 Yeah, so thank you and welcome to this last talk this evening I think there will be a film at 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 was for more less simple equations. You can really explain a lot of stuff And I'm a communication engineer, so I will stay in three dimensions Back when I was studying I actually also visited the lecture about relativistic Electrodynamics which is all this Maxwell in four dimensions and I also I passed it somehow, but yeah, what you can see here on this nice picture is A am broadcasting station with an am antenna array. I think it was medium wave here In Brazil, it was I think in Rio or Sao Paulo. I was 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 Coming together in the field of antenna arrays, so I will get the the topic to this and Also, I think for everybody some fundamentals of wave propagation and how antennas are working which now everybody is has in it His or her pocket. It's very handy in many situations So Here are for Maxwell equations. We have Gauss law. We have Gauss law for magnetism We have the law of induction paradise law of induction. Oh, I think could it be that this microphone is on? No, okay, good and the fourth one is I'm past circuit law here and a bit more details so Gauss law of Induction actually describes the relationship between a static electric field and the electric charges that cause it So here we have two 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 nabla operator with the C that is the divergence of a vector It's a dairy rate of each value In in space so in X Y and Z coordinates And then they are added up So actually this measures the magnitude of a vector fields source or sink at a given point And if we later come on to free space propagation This row here so we have no charges in free space So this row becomes zero and you can simplify this equation So the next one Gauss law for magnetism is the divergence of the magnetic flux density equals zero That states that there are no magnetic charges or magnetic monopoles You all probably know what happens if you break a magnet into two parts So you've got two magnets with a plus and minus pole Yeah, and the this equations state that the magnetic field lines so the circles here Neither begin or end but make loops or extend to infinity and back The third one is paradise law of induction This one describes how a time varying magnetic field creates or induces an electric field This lengthly term here is the curl of a vector. This actually describes the direction So it's the direction which is like orthogonal to the other ones 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 in a nearby wire so you get your electricity by moving your magnetic field and the last equation here is Ampere Ampere's law with max worth addition and this one states that magnetic fields can be generated in two ways one way is by electrical current and this was the original Ampere's law and Max worth addition then added that also by a changing electric field a Magnetic field can be generated and this addition So this is this part here like the the e field the electric field Derivated 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 of and that law of induction But also changing electric field induce Magnetic field and therefore these equations allow ourselves sustaining electromagnetic waves to travel through empty space So on a whole we have those four equations, please keep them in mind for a moment. I will come to back to them later First some history because it's exactly 150 years ago that the These equations or max worth paper a dynamical theory of the electromagnetic field were accepted for publication by the Royal Society but some remarks what was going on and About technology at this time So here 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 at goddamn Sorry in the UK and it was switched on in 1881 so probably Maxwell didn't had electric light when he write 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 and mysterious What he called a mysterious invisible electronic state surrounding the magnet what we were today called a field or a vector but vector calculus was not invented yet Faraday also Realized 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 makes or also didn't had 20 equation for 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 were understood by someone else and It was this actually self-taught British engineer metametrician and Physicist heavy side who put the equations then in their present form like and to this four equations Some years later Hertz Heinrich Hertz brought the Experimental proof of Maxwell 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 the proof came up that light also is a an electromagnetic wave So back to Maxwell's equations If we come to free space propagation In a vacuum we have no charges and we have no currents So this row here in Gauss law equals zero and the J in an ampere circuit law also equals zero So the equation simplified to this one Which looks pretty Symmetric Except of here's the miners and here are this permeability and permittivity Which can be summed up to the speed of light here see 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 Cosinos or senors What we do is we take the curl of the curl equations I put those Maxwell's equations here and to the side I will show it here for the law of induction for the if a if field Electric field for the magnetic field. It actually works the same So we take the curl of the curl equations Here Do some vector calculus? So the curl of the curl of a vector equals this one is the gradient of the Divergence of a vector minus the square gradient of this vector Then we come to this equation here Here our divergent we see this up there equals zero though all this stuff equals zero and this part here Pretty much looks like this part here, so we can change this actually the beamers stealing some lines I think so this is also a division here And we end up in Then we put this to the other side and we end up in those work hard the wave equations This are still two-part share differential equations 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 get Here our amplitude here the e zero we get a cosy nose like the the wave form Then we get our omega like the frequency Depending on the time the K here is the wave vector and here we get our dependence on the location and a face This wave number K actually represents the rate of change of the face and is also pointing in the direction of Propagation a plane wave can be seen here for example, so We got a e field and an orthogonal magnetic field plane waves are defined like to have a constant frequency The wave forms are parallel planes of constant peak-to-peak amplitude and all this and normal to the face velocity vector and Such a plane wave always have a pointing vector The s here 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 boat to the two fields to the e and the b field Then every wave has a polarization the polarization is defined as The alignment of the e field the electric field so for 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 And this occurs when we have two orthogonal e components 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 wave It's called a qf h at what three feeler helly Coedal or something like this antenna and I built this one for receiving like some No, I weather satellite pictures which are sent out in FM and it's kind of very cheap to build this antenna with some wave some waste pipe some copper cabling and The receiving can be done for example with a really cheap software radio such an RTL SDR And with this you can see Europe kind of from above you can show you one One picture, which is also not so good on the beamer here. So this is the RTL SDR This is this qf h circular polarize I polarized antenna in the countryside Here you get some open source software for receiving the signal. This is the program is called GQ RX Which is really does nice FM demodulation and then there's a program to to 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 It's this is Italy like the boot of Italy can be seen here and Yeah, here's What this is the Mediterranean Terrainian with some clouds and this is kind of here central Europe So Was 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 satellites But back to some propagation first So we got the the vertical and we got the circular polarization There's also elliptical polarization that comes up If you've got also two components like the circular polarization, but they have different amplitudes So we don't have the circle, but the ellipse elliptic ellip. I don't know I'm Regarding polarization if you want to receive for example a horizontal polarized signal with a 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 actually you got something It also depends on whether you are in or out or because every reflection and all the scattering and stuff Also manipulates your your signals. 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 to receiving antenna that do some kind of receiver diversity to get both components of a signal if we take a look On free step is free space propagation in 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 is Exceeds the antenna length and also the wavelength by several multiples because in this case you can You can your Pointing vector like the s from before Seems to radiate from a single point and We can use the Fraunhofer far field approximation just called which simplifies a lot because We can divide our term of propagation like the point The 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 propagation the area on a sphere cross So here we get a small area and then we if we move farther away from our transmitting antenna here in the middle the area on this fear grows proportional to the square of the distance and At the same time if we use the density this one drops inversely proportional So this behavior is the 4pd Square in 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 gr the antenna pattern gr and here Lambda square or wavelength divided by 4p And the antenna aperture Determines how well an antenna can pick up power from an incoming electromagnetic wave and a tire frequency Can we seen like that the antenna in proportion to the distance is smaller and therefore we Cannot pick up as much power And then yeah, we can put in here 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 free space Multiplied with the antenna aperture then we can put all the stuff here the s and the a 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 is a freeze Transmission equation that defines the ratio of power available at the input of the receiving antenna to the output power of the transmitting antenna And Here the inverse factor of this equation is called The free space loss which is actually the minimum loss you always have if you have two antennas Sending around something Mostly you get additionally Reflections diffractions at a nation's from the atmosphere and so on but yeah, this is the minimum loss you have when it then Comes to antennas We always like this antenna patterns because they describe like how much of the energy is sent in which direction This pattern depends on the current distribution on the antenna Because here we really 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 max-worth equation again 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 This year was calculated with for neck to which is a really nice program. It's free and I think it's not open source, but It's also for windows, but it works also fine with wine and the linux It is based on the numerical Electromagnetic code, which is the neck here in between And the code is based on the more method of moments Solution of the electric field integral equation Um Neck was originally written for the US military and is then put under public domain It's a bit complicated to build your own Antennas with this so it's 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 a program So for example also this QFH antenna I showed before for receiving the NOAA weather satellites 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 windows here you can choose Yeah, I want to calculate the far field pattern of my antenna then you can just go to generate and Then you get a nice you get 2d patterns, but you get also get a nice 3d pattern for example here it can be seen this antenna is For this weather satellites who are running like above you from horizon to Horizont so you want to have an antenna pattern which also goes up from horizon to horizon 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 two waves you always have There's always constructive and destructive interference so for example When it comes to interference here, you can see a swimming pool Interference done by I think this is a French astronaut who is doing this like putting two Arms in the water and then this the waves coming from two sides are interfering by each other so we got here we got some peaks of the of the water and Sometimes it goes down Here if we got two waves and they are in phase so which means they are Starting at the same time and location they are causing constructive interference and if those two waves are 90 degree out of phase which can be seen here you get destructive interference so they cancel each other and Yeah, for anything in between you get also get some some interference in between which makes this Resulting signal a bit smaller or a bit better a bigger depends I also found this nice picture of two interfering waves coming from two points here on Wikipedia So can take a deep look Okay, thanks a Very descriptive Antenna for explaining the interference stuff is a Yagi antenna You can see here for example Yagi antenna built for the Freifunk wireless Network like to get a directional antenna for two point fee for gigahertz You always got a driven element which is this one in this case and then you get some parasitic elements Director here now the directors are in front and a reflector here in the back 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 our half lambda Wave length and this creates a capacitive or inductive reactance and this reactance modifies the face of the elements current with respect to the to its Excitation from the driven 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 signal is 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 would for example happen 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 then a phased array Here for example, we have a lot of small antennas then we have a face shifter. So it's in German here I only found this in German and Then by manipulating the face of each antenna we can change the direction of this array or 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 equals The main direction of each antenna. So it's going straight forward in this direction in the other case if we Delay the other face of the upper antenna slightly Then the lobe 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 Very high antenna gains and by manipulating the faces you can then move the lobe direction as wanted There are different techniques to do the Face shift the first one once were in hardware. So you get just longer cables for example Carved in and brown invented this technique in 1905 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 their interfore metric radio antennas But more on this later An interested thing is When you mix or like some time ago software define defined radio this technique came up in a large Scale and if you mix this was antenna arrays you get a really a lot of flexibility Into this faced 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 can change the direction of the beam and also mix this with MIMO techniques so with MIMO multiple input multiple output you additionally do some pre-coding on each signal from coming from from each antenna And with this pre-coding you try to take advance of the Channel properties for example in a very scattering environment a channel Has a lot of different uncorrelated path is so you can Increase the data rates for example. It's also used within the newer wifey standards It's also getting cheaper. So Not only the military say I can use it now also like the mobile for mobile broadband They are doing a lot of research at the moment for example for 3d beam forming This is can be seen here in this picture. So we got our base station when 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 how they shall transport all those data those mobile data So they can actually reuse frequencies with this beam forming So the latest headline came from ZTE and China mobile Which who did a test with the 2d arrays with the total of 128 antennas Yeah, as I already told this software faced array technology It's 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 if it's used for transmission or reception. So also You if you you know that you need a really precise time stamp of each signal on each antenna and then you can like Process the signal from the different antennas with different phase 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 a long 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 Unhandy like if you if you see the The dishes They already started like building this dishes in wellies But then it becomes quite unhandy like 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 And The angular resolution of a telescope here depends on the wavelength Divided by D D is either the diameter of the telescope or it's the baseline So the length of the maximum physical separation of the telescope in the area and a nice example is for example the Lofa the low frequency array Because they want to observe radio frequencies from 10 to 250 megahertz So you got really kind of long wavelengths from 30 to 1.3 meter So what they do they build a lot of different Stations and distribute them over half Europe It's in a total it's around 25 down small antennas Concentrated in 48 large Stations, they are also still building new stations. I think the last one was Kind of in 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 two one arc seconds and the wider space line is something like 1,000 Kilometer and at the highest frequency And if you build such stations In software it's also built with the software radio technology also the data processing becomes quite interesting Because perhaps you remember you get your audio CD you get 80 minutes of music you get around 700 megabytes of data You can hear From 20 to 20 Hertz to 20 kilohertz. So you get like around 20 kilohertz audible bandwidth Nyquist told us that we need the double sampling rate And so we often use the forty four point one kilohertz 16 bit and two channels Here we got frequencies from 10 to 250 megahertz Which makes it quite? Bigger bandwidth and we get got like 25,000 antennas which all generate a Lot of data what they then Do is they do a kind of preprocessing of the data at the station already Like they have to decide before which direction they want to to get the signals from and then they do this Correlation of the signals already partly At each station and then they sent the date to the Netherlands to Groningen Where a blue gene supercomputer does the final processing from the distant stations then This loafer telescope is also a pathfinder project for the square kilometer array This one is in pre-construction phase at the moment It's a It's planned to be built in Australia a part in another part in South Africa The plan is to cover a 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 really built of the dish antennas And phase one shall provide ten percent of the total collecting area at low and mid frequencies by 2020 20 by 20 20 and phase two then Shall complete the full array at low and mid frequencies by 20 25 and then phase three shall go up to 30 gigahertz It's actually three telescopes because of the of the huge bandwidth So two dishes here you can see the animation of one of the dish antenna arrays and For the low frequencies you get an array of dipoles The maximum baseline of this antenna are 3,000 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 quite huge amount of data. I Had an interview with the technical director of this SKA earlier this year and he told that they are they are Blending to have more data than the internet carries today on there 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 most law to process all this data though They wait until they buy the hardware until Yeah later It's really needed Um the scientific goals of this this Array this telescope is Between others the 21 centimeter hydrogen line that shall map a billion galaxy Out to the edge of the observable universe They will do research in the processes resulting in the galaxy formation and evolution will be done And research and the evolution of cosmic magnetic fields and The epoch of free in 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 Okay As always there's four microphones one there one there one there one there just line up if you have any questions Maybe you need a little refreshment and vector calculus. Maybe you just want to know some physics Just ask Do we have questions from the Internet? Oh The Internet is already asleep. Okay. 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 a kind of good documentation in the Internet Yeah Just a search around for no satellites and SDR I also wrote an article about this in the hardware hex, but it's not online unfortunately So you have to buy the magazine Okay Does the software you presented? consider cases of non-free propagation so if 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 what's the name? Flächen anten in German But I think that don't it 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 for neck to perhaps Better have a look there Thank you Okay, to the right, please. Okay in the plot with a Yagi antenna the empty field amplitude of the Passive element was higher than the field Field of the amplitude of the driven element. I wonder how that could be. Is it magically? Producing some energy or where where did this bigger field size come from in on that plot Yeah From Wikipedia No, actually it shall be smaller because yeah, you always have some some losses When you when when the element received and then again sent the stuff. So yeah, you're right Okay Yes, how do you deal with noise being generated by the antenna itself? Okay, can you do other ways to actually lower them and the noise of the antenna itself or are there other ways of Making sure you have the maximum Secret noise ratio You mean in a faced ray or in this yagi or for example or with with the with the dish antenna like In the later square kilometer array. Oh I don't know actually I'm 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 Yeah, often like often your noise have some your regularities. So you you collect Large amount of signals and then you can kind of calculate the noise out So that's how you normally do it and yeah Okay, internet We have two questions here one is Is intercontinental SS TV possible and if yes, which type of antennas would there Needed two twosies and how big would these antennas be? Intercontinental what a slow scan TV slow scale TV. Yes, someone said yes Okay, I Actually, don't know what slow scale TV is No, as a TV is moving less TV is possible an HF so intercontinental as a TV is possible but You need time because it's extremely slow because of the low frequencies So you use this ionosphere stuff reflecting stuff at high frequencies. Yeah Okay on 20 meters the right place Maybe I missed something but What is the connection between all this Maxwell stuff and the face area stuff? because this face area you can use with Conventional waves like ultrasonic or something Where's the connection between is this Really used for this face array. This is only a superposition of Elementary waves in the far field. So I don't see the connection to the Maxwell equations there So the Maxwell 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 all do with a different field of this wave propagation and regarding to antennas but the This what you use afterwards It's not not a property or it doesn't use a property or as a unique property of radio frequencies For this beam forming stuff. So this is Without your waves for example, yeah That's right. So, okay Okay It's on would you all will be always be the case that I would need multiple receivers to make any use of a receiving array or Could there be any way to use this one receiver? with an internal array And somehow Calculate the direction So just if you just use one receiver of the antenna ray and and to do what to I Don't know if you want it like a directional reception or something like that This is always the case that I I need to one receiver per one part of the antenna Yeah, you need some kind of construction that does the directivity So you can you don't need an antenna array. There are also other forms of antennas which are directional but within the array like you need different signals to get This different phases like to to create your directivity then Please go to the mic if you want to say something because the stream can cannot understand you Well for the case of antenna arrays You don't need several receivers at every antenna part You can also combine the signal and hardware with the phase shift is like she said and After you have combined the signal over some power combiners. You can just put it into one Single receiver, but you have to do all those fancy phase shifting stuff in hardware And that's hard is and to combine the signals after you have digitized them. Thank you Okay, thank you any more questions, okay internet Yeah, I have one question about the Maxwell equations and This question is is the second equation meant as statement on a specific point or of the whole file On what on a specific pulse On a specific point or so who filed You mean field a field. Yes You It's it doesn't need to be a point. So for example, it's also if you've got capacitors you can have rectangular or whatever form of I Know this was the first one. What the second Maybe just show the slide so we know what you're talking about So so it was the second equation, right? Yes, and then if it's one point or if it could be a field If if this equation is meant as a statement on a specific point or who field Sorry, I don't understand the entire field B is the magnetic field Not a magnetic point which does not exist Thank you Technically this is a statement about the sources of the magnetic field So the second Maxwell equation just says that there are no sources for the magnetic field Which basically means there are no monopoles Do we have more questions? Okay, thank you. Thank our speaker again, please