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Hello, and welcome to today's lecture on Dipole
Antenna. In the last lecture we had started
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talking about dipole antenna, we took an example
of infinitesimal dipole antenna, which I had
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actually said that instead of considering
that as infinitesimal dipole let us assume
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that to be a uniform current because no matter
how small the dipole is current will never
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ever be uniform it will be always 0 at the
end. So, we did the derivation assuming just
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an imaginary current carrying conductor which
has a uniform current along the length.
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Then from that we had actually calculated
various far field expression and we also looked
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at the criteria for far field distance. So,
one of the criteria is r should be greater
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than 2 d square by lambda where d is the maximum
dimension, but please do not use that only,
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there is another condition that r must be
much larger than lambda by 2pi. So, I generally
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say the criteria should be r greater than
2 d square by lambda or r should be greater
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than lambda whichever has a higher value.
So, that should be far field criteria.
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And then we saw that the radiation pattern
of the dipole antenna is nothing but very
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similar to the way we look at a pen. So, maximum
radiation or maximum intensity we see a perpendicular
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to this here. So, just like a pen we see a
maximum and then if we go on the top we see
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0. So, the radiation pattern of the dipole
antenna is nothing but 0 here maximum. So,
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it makes a figure of 8 like this here and
it has a uniform pattern which is known as
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the azimuth pattern, this is known as elevation
pattern.
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Then from infinitesimal dipole antenna we
looked at the finite dipole antenna or a still
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small dipole antenna whose length should be
less than lambda by 10 we found out how to
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calculate the radiation resistance, and then
we also looked at how we can use a transmission
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line concept to find out the reactive part.
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So, let us continue from here we look into
the concept where we left in the last lecture.
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So, here is a transmission line which is terminated
in load impedance for this we can calculate
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what is the input impedance. We look at the
3 different cases, but now let us focus on
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this particular case here which is ZL equal
to infinity for this is the case where we
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will have an open circuit here. So, that is
what it would be dipole element which is open
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circuited at the end.
So, for this case input impedance is given
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by this expression and we saw that for open
circuit then Zin is capacitive provided length
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is less than lambda by 4, but let us see what
happens if length becomes more than lambda
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by 4 and please recall this is the half wavelength
we are talking about half of the dipole, full
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length will be double of that. So, less than
lambda by 4 means l will be or the total length
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of the dipole will be lambda by 2.
If suppose if it is more than that then what
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really happens - in that particular case we
substitute the value and this is the half
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length is between lambda by 4 to lambda by
2 then in that case 10 beta l will be substitute
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the 10 beta l is nothing but 2 pi by lambda
into l which is here than 10 beta will be
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negative. So, in this particular situation
for open circuit it will become a inductive
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impedance. So, please remember now for a small
dipole antenna Z input will be capacitive
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along with the radiation resistance for larger
dipole antenna this term become negative it
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may become inductive.
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So, from this now, let us talk about half
wavelength dipole. So, for a half wave dipole
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again we can do the same process find the
vector magnetic potential; integrate over
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the length from that find out the far field
pattern. So, I have just given here the expression
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for far field pattern E theta and H phi; will
see how the pattern varies for different lengths.
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But now the directivity of the dipole antenna,
for half wavelength the numeric value is about
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1.643 which is equal to 2.1 dB and for a very
small dipole antenna this value is nothing
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but d 0 equal to 1.5. So, for small dipole
it is 1.5 as the dipole length increases to
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lambda by 2 then it becomes 1.6 or which is
2.1 dB.
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Now as far as the input impedance is concerned,
the dipole radiation resistance is nothing
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but 73 ohm. Now if you have read several books
they actually say that input impedance for
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lambda by 2 dipole antenna is 73 plus j 42.5
and they still call it a resonant length lambda
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by 2, well that is not really correct. If
the dipole is a resonant configuration then
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the impedance should be real that is how we
define a resonance condition. Resonance condition
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is where reactive part becomes equal to 0
so, but for lambda by 2 dipole antenna this
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impedance is 73 plus j 45.5.
So, where is the problem? where are the issues?
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The issue is that when the length is equal
to lambda by 2 dipole antenna. So, what will
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be the half length? Half length will be lambda
by four. So, let just go back and see that
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dipole antenna configuration first.
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So, what is really happening? So, we can see
that over here when there is a dipole there
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are fringing fields associated with this,
now because of the fringing field effective
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length of the dipole antenna is slightly more
than the physical length of the dipole antennas
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and that is the reason when the physical length
is slightly less than the effective length.
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So, what happens then? Half the length is
lambda by 4. So, effectively because of the
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fringing field that length becomes greater
than lambda by 4, effective length, and if
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the effective length is greater than lambda
by 4 which I was talking about here then the
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transmission line represents basically the
capacitive will become inductive because it
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is now negative. So, that is why input impedance
of a lambda by 2 dipole antenna is inductive.
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So, what has actually happened in the process?
As we were increasing the length of the dipole
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antenna, so it was initially capacitive then
it became real and then it became inductive.
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So, from capacitance to the real value to
the inductive values, so really speaking what
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is happening that this effective length is
slightly more than the lambda by 2 and; that
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means, effective half length is more than
lambda by 4 which is giving rise to this imaginary
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term. So, if you want the imaginary part to
be 0; that means, antenna length should be
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reduced in such a way that effective length
becomes lambda by 2; that means, physical
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length should be slightly less than lambda
by 2, so that the total length including the
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fringing field will become lambda by 2 and
if that is the case then input impedance becomes
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real.
So, let us see now how we can design a dipole
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antenna. So, please remember now what was
this here l equal to lambda by 2 which is
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equal to 0.5 lambda. Now in all these derivation
we had ignored the diameter of the dipole
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antenna, all the dipole antenna will have
a finite diameter. So, here is a very very
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simple thing to design. So, l plus d which
is the length of the dipole plus d which is
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the diameter of the dipole should be equal
to 0.48 lambda, you can see that this term
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is slightly less than 0.5 lambda and this
is because we have fringing field. So, account
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for the fringing field. So, if you take this
particular expression then that will give
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us length equal to approximately the effective
length will be approximately equal to lambda
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by 2 and that particular point then for this
value the real input impedance will be there
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and approximately that value will be about
68 ohm which is slightly less than 73. So,
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we will now see the different configurations
now.
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So, let see current distribution for different
dipole length. So, here is a dipole length
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which is equal to lambda by 4 and lambda by
4 total dipole length means half length will
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be lambda by 8. So, that is still approximated
as a triangular distribution. When the length
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is lambda by 2 then half will be lambda by
4, so will have a sine wave going from here
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0 to maximum and coming back to 0.
When the length is equal to lambda, for lambda
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the plot will is given by, so this is the
lambda here will be means this will be lambda
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by 2 this will be lambda by 2. So, there is
a half wavelength variation here and another
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half wavelength variation here and if the
length increases so will be the more number
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of current variations along this. But just
to tell you practically we do not use dipole
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antennas which are much larger than the wavelength
here.
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So, this is how the radiation pattern varies
of a dipole antenna for different lengths.
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Here I have shown the radiation pattern and
by the way these curves have been taken from
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the Balanis book. So, I just want to mention
here that this length is, let say the total
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length is lambda by 50 that is shown as dotted
line. So, that is the current variation for
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that will be along this here this is the radiation
field in E plat pattern and that is how it
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looks like and for this case half power beam
width is about 90 degree.
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So, let us look why that is the case - see
we saw that the radiation pattern variation
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for E field was given by the term sine theta
was there. So, if you look at sine theta,
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theta is measured from here. So, sign 0 will
be equal to 0 so that is the 0 radiation,
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theta term then theta equal to ninety sine
ninety will be equal to 1, so that is the
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maximum radiation here.Now sine 45 degree
will be equal to 1 by square root 2 so that
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is the sine 45 degree. So, that is where on
a 45 degree means also implying 1 by square
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root 2 implies half power. So, half power
means half power beam width is not defined
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between this and on the other side the same
thing. So, 45 and 45 will become 90 degree.
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So, that is why 3 dB beam width is 90 degree
for small dipole antennas.
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Now as the dipole length increases one can
see that now the pattern is slightly narrower.
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So, narrower pattern would mean beam width
is now slightly reduced 87 degree. So, for
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lambda by 2 half power beam width is 78 degree
and as we keep on increasing this is for lambda
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half power beam width is about 47.8 you can
actually see that this is a much narrower
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beam here.
So, one can actually see that from here to
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here to here to here if we are increasing
the length beam width is becoming smaller
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that would mean gain is increasing and we
know that gain is directly proportional to
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the aperture. So, if the length is increasing
gain should increase correspondingly half
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power beam width should reduce. Now in all
these cases we actually notice that the there
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is only one beam over here.
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Whereas for the next case we will show you
that is when the dipole length is equal to
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1.25 lambda in this case there is another
minor lobe which has come in between. So,
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just recall up to l equal to lambda this pattern
was from here maxima it was going to 0, but
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now for this here there is a side lobe is
also coming and since everything is symmetrical
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with respect to this here, if you just look
at this pattern here, you can actually repeat
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that on this side and repeat on this side
and this side.
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And this is the 2-D pattern this is the three
dimensional pattern. So, you can see that
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the beam is maxima then it is going to 0 then
in between a side lobe comes and then comes
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back over here. So, this is the pattern.
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Now why did I show this pattern? There is
a reason for that because for this particular
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pattern we actually get maximum directivity.
So, what is this curve here? Well you can
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see multiple curves here I will go one by
one. So, what we have here along the x axis
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that is a dipole length in terms of wavelength.
So, that is a normalized dipole length so;
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that means, 0.5 here means length will be
lambda by 2, here length will be lambda, here
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length will be 1.5 lambda and so on. Now why
did I show the case of the case which is a
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1.25 lambda? So, when length is equal to 1.25
lambda you can see that directivity is maximum.
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So, this is the curve for the directivity.
Now the values of directivity are shown over
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here this is the dimensionless. So, 1.5 or
2 here you have to actually take in terms
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of dB we have to take 10 log 1.5 or 10 log
2. So, corresponding to this here you can
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see that this value is approximately equal
to 1.5 so; that means, for very small dipole
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antenna directivity is equal to 1.5 as this
one is increasing. Now, corresponding to lambda
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by 2 length you can see that this is slightly
more than 1.5 which is somewhere coming here
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and we saw that the directivity of a dipole
antenna is approximately equal to 1.64 of
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course, in terms of dB it will be 10 log of
1.64 which is equal to 2.1 dB.
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Now corresponding to this here you can see
that the directivity is increasing. So, maximum
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directivity is obtain which is equal to 3.25
you can say that that is more than double
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than a small dipole antenna, but after that
the directivity keeps on decreasing and then
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increasing it varies because mainly what is
happening that many other side lobes are coming
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in between. So, in reality even though we
are increasing the length of the dipole antenna
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considerably directivity is not at all increasing.
So, that is why higher order modes of dipole
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antennas are almost never used.
Now what are the other curves here? So, another
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curve let us just look at is a radiation resistance
curve. So, here is a radiation resistance
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curve and you can see that it is very very
small, just recall for a small dipole antenna
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I had given the expression which is 20 pi
square multiplied by l by lambda whole square
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, 20 pi square can be approximated as 200.
So, 200 times l by lambda square. So, you
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can see that when l by lambda is approximately
equal to 1 you can see that this value is
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getting closer to 200 ohm. So, you can see
here of course, it is not perfect because
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that l by lambda square assumed that it is
a triangular distribution, but in reality
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there will be a sinusoidal variation. So,
do not use that formula all the time. So,
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this is the variation for R r you can see
that these values are also changing and as
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I mentioned very rarely we use these modes.
So, we really need to look into this here.
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Now then what is this third curve here? That
is R input. So, R input curve you can see
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that R input curve is almost similar to R
r as long as the dipole length is small, but
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then R input changes here and when the dipole
length is approximately 1.5 lambda R in is
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equal to R r. So, what is the reason for that?
Actually for that you have to see the current
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distribution, so let me just show you the
current distribution first. So, one can actually
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see again I will go back. So, this is the
lambda by 4, so you can see that the current
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is maximum, how do we find radiation resistance?
In general we can say resistance is nothing
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but voltage divided by current. So, that is
the current here. So, here also current is
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maximum, but at this point what is the current
here current is going close to 0. So, voltage
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divided by 0 current here will give rise to
very high impedance, and this current distribution
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is for lambda length and this will be lambda
by 2 this will be. So, for l equal to lambda,
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current is approximately equal to 0 and that
is why input impedance is going to be very
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large.
Now, again for let us say the length when
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it is equal to 1.5 lambda then the current
is maxima hear. So, since the current is maxima
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R in is similar to R r. So, one can see that
when we are feeding a dipole antenna let us
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say if it is a lambda by 2 dipole antenna
we can see R in will be very similar to R
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r, but the imaginary part that, but at close
to this one here length equal to 1 you can
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see that the input impedance becomes very
very high here and then it changes here, now
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this is about the real part, what about the
imaginary part.
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So, for imaginary part you have to think about
that transmission line concept which I had
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mentioned to you. So, up to here to here the
whole impedance will be capacitive then it
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will become inductive then again becomes capacitive
and so on and so forth. I will give you the
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plot which we have simulated for different
dipole antenna will explain you this part
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again.
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So, here is the case here, we have taken just
a simulation of plot dipole antenna. So, instead
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of taking a wire which will have a diameter
here we have taken a plot dipole antenna and
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that is in air. So, we have a one strip here,
one strip here, this simulation has been done
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using IE3D software which is available from
mentor graphics. So, here for simulation there
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are 2 segments are there - one segment here,
one segment here. It is being fed with plus
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1 and minus 1 which basically is giving me
a balanced current here. So, from this side
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if I feed things like this is plus and this
will be minus. So, we have taken length as
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50 mm, 50 mm total length will be about 100
mm; width of this trip has been taken as 4
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mm and gap is taken as 2 mm.
Now, for this one here one can see that there
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is a, this is the resonance curve here. So,
we can actually see that there is a resonance
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over here and that is what is showing as the
reflection coefficient plot here and generally
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we define bandwidth for S 11 less than minus
10 dB. Now this is approximately equal to
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corresponds to VSWR equal 2 to a minus 10
dB reflected power basically implied reflected
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power will be equal to 10 percent. So, one
can see that the bandwidth for this antenna
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is from 1.39 to 1.54 gigahertz. So, what you
need to do it is you just look at the S 11
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less than minus 10 dB draw the horizontal
line and then read the lines from here and
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that will give us the bandwidth. So, this
is the bandwidth is about 150 megahertz which
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is about 10 percent bandwidth.
But now let us just see how the curve is varying
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with frequency. So, this is the lowest frequency
and frequency is increasing. So, now, if you
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are familiar with the smith chart I will just
repeat one more time. So, this is the 0 impedance
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then impedance increases along this line it
is a real impedance was 0 ohm, 10 ohm, 20,
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at the center it becomes 50 and then it becomes
infinity here; the upper portion represents
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inductive part, the lower portion represents
capacitive part.
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So, now, one can see that as frequency increases
at very low frequency this dimension will
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become much lesser than lambda. So, this is
equivalent to something like lambda by 50
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or more at a lower frequency. So, that is
how the variation is. So, you can see that
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the impedance here corresponding to this point
is very low if you look at this point also
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here impedance is relatively low. So, as the
frequency increases impedance is increasing,
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but it is still capacitive.
So, this is the point where it is crossing
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the real axis and then the impedance becomes
inductive. At this point here which is actually
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the second order mode theoretically it should
have been infinity, but it is actually very
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large and that point corresponds to over here.
Now this is where the third order mode is
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coming into picture, so you can see that this
is the frequency which is let us say approximately
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1.5 and the third order mode is coming approximately
at 4.5. So, that is the third order mode second
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order mode impedance is very high. So now
let us see; what are the radiation patterns
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at different frequencies.
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So, now I have shown the radiation pattern
at 3 different frequencies and I will tell
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you why also. So, this is the radiation pattern
at 1.5 gigahertz and that is the pattern which
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is of a lambda by 2 dipole antenna at this
frequency it is acting like a lambda by 2.
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So, you can see that this is the position
of the dipole maximum radiation is perpendicular
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to this side here and minimum radiation which
is represented by a blue color is in this
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direction. So, as we move from here to this
side here which is maxima then you can see
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that the color is changing from blue to green
to yellow to orange and red - red representing
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the maximum power.
Here we have actually shown the simulated
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plot here. So, one can see that this is the
simulated plot going on. I just want to highlight
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here this is the plot directivity and not
the gain, so it is a directivity plot. I had
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mentioned to you the gain plot will be directivity
multiplied by efficiency and gain also includes
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the VSWR reflection also.
So, here it is simply directivity and one
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can actually see that the directivity is increasing
this is very similar to the directivity curve
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I have shown and we can see that the directivity
is approximately 4.8 dB and that is at 3.75
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gigahertz where dipole length becomes 1.25
lambda and let us see the plot over here.
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So, we had seen that for 1.25 lambda maximize
here then it comes to 0 value, then there
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is a side lobe and then it comes here. So,
you can see that it is following the similar
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thing maxima, then reducing the color changes
to 0 which is bluish, then greenish and then
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coming back over here you can see a little
blue dot over there so it is coming down to
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0 value here.
Now, this is the pattern for third order mode.
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We saw that 1.5 is lambda by 4, half wavelength,
lambda by 2 is the full length and this is
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the 3 lambda by 2 lengths at triple the frequency.
Remember length we have kept fixed we are
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only changing the frequency, so by changing
the frequency lambda is changing and hence
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l by lambda is changing. So, you can see that
for this particular frequency the radiation
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pattern is not even maximum at perpendicular
to the dipole axis it is actually a more like
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a conical pattern over here. So, so you can
see that a cone is being formed.
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So, dipole is in this here. So, in this side
here along the axis the radiation is still
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close to 0, but it is actually making a cone.
So, if we require a conical pattern then only
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we should really be using third order mode
you can also see that the gain is not very
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significant.
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So, here is an example where I have taken
an example of a printed dipole antenna, what
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we have done is we have printed this dipole
antenna on a very low cost FR4 substrate this
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is actually known as also a glass epoxy substrate
we use a dielectric constant of 4.4. Typically
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FR4 substrate dielectric constant may vary
from 3.8 up to 4.6. So, this is the substrate
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which we have. So, 4.4 we took the thickness
of the substrate as 1.6 mm.
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Now since it is a low cost lossy substrate
tan delta is high which is 0.02, but it is
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not affecting too much in this particular
case because there is no backing here. So,
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this substrate when we print on the substrate
it is only printed on the one side of the
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substrate other side is blank or there is
a no metal on the other side. So, when you
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look at the magnetic field which will be around
this here. So, most of the magnetic field
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will be in the air only the part of the magnetic
will be confined within this substrate parameter.
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So, effectively efficiency is still pretty
good here and here I have taken exactly the
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same dimension as before, but because of the
presence of the substrate part of the magnetic
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field and electric field will be confined
within the substrate here. So, one can see
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that the resonance frequency has reduced slightly.
So, basically length remains same, epsilon
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00:28:15,899 --> 00:28:22,210
effective has changed earlier for air epsilon
effective was equal to 1. Now epsilon effective
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because of the presence, no, it is not effective
here is not equal to 4.4, 4.4 substrate is
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there only for this thickness and the rest
everything is air. So, hence epsilon effective
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is still close to about 1.1 to 1.2 and correspondingly
then epsilon effective is reduced.
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So, which actually changes the lambda, lambda
becomes now lambda 0 divided by square root
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epsilon e lambda 0 is nothing but c by f.
So, that is why frequency is reduced slightly
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and here we are getting about a bandwidth
of roughly 140 megahertz.
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Now in the next lecture we will see how we
can increase the bandwidth of the dipole antenna.
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So, will take different examples, we will
actually see that the bandwidth of the dipole
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antenna is proportional to its diameter or
the strip thickness, will also see what are
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the other techniques for the dipole antenna,
then we will also study a few other things
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like how to do the Balun design because most
of the feed are coaxial feed for example,
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then from coaxial feed we have to get a balanced
line which should feed plus and minus. So,
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that is where the concept of balun comes into
picture. Balun – b a l is for balance, u
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n is for unbalanced.
So, balanced to unbalanced concept come. So,
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we will tell you how to even design very simple
balun also so that you can realize it very
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efficiently. Then we will also look at how
to design folded dipole antenna.
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Thank you very much. Bye.