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Yeah, so thank you and welcome
to this last talk this
evening.
I think there will be a film at, what,
zero o'clock?
But the last talk for this
evening is for Maxwell to
antenna arrays.
You probably all know Maxwell's
equations, the four equations.
I actually like the idea
that with four more or less simple
equations, you can't really explain a lot
of stuff.
And I'm a communication
engineer, so I will stay in three
dimensions.
Um, back when I was studying,
I actually also visited the lecture
about relativistic electro
dynamics, which is all this mix
will in four dimensions.
And I also I passed it
somehow.
But yeah, what you can see
here on this nice
picture is
AM Broadcasting Station
with an antenna
array.
I think it was medium wave here
in Brazil.
It was I think in previous Apollo
I was for more working with stuff
like this.
At the moment I work as a science
journalist and
it's quite interesting how a lot of
stuff like mobile broadband and also
things like radio astronomy are
coming together and the field of antenna
arrays. So I will get the
the topic to this.
And also, I think for everybody some
fundamentals of propagation
and how antennas are working, which now
everybody has his or her package.
It's very handy in many situations.
So here are
four Mexi equations.
We have got law.
We have Koslov for magnetism.
We have the of induction, Faraday's
law of induction, I think.
Could it be that this microphone is on?
No. OK, good.
Um, and the fourth one
is Amperes Circuit Law here.
Um, a bit more details.
So Gauss law
of induction actually
describes the relationship between
a static electric field and
the electric charges that caused
it. So here we have to
point of charges
and the static electric field points
away from the positive charge on
this side here towards the negative
charge.
And very easy example as a capacitor.
You all know this.
You have your two two sides of
the capacitor where the charges
are, and then you have the electric field
in between a little bit of
mathematics.
So here we have the this
knob operator with the C that
the divergence of a vector.
It's a derivate of each value,
um, in in space or in
X, Y and Z coordinates,
and then they are added up.
So actually this measures
the magnitude of a vector fields
source I think at a given point.
And if we let come on to free space
propagation this role
here. So we have no charges and
free space. So this row becomes
zero and we can simplify this
equation.
So the next one goes off.
A magnetism is the divergent
of the magnetic flux.
Density equals zero
that states that they are no
magnetic charges or
magnetic monopoles.
You all probably know what happens
if you break a magnet
into two parts.
So you get two magnets
with a plus and minus pole.
Um, yeah, the
the equations state that the magnetic
field lines.
So the circles here
neither begin nor end that make loops
or extend to infinity and back.
The third one is Paradise Lost,
and actually this one describes
how a time varying magnetic field
creates or induces
an electric field.
This lengthily term here
is the kernel of a
vector.
This actually describes the direction.
So it's the direction
which is like orthogonal to the other
one's.
A good example is
where this law is working
is an electric generator.
So, for example, it has a rotating
bar magnet which creates
a changing magnetic field
and which in turn generates
an electric field and nearby wire.
So you get your electricity by moving
your magnetic field.
And the last equation
here is pure pass
law with MEXT Worth, Ed.
and this one state that magnetic
fields can be generated in two ways.
One way is by electrical current.
And this was the original Amperes
law.
And Maxwells addition
then added
that also by changing electric
field,
a magnetic field can be generated.
And this addition.
So this is this part here like the
the if fear the electric field,
they're related to the time.
So the change of the electric field,
this is especially important
because it shows that not only
does a changing magnetic field induce an
electric field. So this was the law
and that law of induction,
but also changing electric field
and use magnetic field.
And therefore, these equations allow
after sustaining electromagnetic
waves, to travel
through empty space.
So on a whole, we have those
four equations.
These keep them in mind for a moment.
I would come back to them later.
First, some history, because
it's exactly 150 years
ago that
these equations or Maxwell's paper
dynamical theory of the
electromagnetic field were accepted
for publication by the Royal Society.
But some remarks, what was going
on, unknown about technology
at this time.
So he had the average lifetime
of a light bulb at 1870
was around 10 hours.
The first central station
providing public power is believed to be
one goddamn Surrey
in the UK and it was switched on
in 1881.
So probably Maxwell didn't
get electric light when he Wright
wrote this paper.
There was also a lack of mathematical
fundamentals.
So already Faraday, which
which had which
were who was also researching
a lot in this field, envisioned
in 1830 a mysterious
what he called a mysterious, invisible
electronic state surrounding the magnet,
what we would today call a field
or a vector.
But vector calculus was
not invented yet.
Faraday also hypothesized
that light itself was
a magnetic wave, but shaping
this ideas into like
and a complete theory was way
beyond his mathematical abilities.
So actually, IMEX also didn't
had 20 equations, four
equations, but he had 20 equations.
So you can see some of them here
on the right side.
And it took another 20 years
until they understood by someone
else. And it was
this actually self-taught British
engineer, mathematician and physicist
heavy side who put the
equations then in their present form
like and to this four equations
some years later had
finally had brought the
experimental proof of Maxwell's theory.
He verified that electromagnetic
waves exhibit like light,
like behavior of reflection,
refraction, diffraction and polarization,
and also that the speed of light
and that of electromagnetic radiation
seemed to match up pretty well.
So, um, the proof came up that
light also is an electromagnetic
wave.
So back to Maxwell's equations,
if we come to freespace
propagation in
a vacuum, we have no charges
and we have no currents.
So this role here in
Gulf law, it was zero and
the ChÃ© in an umpire
succored law also equals zero.
So the equation simplified to
this one, which
looks pretty symmetric,
except of here is a minus,
and here are the permeability
in perpetuity, which can
be summed up to the speed of light
here. See?
Um.
When we then want
to come from those equations,
perhaps to something that looks more like
a wave, like we know this waves
are like causing us,
what we do is we take the curl of
the curly questions.
I put those Axworthy
questions here and to the side,
I will show it here for the
love and action for the effect Ifield
Electric Field, for the magnetic field.
It actually works the same.
Um, so we take the koloff,
the current equations.
Here, do
some vector calculus.
So the curl of the
kernel of a vector equals
this one is the gradient of
the divergence of a vector minus
the square gradient of
this vector.
Um, then we come
to this situation here.
Yeah, our divergent we see this
up there equals zero, though, all
this stuff equals zero,
and this
here pretty much
looks like this partya so we
can change this.
Actually, the bema stealing some lines,
I think so.
This is also a division here.
And we end up and
then we put this to the other side and we
end up and those were
called the verifications.
This are still to patcher differential
equations.
And the simple solution of
those equations is a plane
wave, which then you
can see here or
something is happening here.
Yeah. And they are already pretty much
looking like waves like we got
here. Our amplitude here, the
zero, we get a coziness
like the the waveform.
Then we get our omeonga, like the
frequency depending
on the time.
The K here is the vector
and here we get our dependance
on the location and
the face.
This way, if Namak actually represents
the rate of change of the phase and
this also pointing in the direction
of propagation.
A plane wave
can be seen here, for example,
so we get to
you feared and talk on
a magnetic field.
Airplane waves are defined like to have
constant frequency, the way
phones are parallel planes of constant
peak to peak amplitude and
all this normal to the phase velocity
vector and
such a plane wave always
have a pointing vector.
The fear, the pointing
vector represents the energy
flux density of
this wave
and is also
in the direction of propagation, which is
always orthogonal to the to the
to fields, to the E
and the Beefheart.
Um, then every wave has
a polarization.
The polarization has defined us
as the alignment of the
Eastfield, the electric field.
So from here, for example, we have a
horizontal polarization
and we have a linear polarization
here because we have only parts
in one direction.
There are also other forms.
For example, here you can see a
circular polarization.
Um, this occurs when we have two
orthogonality component components
with exactly the same amplitude,
which are 90 degree out of phase.
And those two waves actually then
behave like a wave circling around.
For example, here is an antenna which
can be used to receive a
circular circular
way, if it's called
a QF h.
What they feel are healthy
dial or something like this antenna.
And I did
this one for receiving like some
NOAA weather satellite pictures,
which I sent out in FM.
And it's kind of very
cheap to build this antenna
with some waste, some
waste pipe, some copper cabling.
And the receiving can be done, for
example, with a really cheap software
radio, such an ATSDR.
And with this you can see
Europe kind of from above
can show you one one picture,
which is also not so good
on the bema here.
So this is the ATSDR.
This is the skew
of age, circular, polarized,
polarized antenna and the
countryside here.
You get some open source software
for receiving the signal.
This is the program is called
Geek. You are X,
which is really does nice
FMJ modulation.
And then there is a program to to,
um, to calculate from the
signal the satellite
picture, which.
Yeah, it's just an FM modulated signal.
And here for example, there are
a lot of clouds here.
This is Italy, like the boot of Italy
can be seen here and
yeah.
Here is
what this is the Mediterranean
Reunion with some clouds.
And this is kind of Central Europe.
So we're kind of 20,
25 euros.
You can just see Europe from above.
So if you have some spare time,
you should really go out and
hunt for some satellite.
Um, but back to some
propagation first.
So we get the the vertical and we
got the circular polarization.
Um, there's also elliptical polarization
that comes up.
If you got also two components, like the
circular polarization, but they have
different amplitudes, so we don't
have to circle back to it.
Let's take a
look. I don't know, um,
regarding polarization, if you want
to see, for example, the
horizontal polarized signal with
the vertical polarized antenna,
you always lose
some signal power.
Now, for example, if your circular
antenna is
circling in the wrong direction of
the signal,
um,
it's actually you got something.
It also depends on whether you
are in or out, because every
reflection and the scattering
and stuff also manipulates
your signal.
So you don't only have a vertical
component, but often it makes sense.
Like to move the antenna a bit.
If you have bad signal or in many
modern equipment, you have
like two receiving antenna that do some
kind of receiver diversity to
get both components of a signal.
If we take a look,
unfreeze step is freespace propagation
and the real world, we
assume we have a certain distance
between the transmission antenna and the
receiving antenna,
and it's good to assume that this
distance exceeds
the antenna length and also
the wavelength by several multiples,
because in this case, you can
you can you're
pointing vector like the Earth from
before, um,
seems to radiate from a single
point.
And we can use the phone of
a perfect approximation just
code, which simplifies a
lot because we can divide
our term of propagation, like the point
that the energy flux density
here in a
spherical propagation part.
So you can this can
be seen in the figure here.
We can divide the propagate
the area on a sphere cross.
So here we get a small area and then
we if we move further
away from our transmitting antenna
here in the middle, the area
on this fear grows
proportional to the square of the
distance.
And the same
time, if we use the density,
this one drops inversely proportional.
So this behavior is
the four P.D.A square
and this part.
And then we have the three
dimensional profile coming
from the antenna pattern.
So on the whole, this becomes quite
easy for propagation.
You also know that higher
frequency do not reach as far
as lower frequencies and
this is caused by the antenna
aperture.
The A here
equals the pattern G
are the antenna pattern.
Ah, and here Lundahl
Square, our wavelength
divided by four P.
Um, and the antenna
aperture determines how well an antenna
can pick up power from an incoming
electromagnetic wave and
at higher frequency
can be seen like that.
The antenna in proportion to the
distance is smaller and therefore
we cannot pick up as
much power.
Um, and then,
yeah, we can put in here,
um.
No, that's afterwards,
then at the receiver here, we get the
power PR, this equals
the energy flux density,
which is like the wave in the
in the freespace
multiplied with the antenna aperture.
Then we can put all the stuff here, the S
and the AI
in here, and we got this term
for our receiving power.
At the receiving antenna now
dependent on the distance
and also on the frequency.
And
then we one term, which is
often used as a phrase
transmission equation that defines the
ratio of power available at the input
of the receiving antenna to the
output power to,
um, of the transmitting antenna.
Um, and
here the inverse fact of this
equation is called
the freespace loss, which
is actually the minimum loss you always
have.
If you have two antennas
sending around something,
mostly you get additionally
reflections, diffraction detonations
from the atmosphere and so on.
But, um, yeah, this is
the minimum loss you have.
When it then comes
to Antenna's, um,
we always like this antenna
patterns because they describe like
how much of
the energy is
sent in which direction.
Um, this pattern depends on
the current distribution on the
antenna, because here
we we we have mostly
some metallic materials.
So we get some current.
So J isn't
equal to zero.
For example, here we get a half
Lambda Dipole.
The calculation of the pattern is
then based on Maxwell's
equation. Again, um,
you normally work with a vector potential
and everything in circular
coordinates and it
becomes a bit complicated.
So fortunately there are a lot of
nice programs who do the work
for you.
Um, this year
was calculated with
Fornicator, which is a really
nice program.
It's free and uh,
I think it's not open source, but
it's also for windows.
But it works also fine with Vion
and Linux.
Um, it is based
on the numerical electro
magnetic code which is
the neck here in between.
And the code is based on the
method of moment solution
of the electric field into
equation.
Um,
Nick was originally written for the US
military and is then
put under public domain.
And um, it's a bit complicated
to build your own antennas
with this. So it's possible.
But yeah, probably
there are lots of very expensive program
which makes it easier.
But the cool thing about this program is
that it has many, many example
antennas with which comes
along with the program.
So, for example, also this queue
of antenna I showed before for
receiving the NOAA weather satellites,
um, was also
already included in the examples.
So here you can see the
main window of the program.
Then you can go here to calculate.
Then you get this window here, you can
choose. Yeah, I want to calculate the
pattern of my antenna.
Um, then you can just go to
generate and then
you get a nice you get to
do your patterns but you get also get
a nice Preedy pattern.
For example, here it can be seen this
antenna is for
this weather satellites were running
like above you from Horizon
2000.
So you want to have an antenna pattern
which also goes up from horizontal,
horizontal and which also does
the circular polarization.
So this fits pretty
well.
An important principle
when it comes to antenna patterns
is the interference between
different signals.
So if you get, for example, to
Vegas, you always have a
there's always constructive and
destructive interference.
So, for example,
when it comes to interference here you
can see swimming pool interference
then by I think this is a French
astronaut who is doing this like
putting two arms
in the water and then the waves
coming from two sides are interfering
by each other.
So we got here, we got some peeks of the
of the water.
And sometimes
it goes down
here if we got to where
they are in faith.
So which means
they are starting at
the same time and location,
they are causing constructive
interference, interference.
And if those two
waves are
90 degree order, phase faith
can be seen here.
You get destructive interference.
So if they cancel each other
and for anything in between,
you could also get some some interference
in between, which makes this
resulting signal a bit smaller or better.
Bigger depends.
I also found this nice picture of
two interfering waves
coming from two points here
on Wikipedia so I
can take a deep look.
OK, thanks
very descriptive antenna
for explaining the
interference stuff as the antenna
you can see here, for example, Yagi
antenna built for the
flight from a wireless
network, like to get a directional
antenna for two point fifty four
gigahertz.
You always got a driven element, which
is this one in this case,
and then you get some parasitic
elements, a
director here, another
direction in front
and reflect here in the back.
Um, the parasitic
elements are receiving the signal from
the driven element and at the same time
also sending it out
again.
And they are not exactly resonant,
but somewhat shorter or longer than
are
half lambda wavelength.
And this creates a capacity
for inductive reactants.
And this
reactance modifies the face
of the elements current with respect
to the to its excitation
from the Triveni element.
So you can see this
for this two element.
Yagi, we got the driven element and
the emission from this element
and then we get the director
and the emission from the director
is out of phase in
such a way that here to the front of the
antenna we got a constructive
interference.
So the signals getting getting
bigger and to the
back, the backward emission,
we got a destructive interference
so we get less power
to the back and more power to the front
as wanted.
So what,
for example, if we connect all
this Yagi elements here to
a source and then we could,
for example, manipulate the
face of each element in G individually?
So we can see this here,
this is called manifest right
here, for example, we have a lot of small
antennas, then we have a face
shifter. So it's in German here
on your phones is a German.
And then by
manipulating the face of each antenna,
we can change the direction
of this array.
Um,
the direction of propagation
here is another example,
we got two antennas.
If we put
signals on each antenna with the same
face, the main lobe of
this array, EQUASS,
the main direction of each antenna.
So it's going straight
forward in this direction.
In the other case,
if we delay
the of the face of the antenna
slightly, then
the slope moves up, the lobe
of the antenna array moves up,
and the gain of the resulting
antenna always consists
of the gain from each single antenna.
And then there is an array factor.
So if you have a lot of antenna, you can
create a very
high antenna gains.
And by manipulating the faces,
you can then move the slope direction
as wanted.
There are different techniques to
do the
Festschrift the first one.
Once we're in hardware, so you
get just longer cables, for
example, a car.
Ferdinand Braun invented this technique
in nineteen five.
Then it was mostly used
as often for military
purposes.
For example, it is still highly used in
radar systems.
It was later then also adapted to radio
astronomy, leading also to a Nobel
Prize for physics for
Anthony Hewish and Martin Ryle
for the entire four metric
radio antennas.
Um, but more on this later.
An interesting thing is
when you mix or
like some time ago, a software defined,
defined radio, this technique
came up in a large scale.
And if you mix this with antenna
arrays, you get a really a lot of
flexibility into this
phased arrays.
You can, for example,
manipulate the face of each signal and
software.
You get a very flexible, for example,
beam forming.
Depending on the face you set in
software, you could change the direction
of the beam and also mix
this with Minamo techniques.
So with MIMO multiple input, multiple
output, you additionally do some
recording on each
signal from coming from from
each antenna.
And with this recording, you
try to take advantage of the
channel properties.
For example, in a very scattering
environment, a channel
has a lot of different uncorrelated
paths so it can
increase the data rates, for example,
its use within the new WiFi
standards.
It's also getting cheaper.
So not only
the military's can use it now.
Also, like the mobile app for mobile
broadband, they are doing a lot of
research at the moment.
For example, for a 3D
beam forming.
This is can be seen here in this picture.
So we've got our base station.
Then we get one beam
here down and
several beams to the skyscraper
here.
And the idea is, for example.
To cover different levels of a skyscraper
with different beams on the same
frequency so they are always
afraid to or how
are they shell transport all the data,
those mobile data, so they can
actually reroute frequencies with
this beam forming.
So the latest headline came from
the East China Mobile, which who
did a test with the to the race
with a total of one hundred twenty
twenty eight antennas.
Yes, I already told this
software faced away.
Technology is also
used in radio astronomy
there. It's for receiving
signals and that's
also very general.
An antenna always behaves
the same no matter if you're if it's used
for transmission or reception.
So also,
if you're you know, you need a
really precise time stamp of
each signal on each antenna
and then you can like, um,
process the signal from the different
antennas with different faith
shifts,
depending on which direction
you want to you want
to receive the signals from.
And yeah, you can get a really
good antenna gain by using
a lot of antennas.
And that's also important
to distribute them on.
Along the way, the radio astronomers
actually have the problem
that to explore signals
at lower frequency,
the telescopes need to be really,
really big to have a good resolution.
And it becomes quite handy.
Like if you if you see the,
um, the
dishes, they already
started, like building the dishes and.
Well, yes, but then it becomes quite
handy, like if if they want to get a
signal from another galaxy, which is not
right above the dish, but
at some other location.
So it's just
not possible to move it anymore.
Um, the angular
resolution of a telescope here depends
on the wavelength divided by D.
D and the diameter
of the telescope, or it's
the baseline.
So the length of the maximum
physical separation of the telescope
and the error.
And a nice example is, for example, the
loafer, the low frequency array,
because they want to observe
radio frequencies from 10
to 250 megahertz.
So you got really kind of
long wavelength from thirty
to one point three meter.
So what they do is they build a lot of
different
stations and distribute
them over half Europe
and a total at around 25000
small antennas
concentrated in 48 large
stations.
They are also still building new
stations. I think the last one was
kind of last summer they they
built the latest station in Germany
near Bremen or Bremerhaven, something
like this.
Within Lofa, the angular resolution
goes down to zero point to
one arc seconds.
And the whitespace line is something
like 1000
km and at the highest
frequency.
Mm hmm.
And if you built such stations
in software, it's also built with this
software, radio technology.
Also, the data processing becomes
quite interesting because
perhaps you remember you got your audio
acidy, that 80 minutes of
music, you get around seven hundred
megabytes of that data.
You can hear from
twenty to twenty hertz
to a 20 kilohertz.
So you get like around 20 kilohertz.
Audible bandwidth.
Knackwurst told us
that we need to double something.
Right.
So we often
use the forty four point one kilohertz.
Sixteen bit and two channels.
Um, here we got frequencies
from 10 to 250
megahertz.
Which makes it quite a
bigger bandwidth and
we get that like 25000
antennas, which all
generate a
lot of data, what they then
do is they do a kind of pre
processing of the data to station
already, like they have to decide
before which direction they want to
go to get the signals from.
And then they do this correlation of
the signals already partly
at each station, and then they
send the data to
the Netherlands, to Corning and
wear blue gene supercomputer.
Does the final processing from the
distant stations then?
Um, this Lofa telescope
is also a Pathfinder project for
the square kilometer array.
And this one is
in preconstruction phase
at the moment.
The and
it's planned to be built in Australia
apart in another part in South Africa.
The plan is to cover frequency range
from 50 megahertz up to
14 gigahertz
in the first two phases of the
construction.
So here you can see
an animation.
It's not very big of
the dish antennas.
And Phase one shall provide
10 percent of the total
collecting area at low frequencies
by 2020,
20 by 2020,
and phase two, then share
complete the full array at lower
frequencies by 2025
and then phase three shall go
up to 30 gigahertz.
It's actually at three telescopes because
of the of the huge bandwidth.
So two dishes.
You can see the animation of
one of the dish antenna arrays.
And for the low frequency
is you get an array of dipoles.
The maximum line of this
antenna are three thousand kilometers
and the collecting area is one square
kilometer. Therefore, it's called square
kilometer array.
And within this project, also the main
challenge is the huge
amount of data.
I had an interview with the technical
director of the CIA earlier
this year, and he told that they
are they are
planning to have more data than the
Internet carries today on are all
together on their stations.
And all this data has to be processed,
transported and made available for
the scientists.
They plan to deploy like fiber
optic with the length that would reach
around the world twice.
And they actually trust in Moore's
Law to process all the data, although
they wait until they buy
the hardware until, yeah,
later is really
needed.
Um, the scientific
goals of this
this array,
this telescope is
between others.
The twenty one centimeter hydrogen
line, that channel map,
a billion galaxy out
to the edge of the observable
universe.
They will do research and the process
that's resulting in the galaxy formation
and evolution will be done
and research and the evolution of cosmic
magnetic fields and
the epoch of ionized
ionization after the Big Bang.
But yeah, here all this
stuff is again connected somehow
to relativity creation of
the universe.
So I will end here.
Thanks for your attention.
Yeah. And if you have some questions, I
can try to answer them.
OK.
As always, there's four microphones,
one day, one day, one day, one day, just
line up.
If you have any questions,
maybe you need a little refreshment and a
vector calculus.
Maybe just want to know some physics.
Just ask,
do we have questions from the Internet
on Internets already asleep.
OK, go ahead.
When when you were getting the
images from the satellites, could you
rely on good documentation or
was it a lot of trial and error?
No, there's actually kind
of good documentation and the
Internet.
Yeah, just
search around for no satellites
and FDR.
I also wrote an article about this
and the hardware projects, but it's not
online, unfortunately.
So you do have to buy
the magazine.
Thank you. Thanks.
OK,
that's a software you presented.
Consider cases of
non free propagation.
So if an
electromagnetic active medium
is present in the near field.
This antenna software,
I don't think so, actually,
you can you can do like
areas like
Watson name.
Fletching and in German,
um, but
I think that Dawn doesn't
support, like, different materials
of the surrounding space, but
I'm not quite sure.
So there's also a lot of documentation
on the website from Phonic
to perhaps better have a look there.
Thank you.
OK.
To the right place in the
plot with a Yagi antenna,
the amplified amplitude of the
passive element was higher than the
field, uh, field
of the amplitude, often driven element.
I wonder how that could be if a
metrically producing some energy
or whether this big field
size come from on that plot.
Yeah. Um, from Wikipedia.
No, actually it shall be smaller
because yeah.
You always have some, some losses
when you're when, when the
elementary CFED and then again sent
the stuff.
So yeah.
You're right.
OK, yes.
Uh yes.
How do you deal with a noise being
generated by the antenna itself.
Can you do the waterways quickly
lowered the noise of content itself or
ways of making sure you have the maximum
noise ratio?
Um, you mean in a phased
array on the Yagi,
for example, or with, uh, with with
additions like, uh, you
in the later square kilometer array?
Oh, I don't know, actually.
And not so much into
the technology, I think
they have to deal with it because
probably they will catch up a lot of
noise, but yeah, probably,
you know, often lack of noise
have some regularity.
So you collect a
large amount of signals and then you can
kind of calculate the noise out.
So that's how you normally do it and
yeah, OK, Internet,
we have two questions here.
One is it is
intercontinental assessed to
be possible.
And if yes, which
type of antennas would they
need to do this?
And how big facilities, antennas be
intercontinental.
What is those given to
you? Yes.
Slow skating?
Yes, someone said,
yes, it's quite
slow.
OK. I actually
don't know what slow scale
TV is.
No, as far as
mass TV is possible
and H.F.
so as a TV is possible,
but you need time
because it's extremely slow, because of
low frequencies.
So you use this ionosphere
stuff reflecting stuff at
high frequencies. Yeah, well
OK.
On 20 meters the right
place.
Maybe I missed something, but
what is the connection between all this
Maxwell's stuff and the face area
stuff?
Because it does face array you can use
with conventional
ways to like ultrasonic or something.
Where's the connection between is this
really used for the space array?
This is only a superposition of
elementary waves.
Yeah, the farfield.
So I don't see the connection
to the equations there.
So the mics were equations like explain
or wave propagation.
So it doesn't matter if you have
radio frequencies or light.
So they are kind of explaining
the wave propagation.
And then I try
to explain what you can do with
a different field of the wave
propagation.
And regarding two antennas,
but the this
what you used afterwards, it's not
not a prop.
or it doesn't use a prop.
or a unique property of
radio frequencies for
this beam forming stuff.
So this is a fear that
with all your waves, for example.
Yeah, that's right.
So, OK.
OK,
John, what do you I will always be the
case that I would need multiple receivers
to make any use of a receiving
array or
be any way to use just one receiver
with an array
and somehow calculate
the direction.
So just if you just use
one receiver off the antenna
and to do what to
I don't know if you want like a
directional reception or something like
that, it
is always the case that I need one
receiver for one part
of the antenna.
They you need some kind of
construction that does the dove
activity, so you don't
need an antenna.
There are also other forms of
antennas which are directional,
but within the area, like you need
different signals to get
this different faces like to to
create your dove activity
then.
Please go to the mic if you want to say
something so extreme, can cannot
understand you.
Well, for a case of a race,
you don't need several receivers
at every antenna part.
You can also combine to signal.
And HeartWare was the face shifters, like
she said. And after
you have combined to signal over some
power components, you can just put
it into one single
receiver. But you have to
do all those fancy face shifting
stuff in hardware and that's how it is.
And to combine the signals after
you have digitalize.
Thank you.
OK, thank you.
Any more questions, OK?
Internet?
Yeah, I have one question about
some excellent questions.
And this question is,
is a second secret men's
statement on a specific points
or officer who fired?
And what on a specific path,
on a specific point or
so, who will filed?
You mean field the field?
Yes, um,
you know, it's it
doesn't need to be a point.
So, for example, but also if you got
capacitors, you can have
rectangular or whatever
form of
um.
I know this was the first one.
What the second.
Maybe just show the slide so we know what
you're talking about.
So.
It was the second equation, right?
Yes,
and then if it's one point
or if it could be a kid,
if if this equation
is meant as a statement on a specific
point or who field.
Sorry, I don't get to stand on
the entire field because
the magnetic field, not
a magnetic point, which does not exist.
Um.
Thank you.
Technically, this is a statement about
the sources of the magnetic field, so
the second makes the equation just
says that there are no sources for the
magnetic field, which basically means
there are no monopoles.
Do we have more questions?
OK, thank you, thank us, speaker,
again, please.