.811 --> 00:18:21.000
analysis we do like this now obviously you
can now look at that what is the value of
00:18:21.000 --> 00:18:30.730
this output noise power since this amplifier
as gain G so it will multiply this whatever
00:18:30.730 --> 00:18:39.640
this input noise power is coming that this
G into NI So that we are recognize NI we know
00:18:39.640 --> 00:18:48.980
that from this definition it is K B and T0
and also it will add its own power it that
00:18:48.980 --> 00:18:58.870
it is G into K BN T that whatever amplifier
amplifier added noise and this is amplifier
00:18:58.870 --> 00:19:07.330
input noise this should be amplifier added
noise so that input noise it is multiplier
00:19:07.330 --> 00:19:15.580
with the gain and its own noise that also
is generated here that also getting multiplied
00:19:15.580 --> 00:19:24.390
by its gain . now minimum deductible signal
is what because ultimately we will have to
00:19:24.390 --> 00:19:30.240
deduct the signal so what is the minimum deductible
signal now this you know that noise figure
00:19:30.240 --> 00:19:38.760
and equivalent noise temperature they are
related by this So if you put this the N0
00:19:38.760 --> 00:19:46.290
becomes this that we have already seen now
KT0 K is the . . constant T0 is the two ninety
00:19:46.290 --> 00:19:55.080
degree generally in European or America or
advanced countries they fix this standard
00:19:55.080 --> 00:20:01.180
as seventeen degree centigrade which is two
ninety kelvin so this is the constant term
00:20:01.180 --> 00:20:08.670
so that turns out to be minus one seventy
four dbm So we can write that output minimum
00:20:08.670 --> 00:20:16.630
detectable signal that expression will be
minus one seventy four dbm plus you see from
00:20:16.630 --> 00:20:34.690
that hmm this PO it is SO plus NO so now minimum
value is given by this that POmds is miinus
00:20:34.690 --> 00:20:44.960
174 dbm plus 10 log Bn plus F is the noise
figure plus GA plus X this is the SNR margin
00:20:44.960 --> 00:20:52.250
I was talking about noise floor . . so this
is the minimum detectable signal or this is
00:20:52.250 --> 00:21:01.330
the of the output side so it is always given
by this so knowing the your amplifiers noise
00:21:01.330 --> 00:21:09.600
eqiualant band width knoweing its noise figure
knowing its gain and knowing that SNR margin
00:21:09.600 --> 00:21:18.750
you fixed is typically if nothing fixed take
it either 3 or 4 db above the noise floor
00:21:18.750 --> 00:21:28.550
So you can find the POmds once you have that
then you can define the dynamic range . you
00:21:28.550 --> 00:21:34.010
see dynamic range is now analytically what
is it previously we have seen it graphically
00:21:34.010 --> 00:21:41.480
now we say that it is P output this is the
output dynamic range PO output from 1 dbm
00:21:41.480 --> 00:21:50.070
compression point minus POmds we know how
to calculate mds we know how to haaa we have
00:21:50.070 --> 00:21:55.420
seen in graph this later will find out how
to find this point then you can always find
00:21:55.420 --> 00:22:01.410
the dynamic range what is the physical significance
of dynamic range ? that means within this
00:22:01.410 --> 00:22:09.160
zone if my output power level goes depending
on what gain I have so I can have the corresponding
00:22:09.160 --> 00:22:15.780
input power level also Input dynamic range
so within that level if we keep my system
00:22:15.780 --> 00:22:22.809
if I keep my amplifier it will be linear so
all whatever we discussed before aaah of designing
00:22:22.809 --> 00:22:30.950
a small signal based amplifier concept that
design concept you can put so you need know
00:22:30.950 --> 00:22:37.460
that in the power amplifier I will have this
much dynamic range so I can barring my input
00:22:37.460 --> 00:22:45.840
level or output power level same thing so
that within this range I am linear so all
00:22:45.840 --> 00:22:51.010
my amplifier design concept will tally so
this is the definition of the dynamic range
00:22:51.010 --> 00:23:04.600
ok . now you see that there are if I have
a single spot frequency then that dynamic
00:23:04.600 --> 00:23:11.549
range concept is sufficient but as I said
generally we have in bass band suppose when
00:23:11.549 --> 00:23:17.850
am talking this bass band the voice bass band
that is from 20 hertz to 20 kilo hertz so
00:23:17.850 --> 00:23:25.610
I have various frequency components presents
over a band also if I have a video signal
00:23:25.610 --> 00:23:34.320
I have typically 4 megahertz but if I want
to play it or band width for that also I have
00:23:34.320 --> 00:23:42.110
various frequency components presence Now
let us see the transfer characteristic of
00:23:42.110 --> 00:23:52.919
any power amplifier device so output voltage
V0T that I can express as a power series because
00:23:52.919 --> 00:24:03.539
in general I will try to make it as linear
but when I have as I said various interconnect,
00:24:03.539 --> 00:24:10.480
joints etc so they are all not linear component
so they are that linear means electronic means
00:24:10.480 --> 00:24:16.929
we always say super position principle so
for them super position principle is not valid
00:24:16.929 --> 00:24:22.460
that means the additive property and scaling
property those are not valid so there I can
00:24:22.460 --> 00:24:29.470
also have this components that the square
of the input that Cube of the input etc with
00:24:29.470 --> 00:24:36.700
the proper coefficient Now usually this A2
A3 they are the this components this coefficients
00:24:36.700 --> 00:24:43.539
of the non-linear components they are small
so in small signal values you see if I have
00:24:43.539 --> 00:24:53.270
Vit small then this value is not much this
value is further smaller so that is why we
00:24:53.270 --> 00:25:03.750
that time assume that it is always this but
large signal cases I will see that we cannot
00:25:03.750 --> 00:25:10.780
neglect all of this so A1 is called linear
gain gon gon coefficient because this VOT
00:25:10.780 --> 00:25:19.370
is equal to A1 VIT then this is linear thing
that is why it is linear coefficient A tone
00:25:19.370 --> 00:25:25.250
will generate upto N order harmonic you see
if I have a tone and if the system is non
00:25:25.250 --> 00:25:34.210
linear so this B is square T that will make
the second harmonic come then I have this
00:25:34.210 --> 00:25:39.760
Bi3 that means If A 3 is significant I will
also have third harmonic also get generated
00:25:39.760 --> 00:25:45.740
because you know that if Vit is COS omega
T it will generate a a COS square COS square
00:25:45.740 --> 00:25:53.150
means there is a COS 2 omega term present
similarly if this is present i will have COS
00:25:53.150 --> 00:26:01.350
cube COS cube means I will have COS 3 omega
T so we say that if we have non linearity
00:26:01.350 --> 00:26:09.690
like this let us say upto nth order then a
tome will generate upto oh here we are saying
00:26:09.690 --> 00:26:15.770
nth order so if we have non-linearity upto
N that I have a sizable thing VI to the power
00:26:15.770 --> 00:26:24.510
N then upto Nth order harmonic will get generated
now whether content significant or not that
00:26:24.510 --> 00:26:31.980
depends obviously this coefficient A2 A3 etc
this is called a second non linearity component
00:26:31.980 --> 00:26:39.580
this is called as third non linearity component
if they are significant then we have significant
00:26:39.580 --> 00:26:50.610
harmonics otherwise not . so to have that
how much non linearity we have let us consider
00:26:50.610 --> 00:26:57.770
it 2 tone test what is a 2 tone test? though
we have many frequencies let us assume that
00:26:57.770 --> 00:27:05.929
we have 2 frequencies 1 is omega 1 angler
frequencies correspondingly F1 and F2 so we
00:27:05.929 --> 00:27:14.840
have this with this is their coefficient that
means in my input signal I have this capital
00:27:14.840 --> 00:27:25.549
A1is the coefficient for omega 1 component
capital A1 is 2 omega component also later
00:27:25.549 --> 00:27:31.440
we will see in 2 tone test we assume that
omega 1 and omega 2 they are different but
00:27:31.440 --> 00:27:39.289
they are not very much baah far apart so omega
1 and omega 2 they are nearby but to distinct
00:27:39.289 --> 00:27:47.580
component now assuming that nonlinear system
what will be my output VO output will be A1into
00:27:47.580 --> 00:27:57.250
Vit so in plus Vit I can write this plus A2
Vit square since Vi is this I can write this
00:27:57.250 --> 00:28:08.920
plus A3 Vi cube so if more that is why dot
dot dot now let us see what happens here . so
00:28:08.920 --> 00:28:18.830
if you now make the terms that what is the
DC term what is the omega 1 term there will
00:28:18.830 --> 00:28:26.710
be omega 2 term then there will be 2 omega
1 term there will be 3 omega 1 term etc if
00:28:26.710 --> 00:28:33.909
you list them please do it at your home you
have this please have it you will see that
00:28:33.909 --> 00:28:42.120
DC will have amplitude this You see in the
input there was no DC component our input
00:28:42.120 --> 00:28:53.210
was typically this you see there are no DC
component with the non-linearity etc this
00:28:53.210 --> 00:29:04.360
DC as come there is a DC then desired frequency
component omega 1 is this omega 2 component
00:29:04.360 --> 00:29:19.659
this second harmonic 2 omega 1 is this then
third harmonic is this etc . also not only
00:29:19.659 --> 00:29:33.481
harmonics there will be some other term you
see if i have this term let me see it now
00:29:33.481 --> 00:29:47.700
when I have this term present you see this
A1 A2 etc now there will be if I have this
00:29:47.700 --> 00:29:55.250
then there will be some terms which will be
also omega 1 plus omega 2 or omega 1 minus
00:29:55.250 --> 00:30:05.970
omega 2 or 2 omega 1 plus omega 2 1 omega
1 minus omega 2 2omega 1minus 3 omega 2 etc
00:30:05.970 --> 00:30:15.020
that means harmonics are those that omega
1 So for omega 1 I have omega 2 sorry 2 omega
00:30:15.020 --> 00:30:25.731
1 3 omega 1 4 omega that means integral multiple
or . . half omega 1 or one third omega 1 or
00:30:25.731 --> 00:30:33.030
1 forth omega 1 etc but when I have 2 tone
not only them there will be mixture of omega
00:30:33.030 --> 00:30:46.919
1 and omega 2 that means I can write that
now this is not an harmonic this is harmonic
00:30:46.919 --> 00:30:54.530
of omega 1 mixed with another harmonic of
omega 2 this is called IM or inter modulation
00:30:54.530 --> 00:31:05.230
product so let us see this intermodulation
terms now type what is second order IM now
00:31:05.230 --> 00:31:16.299
if this M whatever may be this plus minus
thing but M plus N if that M and N are integers
00:31:16.299 --> 00:31:31.850
M plus N if it is 2 it is called second order
IM if M plus N I is equal to 3 it is called
00:31:31.850 --> 00:31:42.190
third order IM so you see that when i have
omega 1 plus omega 2 basically I have M is
00:31:42.190 --> 00:31:50.669
1 and N is 1 so 1 plus1 2 this is also even
though it is Cos omega 1 minus omega 2 but
00:31:50.669 --> 00:31:57.929
that actually this coefficient is 1 this is
also 1 so this second order IM then third
00:31:57.929 --> 00:32:06.080
order IM you see 2 omega 1 minus omega 2 so
2 plus 1 that is why it is third order IM
00:32:06.080 --> 00:32:19.669
Here you see 2 plus1 that is why it is third
order IM here you see 2 1 so 3 1 2 so 3 so
00:32:19.669 --> 00:32:25.210
all this are third order IM so that means
frequency components 2 omega 1 minus omega
00:32:25.210 --> 00:32:33.279
2 2 omega 2 minus omega 1 2 omega 1 plus omega
2 omega 1 plus 2 omega 2 all these are examples
00:32:33.279 --> 00:32:47.120
of third order IM similarly if I could have
three omega 1 minus 2 omega 1 now what is
00:32:47.120 --> 00:32:57.130
this? this is actually which IM it is it will
be fifth order IM sorry this is omega 2 because
00:32:57.130 --> 00:33:03.809
this is 3 this is 2 so it is a fifth order
intermodulation product so here we have listed
00:33:03.809 --> 00:33:09.890
what are the amplitudes you can cross check
you do it yourself all this comes that so
00:33:09.890 --> 00:33:14.790
amplitude will be actually I have written
cost to show you the frequency part amplitude
00:33:14.790 --> 00:33:28.220
will be simply 2A1 A2 here 3 4 this so you
see this is interesting that this let us see
00:33:28.220 --> 00:33:39.940
the harmonics In harmonics I have A1 etc A3
etc this is the desired components in harmonics
00:33:39.940 --> 00:33:46.720
you have A2 into this in third harmonics you
have this then intermodulation if you have
00:33:46.720 --> 00:33:55.490
this and . if you see the spectrum of intermodulation
product you see that my actual desired frequency
00:33:55.490 --> 00:34:02.860
is this omega 1 as well as omega 2 because
this is my actual band now you see that DC
00:34:02.860 --> 00:34:10.240
is far away generally this omega 1 omega 2
are RF frequencies so this is far away Omega
00:34:10.240 --> 00:34:18.579
2 minus omega 1 that means this is the second
order intermodulation that is near this DC
00:34:18.579 --> 00:34:26.870
because omega1 and omega 2 are nearby similarly
2 omega 1 it is double of that so it is far
00:34:26.870 --> 00:34:35.791
from this tone 2 omega 2 that is also far
away omega 1 plus omega 2 faraway 3 omega
00:34:35.791 --> 00:34:48.599
3 omega 2 this is third order intermodulation
here this third order intermodulation but
00:34:48.599 --> 00:34:56.940
you see along with my desired zone this third
order intermodulation product some of the
00:34:56.940 --> 00:35:03.950
intermodulation product which are bearing
this minus sign 2 omega 1 minus omega 2 2
00:35:03.950 --> 00:35:13.510
omega 2 minus omega 1 these two are nearby
now what is the problem with this that typically
00:35:13.510 --> 00:35:19.650
what we do when we have this finally we put
a filter and filter out with this portion
00:35:19.650 --> 00:35:25.420
but this portion as also will come nearby
so when I try to filter it is difficult to
00:35:25.420 --> 00:35:31.890
remove this two intermodulation products with
this this third order intermodulation product
00:35:31.890 --> 00:35:37.230
with this you see second order intermodulation
product is far away so I can remove it these
00:35:37.230 --> 00:35:41.800
third order intermodulation this is third
order intermodulation product this third harmonic
00:35:41.800 --> 00:35:46.730
they are further away fourth harmonic fourth
order intermodulation product they will be
00:35:46.730 --> 00:35:51.370
further away I can always filter that but
this third order intermodulation product given
00:35:51.370 --> 00:35:59.500
by 2 omega 1 minus omega 2 and 2 omega 2 minus
1 they are in the same frequency band as my
00:35:59.500 --> 00:36:06.400
desired frequency band so by filtering I cannot
remove them that is the problem that they
00:36:06.400 --> 00:36:13.830
will come and they will disturb my system
because this are not desired frequencies so
00:36:13.830 --> 00:36:19.650
third order intermodulation product where
from it came because of non-linearity it came
00:36:19.650 --> 00:36:26.230
if the system was linear these two are not
generated now non-linearity also generated
00:36:26.230 --> 00:36:33.000
harmonics but by filtering I always remove
them but this I cannot remove so they will
00:36:33.000 --> 00:36:39.960
disturb me thatâ€™s why I will have to more
clear when we have high smaal large signal
00:36:39.960 --> 00:36:47.930
level I have non linearity presence in small
signal also non linearity presence but due
00:36:47.930 --> 00:36:53.490
to small signal level its value is much less
compared to desired my signal
00:36:53.490 --> 00:37:01.160
so always even if its present it does not
disturb but at high values they are comparable
00:37:01.160 --> 00:37:07.080
with my desired frequencies and by filtering
I cannot remove the third order intermodulation
00:37:07.080 --> 00:37:12.790
so third order intermodulation is dangerous
I will have to characterize my system that
00:37:12.790 --> 00:37:18.720
third order intermodulation should not come
because if it comes it will disturb me so
00:37:18.720 --> 00:37:24.601
it is at the low value of the input signal
it is not significant but will see in some
00:37:24.601 --> 00:37:32.280
point high value its starts becoming significant
and I should not take my amplifier into that
00:37:32.280 --> 00:37:46.310
region or that level where it comes so this
we have seen so summary of non-linear terms
00:37:46.310 --> 00:37:53.599
this lecture will finish so we have seen the
danger of third order aam aaam aam inter modulation
00:37:53.599 --> 00:37:59.250
we have seen that due to non-linear terms
bias point of active blocks get changed We
00:37:59.250 --> 00:38:06.570
did not have in the any input DC thing but
the DC thing as changed so the bias point
00:38:06.570 --> 00:38:13.070
of active block also get changed so should
be aware gain compression also I said expansion
00:38:13.070 --> 00:38:19.609
thought generally we do not see expansion
at desired frequency depends on A2 sign this
00:38:19.609 --> 00:38:28.000
gain compression depends on A2 sign usually
A3 is negative remember A3 is the component
00:38:28.000 --> 00:38:39.430
the by which we can characterize the nonlinear
system A3 into bit cube that A3 typically
00:38:39.430 --> 00:38:46.950
is negative that is why we get compression
and 1 db gain compression is figure of merit
00:38:46.950 --> 00:38:54.240
of this A3 sign creation of harmonics we have
seen that due to non-linearity all the harmonic
00:38:54.240 --> 00:39:01.600
gets created creation of intermodulation frequencies
linear combinations of input frequency we
00:39:01.600 --> 00:39:07.460
have seen second order IM we have seen third
order IM and we have seen the danger of third
00:39:07.460 --> 00:39:15.171
order IM so in the next lecture we should
quantify this third order IM and then we will
00:39:15.171 --> 00:39:22.339
try find out that how to characterize our
system so that this type of third order intermodulation
00:39:22.339 --> 00:39:24.020
product do not come thank You