WEBVTT
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Good morning friends, today we will be discussing
about 2 port network syntheses.
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You know in case of a 2 port you have various
specifications now, for a 2 port network Y11,
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Y12, Y22 these are the parameters or may be
A, B, C, D or Z parameters and so on. These
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are the 3 commonly used sets sometimes you
may be given only a gain function G12 which
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you know is given by this or minus Y12 by
Y22, so if this voltage by this voltage this
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is the gain function only the gain function
is given then you are asked to realize a network
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to give that particular gain function all
right.
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So these specifications can be many of many
types unlike 1 port network where we are given
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either Z or Y(s), Y(s) is just inverse of
Z(s). So you have 1 specification here the
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specifications can be in terms of say Y11
and Y12 or Y22 and Y12, any 2 can be given
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or may be just the gain function all right.
So how to realize a network to meet these
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specifications? So before we go into that
we just see the network functions how they
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are related to this 2 port parameters network
elements.
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Let us take a t network okay or a phi network
from a t, you can always find a phi, this
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is start star to delta or delta to star conversion
all right. Normally if you are given the specifications
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in terms of Z parameters you go for an equivalent
t this is easier. Similarly, for Y parameters
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you go for phi network suppose this is given
as YA, YB and YC. Let us take this first what
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is Y11, YA plus YC very good Y22, YB plus
YC and Y12 okay minus Y12 is YC okay.
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Now these elements these elements YA, YB,
YC they can be any RLC combinations okay.
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Let us see Y11 what are the poles of Y11,
the poles associated with YA and with YC will
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be the poles of Y11. Similarly, poles of Y22
will be the poles of YB and YC so YC is the
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common element for the poles of Y11 and Y22
and also minus Y12, so the common poles in
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these 3 will be the poles of YC.
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So in Y11 there can be some poles of YA which
are not included in the other 2 functions
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all right. So poles of YA will be present
only in Y11 nowhere else, similarly poles
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of YB will be present only in Y22. So I can
remove these poles still have such poles can
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be realized as separate elements, I am not
given YA and YC, YB, YC separately, I am given
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Y11, Y22 and Y12 so out of which I find out
the poles which are not present in Y12 but
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present in Y11.
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Similarly, the poles which are present in
Y22 not in Y12, I call them private poles
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of the 2 ports private poles of 1, 1 dashed
and 2, 2 dashed okay poles of Y11 and Y22
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which are not present, which are not present
in Y12 okay. So the poles which are present
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in Y12 will be present in Y11 and Y22 but
the converse is not true okay. So if I have
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a network which is having Y11 dashed Y22 dashed
and Y12 dashed as the parameters then Y11
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as seen from this side will be Y11 dashed
plus YA, any addition of an admittance here
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will be adding to this value only, is it not.
If I have another element another additional
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admittance here that will be changing only
Y11 that will not be affecting these 2, is
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it not because it is only YA which is getting
modified. So Y11 will be this additional element
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plus whatever is a Y11 dashed here. Similarly,
Y22 will be Y22 dashed plus YB but Y12 will
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be Y12 dashed is it not that remains unaffected.
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Similarly, for the Z elements Z11 will be
suppose this I call as Z1, Z2 and say Z3 then
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Z11 will be Z1 plus Z3, Z22 will be Z2 plus
Z3 and Z12 is Z3. So here also you see the
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poles of Z3 that is Z12 poles of Z12 will
be present in Z11 and Z22 but the converse
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is not true Z11 and Z22 will have additional
poles coming out of Z1 and Z2 okay. So if
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I have a series addition of such elements
this is some Z1, Z2 suppose this is having
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Z11 dash Z22 dash and Z12 dash then overall
Z11 from this side I should write small z
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small z11 will be Z1 plus z11 dash, is it
okay.
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Similarly z22 will be Z2 plus z22 dash but
z12 remains same. So once again the privacy
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poles of an impedance, so this is the series
and shunt separation of private poles. Now
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let us see what are the requirements for the
impedance functions? All right, what are the
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requirements for the impedance functions to
be realized? Now let us take a y11, y12, y22
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once again I draw the, now what is the y11,
YA plus YC, so this YA, YC, YB, y22, YB plus
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YC and y12 minus y12 is YC okay.
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So y11, y11, YA minus y12 is it all right
or YA you can write as y11 plus y12 okay similarly,
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YB will be y22 plus y12 and YC is minus y12.
Now given any network, given any network you
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can have a very complex structure of a 2 port
network and so all right that can be bridge
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elements also whatever be the type I can always
reduce by repeated star delta conversion,
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repeated star delta conversion this entire
set to either t or a phi, is it not. Now in
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this repeated star delta conversions what
are the elements? How do you calculate the
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elements of a star delta set? Say in terms
of impedances Z1, Z2 plus Z2, Z3 plus Z3,
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Z1 divided by something all right divided
by Z1 or Z2 or Z3 the operations are all positive,
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there is no subtraction okay.
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Now Z1, Z2, Z3 these will be R plus L, S plus
1 upon SC or their parallel combinations series
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combination, so there all having positive
signs and these after multiplication also
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the signs do not change then again you are
having additions. So all the elements will
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be finally added there is no subtraction,
there is no chance of a negative sign, is
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it all right. So all these elements finally
Z(s) or Y(s) elements here it is YA, YB, YC
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or ZA, ZB, ZC these will be having the forms
some a0 s to the power a0 plus say a1(s) plus
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a2(s) square and so on divided by say an s
to the power n divided by b0 plus b1(s) and
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so on.
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So bn s to the power n okay these elements
YAA these will be all positive real functions,
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so far as YA, YB and YC are concerned these
3 elements are positive real after all they
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are obtained after reduction of some positive
real functions, star delta reductions. So
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this will be having expressions like this.
Similarly, y12 minus y12 will be YC, so y11
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sorry YA, YB and YC are all having positive
coefficients of polynomials in the numerator
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and the denominator. So let us see y11, what
was was our y11, YA minus y12 okay.
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So suppose you are given minus y12 as a0 sorry
otherwise I have a small slip, there was a
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small slip check y11 is YA plus YC okay y22
is YB plus YC all right and y12 minus y12
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is YC okay therefore y11 it may be given,
let us write the denominator may be some polynomial,
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numerator can be any polynomial that will
be a common polynomial if there is no private
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poles okay. We can consider a common polynomial
for the denominator then this can be say a0
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plus a1(s) plus a2(s) square and so on, y22
is b0 plus b1(s) plus b2(s) square and so
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on and y12, c0 plus c1(s) and so on okay.
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So one of the conditions is a0, a1 these must
be greater than equal to 0 that is what we
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have seen all of them should be positive similarly
b0, b1 must be greater than equal to 0, c0,
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c1 etcetera must be greater than equal to
0 all right, what is y11 plus y12? YA, is
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it not, y11 plus y12 is YA is it all right
now YA has to be with all positive coefficients.
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So if I substitute here y11 plus y12 means
a0 minus c0, a1 minus c1 all right into s
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so that gives me a0 minus c0 must be greater
than equal to 0 a1 minus c1 must be greater
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than equal to 0, a2 minus c2 must be greater
than equal to 0 and so on okay.
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Similarly, by the same logic y22 plus y12
is how much, YB and that also we discussed
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after a repeated reductions YA, YB, YC must
have all positive coefficients in the numerator,
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so y22 plus y12 also must be having numerator
coefficients as 0. So b1 minus c1 is greater
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than 0, b0 minus c0 is greater than 0 greater
than equal to 0 and so on, all right. So these
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are the coefficient conditions to be satisfied
when you are given the specifications is it
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all right. So y11 suppose is given 2s plus
5 divided by some denominator, y22 is given
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s plus 2 divided by same denominator and y12
minus y12 is given s plus 7 by the same denominator.
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Is it possible to realize this, let us see
y11 and y12 the coefficients first coefficient
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5 minus 7 is negative, so it is not possible
all right.
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So this must be less than 2 if it is s plus
1 yes, it is possible suppose it is 2s plus
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1 then this is all right but this is not satisfied
okay. So if you are having the coefficients
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of the numerator given like this the polynomials
are given then by applying this rule you can
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check whether it is realizable or not, all
right whether the network can be realized.
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So this is known as Fialkow Gerst Condition.
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So before going for any synthesis we must
see that these coefficient conditions are
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satisfied. There are 2 ways of realizing a
2 port network, one is Ladder Synthesis
that is you try to go for realizing the 0s
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of transmission in steps from one end or there
is a there is another one Lattice Synthesis
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which will be taking up later on that is a
very interesting synthesis. It is a structure
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like this okay if you want you can have repeated
block surface, so this is a Lattice network
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they are Za, Zb, Zb, Za it is like a bridge
basically this is Za, Zb and you take the
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output from here, this is 1, 1 dashed and
2, 2 dash this 1 as 1, 1 dashed, 2, 2 dash
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okay.
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We shall see what are the 0s of transmission
and how to realize them okay. Whenever you
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are having a0 somewhere what do you mean by
0s of transmission transmission 0s means what
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I give a signal at the other end nothing is
received, is it not. Now in how many ways
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that can be ensured I give a signal you take
a water pipe line all right. In what are different
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possible ways, the say delivery of water at
the other end can be disrupted, very good
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there is a leakage so water is grounded basically
the pipe is grounded the entire pressure is
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grounded is there any other way of blocking.
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So if you have some blockade in the series
path or a short circuit in the shunt path
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then you have a 0s of transmission that means
how do you create a 0s of transmission by
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short circuiting
at some frequency suppose at some frequency
I find s squared plus 9 in the numerator that
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means at s equal to J3, this s square plus
9 will be vanishing that is a0 at that particular
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frequency. So at the frequency I want there
should be no transmission of signal and I
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want short circuit at that particular frequency,
no, short circuit means what it should basely
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is resonance if have a series resonance at
s equal to J3 and that element is put in shunt
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okay. So you are having an element like this
there are many such elements in the ladder
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I create this element is say an lc combination.
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Suppose this is resonating at omega equal
to 3 then s squared plus 9 will be giving
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me omega is equal to 3 this is resonating
frequency, this will be the numerator okay.
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So in z12 if I have a numerator of this kind
s squared plus 9 my target will be to create
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a0 in the shunt element such that the elements
are having a resonance frequency at omega
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equal to 3, is it all right or alternatively
I open any of these that means there is no
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transmission after this. So how do I create
that, how do I create that at omega equal
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to 3, now how to create that parallel resonance,
anti-resonance.
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So if I have an anti-resonance element any
of these at that frequency and then there
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are others then also it can be blocked. So
a0 of transmission can be created 0 of transmission
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means because G12 is z12 by z11, so it is
the 0 of this which will be the 0 of this
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transfer function okay, so output will be
0 at that frequency. So that can be created
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either by a parallel resonance here or a series
resonance is here in the shunt element, is
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it okay. So you keep on repeatedly removing
all the 0s by adjusting these elements okay.
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So this is the technique of 2 port synthesis
when you are given the transmission 0s you
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convert them into poles and then try to realize
the pole any 0 can be realized in terms of
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a pole, is it not? How to do that?
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Suppose you are given z12 how do remove that,
how do, how do I remove a pole a0 you take
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inverse of that function if it is in the admittance
form then you convert it into impedance and
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then make partial fraction corresponding to
that pole remove that okay.
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Let us take before we go further let us take
a function Z(s) equal to say any function
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you tell me it is a 2 into s into s squared
plus 4 by s square plus 1 okay I can make
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partial fractions K1(s) by S square plus 1
plus K2 into S okay, K1 comes out as if I
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multiply by S square plus 1 divided by s and
make s square plus 1 equal to 0. So it will
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be 3 into 2, 6, 6S by S squared plus 1 plus
K2 into S, how much is K22 into s all right.
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So that means 2 Henry, how much is this 1
by 6 farad and 6 Henry okay. Now if I remove
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2 s from here from here if I remove this K2
totally, if I remove 2s whatever is left over
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will content only the other pole all right.
If I remove this I am left with only 2s now
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in this the 0s are at 2, 1 and this is a pole,
this is a pole 0 configuration. 0 then pole
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at 1, 0 at 2 and pole at infinity okay.
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Now suppose in this I, when I remove this
I remove the pole at this one, what I am left
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it only 2S, a 0 here and a pole here okay
for this function if I remove this what will
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be the pole 0 configuration for 2, s0 here
and a pole here at infinity if I remove this
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2s then 0 here, pole at 1 and a 0 here okay.
So if I remove this pole totally this 0 also
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gets eliminated all right. If I remove okay,
if I remove this pole, this pole okay means
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this is having a pole at infinity, is it not,
if I remove the pole at infinity then infinity
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becomes a 0 and this pole remains where is
this pole. So this pole remains at 1 but the
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other pole has created a 0 here okay.
32:17.880 --> 32:24.880
Now if I do not remove the poles or the poles
of either this or that totally if I retain
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some part of it what happens that means instead
of 6S plus s square plus 1 suppose I take
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3S by s square plus 1 okay. Then I call that
balance admittances Z dashed S as 3S by s
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square plus 1 plus 2S okay and some Z removed
S is 3S by s square plus 1 that means 50 percent
32:59.320 --> 33:05.159
have removed 50 percent have retained. So
if I remove 50 percent of this means what,
33:05.159 --> 33:12.159
3S by s square plus 1 means allow 3 Henry,
3 Henry and 1 third Farad. Suppose I take
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out an element like this whatever is left
over is Z dash into S, is it not what is Z
33:29.000 --> 33:36.000
dash into S, what will be the poles and 0s
of this, poles will remain same I am not disturb
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the pole what about 0s.
33:42.769 --> 33:49.769
Now this is not totally removed, it will have
a new 0 all right, what I have done is I have
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not totally removed this pole, I have weakened
the pole, I have removed the part of that
33:56.299 --> 34:03.299
residue residue was 6S all right. So I have
taken a part of it, so if I remove a part
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of that pole that is called part removal of
the pole then what do I get in the oral distribution
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of poles and 0s poles remains as they are
they were but what about 0s. So this will
34:19.280 --> 34:26.280
be 3S plus2 S cubed plus2 S all right that
means divided by s square plus1 that means
34:29.849 --> 34:36.849
2 s cubed plus 5 S in the numerator so S into
if I take 2S common then S squared plus 5
34:43.460 --> 34:47.409
by 2, correct me if I am wrong okay.
34:47.409 --> 34:54.409
So the new distribution of pole and poles
and 0s will be 0 at the origin is remaining
34:57.329 --> 35:04.329
intact all right, pole at 1 is again appearing
because I have not removed it completely,
35:09.160 --> 35:16.160
what about this 0, this 0, it is now root
over of 5 by 2, it has earlier it was at 2,
35:23.680 --> 35:30.680
now it has drifted towards this. Pole at infinity
that also remains as it is okay. So this 0
35:36.710 --> 35:43.710
at 2 has now shifted to root over of 5 by
2 okay approximately 1.58 okay. So if I weaken
35:51.050 --> 35:58.050
a pole I can shift a0 to a desired position
I have taken out only 50 percent of this 6S,
36:00.040 --> 36:05.329
this I said you I could have taken any percentage
and hence I could have shifted this to a desired
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location, is it all right. Therefore, by partial
removal of a pole I can create a0 at a desired
36:14.160 --> 36:21.160
position some of the 0s can be shifted, had
there been many other floating 0s means between
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0 and infinity, had there been some more 0s
they would have all drifted towards the pole
36:27.740 --> 36:34.000
all right. The drift will be by different
amounts all right.
36:34.000 --> 36:41.000
I am not bothered about the drift of all the
0s, I may be concentrating on one 0 specially
36:42.190 --> 36:49.190
then nearest one, the one which is nearest
to this preferably to locate it in a new position
36:51.089 --> 36:55.160
and this is not the only pole there could
have been other poles and my desire would
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have been to shift this to this side then
I would have weakened this one, is it all
37:00.089 --> 37:07.089
right. So it all depends on what is the 0
wanted that means in Z12 in the transmission
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I am creating artificial 0s all right by removing
the poles partly this is known as partial
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removal of poles and shifting of 0s okay.
So you can weaken either the pole corresponding
37:30.339 --> 37:37.339
to this or this that means you weaken the
pole here that also you could have seen. Let
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us see now, instead of 2S if I take S what
happens I remove only one hand inductor and
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rest of it, I retain.
37:47.730 --> 37:54.730
Now here I have created a 0 in Z1 dash into
S which is at root 5 by 2 so this element
38:00.500 --> 38:07.500
is having a 0 let me complete this then will
go to partial removal of this pole at infinity.
38:08.119 --> 38:15.119
So I have got a network like this and then
Z dash into S is a function which is having
38:24.280 --> 38:31.280
a 0 at S square plus that is at root 5 by
2 it is having a 0, how do I realize this
38:32.750 --> 38:38.950
any 0 you convert it to a pole. So I correspondingly
I will take Y dash into S which will be giving
38:38.950 --> 38:45.950
me S square plus 5 by 2 in the denominator
okay then there are other factors okay and
38:47.119 --> 38:53.760
this one I will write as K1(s) by s square
plus 5 by 2 plus other factors that means
38:53.760 --> 38:58.869
Y dash the admittance is taken as some Y1,
Y2, Y3.
38:58.869 --> 39:05.869
So this entire Z dashed which was appearing
here is now taken as some Y1, Y1 which will
39:14.430 --> 39:21.430
be corresponding to this all right that means
it will be having, this is an LC series element,
39:22.140 --> 39:27.839
is it not if Y corresponds to K(s) by S square
plus omega square that will give you a series
39:27.839 --> 39:34.839
LC element okay and then rest of it I will
again switch over to Z(s). I am not bothered
39:36.140 --> 39:41.540
about this part, I am interested only rem
in removing that 0, so convert it to a pole
39:41.540 --> 39:48.540
that is go to an admittance function then
realize that and then again the balance you
39:48.760 --> 39:55.760
again invert you will get rest of the elements
1 by 1 you take out the 0s in the shunt elements
39:59.010 --> 40:01.160
okay.
40:01.160 --> 40:08.160
So this will be resulting at root 5 by 2 so
that will be creating the 0 all right by partially
40:10.750 --> 40:17.750
removing the pole we can realize this. Let
us see if we partially remove the pole at
40:18.470 --> 40:25.470
infinity that is let us take again 50 percent
removal just take S.
So we have got 1 henry it is Z dash into S
40:38.829 --> 40:45.829
now, is s plus 6 S by S square plus 1 and
Z removed is just s okay. Now what is Z dash
41:05.579 --> 41:12.579
into S, s cubed plus S plus 6S, so s cubed
plus 6S divided by s squared plus 1 sorry
41:17.829 --> 41:24.829
7S. So s into s squared plus 7 by s squared
plus1 now what will be the pole 0 location,
41:25.589 --> 41:32.589
earlier it was a pole sorry a 0, a pole a
0 and a pole.
41:37.800 --> 41:44.800
Now I have weakened this so under the new
situation Z dash into S this was for Z(s),
41:45.670 --> 41:52.670
Z dash into S is having 0 once again at the
same point, pole at the same point, this pole
41:52.859 --> 41:59.859
is also at infinity but here it is earlier
it was 2, now it is root 7, now it has drifted
42:01.270 --> 42:08.079
to this side. So 0 has drifted towards this
pole which has been weakened, so wherever
42:08.079 --> 42:14.640
you are weakening the pole the 0s will drift
towards that okay. Earlier it was in the other
42:14.640 --> 42:21.640
side so the 0 drifted to that side, so depending
on the 0 that is given in the transmission,
42:24.690 --> 42:28.329
this is corresponding to the transmission
0.
42:28.329 --> 42:35.329
So the 0s are transmission where they are
located and what is given in z11 if you know
42:37.180 --> 42:44.180
that z11 is at 2 and the 0s required 0 of
transmission is at root 7 then I will be weakening
42:44.569 --> 42:49.640
this pole first, so that this drift safe all
right. If I weakened this pole then it will
42:49.640 --> 42:56.640
be drifting to this side I cannot realize
this 0 all right. So this is the technique
42:58.589 --> 43:05.589
that we follow for ladder development and
we want 0 at that particular frequency so
43:19.470 --> 43:25.230
what should be the value of that residue that
is we have seen only 50 percent removal, what
43:25.230 --> 43:30.150
should be the percentage removal? What should
be the percentage removal of the residue,
43:30.150 --> 43:37.150
percentage removal of the residue. So that
we can get the desired location of the 0 okay.
43:40.359 --> 43:47.359
So that is a next question, let us take up
an example it will be clear say z11(S) is
43:53.990 --> 44:00.990
given as s squared plus 9 into s squared plus
25 divided by s into s squared plus 16 okay.
44:07.329 --> 44:14.329
Let us make a plot of this poles and 0s first
and then decide about the shifts, so there
44:21.940 --> 44:28.940
are no private poles z12 and z11 are having
the same poles all right, if there are private
44:29.530 --> 44:36.530
poles remove that first. So poles and 0s are
for z11 is it has is the original 0 pole then
44:45.960 --> 44:52.960
3, 4 okay then not to the scale any way 5
and then at infinity there is a pole, this
45:05.339 --> 45:12.339
is z11, z22, z12 pole, poles are same because
there is no private pole. So the poles are
45:20.160 --> 45:27.160
identical and then this one is at 1 and then
this is at 2.
45:30.770 --> 45:37.770
Now in the transfer admittance, transfer admittance
or transfer impedance, there is no hard and
45:38.470 --> 45:45.470
fast rule that poles and 0s should alternate,
transfer admittances z12, how much is z12
45:49.349 --> 45:56.349
in terms of z1, z2, they need not be okay
we will discuss about it later on, see the
46:05.359 --> 46:12.010
poles and 0s need not come alternatively,
so they need not be positive real functions,
46:12.010 --> 46:19.010
they need not be positive real function, is
that clear. Any question? They need not be
46:29.030 --> 46:36.030
positive real functions how follows us z12
by repeated star delta conversions, you got
46:38.890 --> 46:45.890
z12 as this impedance but this need not be
a positive real function, this need not be
46:46.450 --> 46:49.970
a positive real function.
46:49.970 --> 46:56.970
Only thing is the numerator and denominator
coefficient must be always positive when you
46:57.079 --> 47:01.849
go for repeated star delta conversions you
must get all the coefficients as positive
47:01.849 --> 47:08.849
but repeated conversion of star and delta
that need not guaranty positive real functions
47:09.410 --> 47:16.180
as elements that means the element may not
be realizable, element may not be realizable.
47:16.180 --> 47:23.180
For example you are having an inductor and
capacitor, an inductor, an inductor and resistor
47:25.359 --> 47:32.359
and so on. If I reduce it to star or a delta
this may give you some Z(s) it may not be
47:37.950 --> 47:43.960
realizable it will be having a function all
right with all positive coefficients a1(s),
47:43.960 --> 47:48.450
a2(s) squared and so on divided by b1(s) b2
square but it may not be a positive real function
47:48.450 --> 47:55.450
they may not be able to realize it by RLC,
okay it is a very interesting point.
47:59.260 --> 48:05.640
So this is very clear from z12 itself here
s squared plus 1 into s squared plus 4 by
48:05.640 --> 48:12.640
s into S squared plus 16. So you can see the
0s are coming consecutively coming 2 consecutive
48:13.559 --> 48:20.559
0s and then pole comes, so what should I do
I can shift this 3 so these are the values
48:21.430 --> 48:28.430
1, 2, 4 and 5 either I can shift this 0 here
or this 0 here. So either you can weaken this
48:34.799 --> 48:41.799
or weaken this, is it not. So if you want
to shift this here you have to weaken this
48:51.619 --> 48:58.619
that means a part of this residue has to be
removed okay so z11(s) let us break up z11(s)
49:09.740 --> 49:16.740
if you write as K1(s) plus K2(s) by S squared
plus 16 plus K3 by S, I am not really concerned
49:22.220 --> 49:28.210
about all these, I am interested only in a
partial removal of this.
49:28.210 --> 49:35.210
Suppose I write this as some K1 dashed S plus
z11 dashed S that means this is the part removed,
49:42.030 --> 49:49.030
this is the part removed and this is what
is remaining all right. Now z11(s), so z11
49:54.609 --> 50:01.609
either at j equal to omega sorry omega equal
to1 that is S equal to j1 or s at j2 this
50:03.780 --> 50:10.780
will be vanished all right sorry, the impedance
at that point, impedance sorry impedance at
50:17.520 --> 50:24.520
that point j1 or impedance at j2 I want this
to be 0 for z1, z12 for z12 this will be equal
50:39.880 --> 50:46.880
to 0, is it not. So z11 dashed, z11 dashed
at j1 if I take it as 1 because I am shifting
50:56.799 --> 51:03.799
it here, should be equal to 0 is it not this
must be 0. So what is this if I put on this
51:05.650 --> 51:12.650
side z11 at j1 should be equal to K1 dashed
into j, S equal to j1. So how much is K1 dashed
51:15.770 --> 51:22.770
calculate from here, is it okay z11 that was
given as s square plus 9 into this thing,
51:29.799 --> 51:36.799
so put S equal to j1, so that is 9 minus 18
into 25 minus 1 into 24 divided by 15 into
51:48.650 --> 51:53.849
j okay and this j is there already.
51:53.849 --> 52:00.849
So that gives me K1 dashed into j1 all right
K1 dashed into j1, so calculate this how much
52:02.990 --> 52:09.990
is K1 dash comes out as minus 64. Now check
whether it should be minus z11 j omega plus
52:21.670 --> 52:28.670
K1 dash into j1, j1 is equal to 8 into 24
divided by S into s squared plus 1 or 15,
52:43.760 --> 52:50.760
is it all right. We are trying to make it
at 1 it is a 0, so 1 okay K1 dash it is let
52:55.470 --> 53:02.470
us see whatever be that value minus 64 by
now j into j will be so it will be plus minus
53:16.839 --> 53:23.220
64 by 5 so that means we will have to add
that seems to be some out funny this there
53:23.220 --> 53:24.540
made some slip okay.
53:24.540 --> 53:31.540
Let us see the other one I come back to this
you also, also think over it why we should
53:31.960 --> 53:38.960
get this or what we are trying as K2 dashed
S by S square plus 16 into some z11 double
53:42.819 --> 53:49.819
dashed S either remove this part partly, remove
this partly then it will be shifting to 2
53:55.309 --> 54:02.309
sorry, sorry, sorry, sorry 3 will be 2, thank
you very much that is why this scaling was
54:13.990 --> 54:20.990
very very important. So in any case you can
weaken this to shift it to either 1 or 2 okay,
54:21.910 --> 54:22.910
thank you.
54:22.910 --> 54:29.910
So in that case what will be this one, z11
double dashed at j2 should be equal to 0,
54:36.619 --> 54:43.619
this is a0 which gives me yes, sorry we are
weakening the pole at the origin
55:06.760 --> 55:13.760
that is what I am putting j2, I am going to
write that, that is what
55:55.440 --> 56:02.440
I am going to do, this will be z11. Okay,
let us write it here, okay
57:02.049 --> 57:09.049
we
will continue with this in the next class.
Now time is over we
58:11.280 --> 58:18.280
will continue with this in the next class,
thank you.