 OK, I believe we gave enough margin to the latecomers. So once again, good morning to everyone who decided to join us for our webinar today. My name is Tomasz Wolenski, and I'm a product and marketing manager at RF Elements. And I'll take you through this journey today. So because there is so much to talk about when we consider the topic of antennas, we decided to divide this webinar into two parts. To both horns and patch arrays are topics volumetric enough that they deserve their own time slot, so that we're able to give a good overview of each technology. And in this webinar, we'll talk about the horns, and there'll be another one about the patch arrays in the beginning of October. So if you're interested in all the whys and hows of the patch arrays, make sure you do not miss it. And before we go into the topic, in case you have any questions, I encourage you to type them down into our questions tool, and I'll try to answer these questions at the end of the webinar. So what makes an antenna a great sector antenna? Most whys know about gain, beam width, front of the ratio, maybe a few more. And on top of that, on top of what you might already know, there are many other parameters antennas have. And here you see a list of the most important sector antenna properties from our RF elements point of view for whys networks. Ideally, every deployment you do would get a separate treatment, meaning you look at all the nitty and gritty details of the variables you're working with. But of course, we understand that as being a whisp, your life is very busy, and there might not always be the space to give the proper care to each link. Or, well, depending on your experience, you might as well know immediately what hardware you need to use. What we show here is rather exhausting list as a reference if you have the space to plan optimally. Now, whether you stick to it or not is of course what we call the art of what's possible. But it's a good thing to remember. You can always come back to this presentation because we'll put it on our YouTube channel at some point. And if you subscribe to our YouTube channel, you'll also get the notification when we publish the recording. So because horns are based on waveguide technology and patch arrays on PCB technology, there are fundamental differences between them. And although both types of antennas are used for the same job, the physics of their operation differ quite much. So resulting, which results into different factors, influencing the side-lob level, stability of the radiation pattern or co-location capabilities. So Wisps are increasingly sobering up from the approach of the quote, unquote, cheaper is better in terms of the hardware they choose to deploy. Now, although in the past, there has not been much choice in terms of the hardware. Nowadays, Wisps are having gradually more and more experienced and more education to know that besides the price, the network stability, scalability, or balance of the horizontal vertical chains or the coverage stability are the key elements to running a successful Wisps. And we are aware that this might be a lot to digest. But again, this is why we're here, why we're doing this webinar and make sure to check the recording once it's up on YouTube. If you choose to and if you, of course, find whatever we'll talk about useful or interesting. So as advertised, this webinar will be about horns and we'll look at horns from the angle of Wisps networks, which means that we use the filter of the conditions that Wisps are dealing with in the unlicensed five gigahertz band. And again, this is a very specific lens through which to look at horns and which would be quite different in different industry or different frequency band. But to make this webinar as relevant as possible to you, we focus on the five gigahertz unlicensed band Wisps networks, which Wisps rely on a lot. So horn antennas come in various shapes and sizes. They look and function very differently compared to the patch arrays you might be used to. And even though horns have been around since the end of the 19th century, they're finding their way into the Wisps industry for, well, less than a decade. And let's go into it. And how does a horn antenna work then? Every horn antenna starts with a waveguide. And like coaxial cable, waveguide is a type of transmission line or a cable, if you will. It's used simply to bring the signal or the energy from point A to point B. And this example, we're showing a circular waveguide which essentially is just a hollow metal pipe through which the RF signal travels. And the main advantages of the waveguide is it's the near zero loss it introduces to the transmitting signal and the capability to handle very high power of signals. So while coaxial cable works from zero frequency, you have from the DC, this is not true for waveguide because of the lack of the center conductor. It's just hollow metal pipe. So there is, compared to the coaxial, you're missing that center conductor. So if waveguide doesn't work from zero frequency, what frequency is it working from and where does it start and why? So first let's call this frequency at which it starts working a cutoff frequency. And below this frequency, no signal can travel through the waveguide and whatever is brought to its gate will be reflected back to the radio or whatever the source is feeding the waveguide. Above the cutoff frequency, the signal travels freely. So effectively you can look at waveguide as a sort of a high pass filter. Below the cutoff frequency, nothing goes through and above it, the signal travels freely. So the cutoff frequency depends on the waveguide dimensions. In case of the circular waveguide, it depends on its diameter. And as with most of the things in the world of RF engineering, the physical size of the hardware is inversely proportional to the operating frequency. So in case of the cutoff frequency, the bigger the waveguide diameter, the smaller the cutoff frequency becomes and vice versa. The smaller the waveguide diameter, the larger the cutoff frequency is. At the cutoff frequency, we let's call it FC for short. At the cutoff frequency, the signal starts to travel in the waveguide and its fields only have one mode. The signal which propagates through the waveguide has only one mode, where the mode is the colorful pattern you see on the animation. So the color coding tells you how strong the field intensity is. The red color signifies the strongest field intensity and the blue one is the weakest. And for the rest of the colors, well, it's anything in between. So let's call this mode M1. And this M1 mode is well understood by the physicists and by the engineers. And we know how the waveguide behaves when it's operated in this first mode. So devices which are based on the waveguide operating with the mode M1 are also reliable and well understood. As we keep increasing the frequency though beyond the first cutoff FC, when we cross the FC2, which is another kind of frequency, that means another mode starts to exist in the waveguide and this another mode combines with the first mode and creates the resulting pattern you can see on the slide. And then at FC3, or the third cutoff frequency, yet another mode starts to exist and again combines with the previous two creating the resulting field pattern you can see and so on and so on. This can actually go indefinitely. And these additional modes above the first mode, we call them higher order modes. The total energy of the RF signal which travels through the waveguide is actually distributed among all these modes, of course, depending on the frequency. So we can say that the higher order modes suck the energy from the first mode since we usually pick up and work only with the first mode. So in that sense, the higher order modes are not useful or desirable because once we cross that FC2, the waveguide starts to behave unpredictably. It's not well understood how the operation of the devices based on the waveguide that works with the higher order modes work. So that's why we try to avoid this. So since the higher order modes change their radiation pattern of a horn antenna that might be based on it, the undesired way and make the functioning of the waveguide somewhat hard to predict, we restrict the bandwidth of the operation between FC and FC2 into a so-called single mode regime. So in this bandwidth, we are sure that the first, only the first mode exists in the waveguide which makes the horn radiation pattern and its overall behavior stable and lets us also radiate or deliver maximum power from the radio to the antenna and onwards to the space when it's radiated. So this single mode bandwidth is, you know, what poses the practical limit on the bandwidth in which the horn antennas can operate. You can look at horn antenna as a transition between the free space and the waveguide. So it transforms the guided wave inside the waveguide into a free space wave flying through the air. And horn is an aperture antenna, which means its properties are determined by the shape and the size of the aperture. And in this case, in case of the horn also by the length of the aperture. Two main parameters determine the gain of a horn. So the length of its body and the size and shape of the aperture. So if the aperture of horn is symmetrical, meaning it is a circle when you look from the front, the radiation pattern of the horn will be symmetrical as well. So again, looking from the front, it will be circular. And if the aperture is oval, the radiation pattern will be asymmetrical. The main beam will be wide in the azimuth and narrow in the elevation plane. I mean, at least with the example we're showing here, when you squeeze the horns from the sides, yeah, from like on the horizontal plane. Over the years, the engineers have come up with graphs such as this one to speed up the design process of horns. So there are three curves here in this image which are partially overlapping. So these curves tell us how the gain of a horn changes with the changing aperture diameter, D, yeah. So it tells us the dependence of the gain on the aperture diameter. So the difference between the curves is in the corresponding aperture length, L. The lowest curve corresponds to L equal to half a wavelength. So the length of this aperture is half of the wavelength at which the horn operates. So to L equal six times the lambda corresponds the middle curve, yeah, which has this bump here in the middle. And to the L equal 50 times lambda is the one is the top right corner, carry bump, let's say, and because they're overlapping along this line. And so the design process of a horn starts with a choice of the length L. And then the designer looks on the graph and finds the D depending on the gain one wants to achieve. And there's also a blank dashed line in the graph, yeah. And that one tells us what D needs to be to achieve the maximum gain possible for, yeah, the maximum possible gain of a horn. And this is why there is a hill on each of these curves. Yeah, there is this small bump. So the top of the bump marks the so-called optimum horn, which tells us that for a given length, this is the maximum gain you can achieve. Here are a few examples of various shapes of horns. So some are rectangular, some are flat on the horizontal or the vertical side. Some of them have strange structures inside and so on. Now, each of these variations of horn has its advantages and optimal usage scenarios. Some are white-band, some are easier to manufacture, some have minimum side lobes and so on. For example, this double-riched horn in the lower right corner has this like two fins inside, yeah, in a vertical direction. And those make the horn extremely white-band. Yeah, so whenever you need an extremely white-band, you will go for the double-riched horn. And this is also why, for example, this type of horn is used in the antenna measurements, yeah, because it covers a vast span of frequencies. And we could speak about any of these horns, you know, like they all have their specifics that make them suitable for different scenarios. So let's first have a look at the strengths of the horn antennas and we'll start with the side lobes. The key benefit of a horn antenna is radiation pattern with no side lobes. There is no fields that are diffracted or some parasitic radiation, as with the patch arrays, for example, because the RF wave is fully confined inside the waveguide first, yeah. And the radiation of the fields is a lot more controlled and gradual thanks to the progressive widening of the horn mouth, yeah. And this smooth transition ensures that there is minimum reflections, yeah. And that's why the result of these horn properties is the clean main beam with no energy wasted in unwanted directions. And as a result of that, no noise collected from unwanted directions or transmitted. Some of you might already know our antenna, so I'm sure you heard it a hundred times, that yes, our antennas don't have any side lobes, but is there a way to quantify side lobes? Is there a numerical variable that describes the amount of the side lobes an antenna has? Well, indeed it's beam efficiency. So beam efficiency is the ratio of the energy contained in the main lobe to the total energy the antenna radiates. In other words, it tells us what part of the radiated energy is going into the main lobe. So the higher the beam efficiency is, the more energy is in the main lobe. In other words, where we want it to be, and less everywhere else. And in other words, meaning in the side lobes. So beam efficiency quantifies the side lobes. It gives us a numerical value that very clearly says how many side lobes an antenna has. So comparing any antennas in terms of the side lobe performance is extremely easy. The higher the beam efficiency of an antenna, the less side lobes it has, period. As simple as that. Here we're looking at a radiation pattern of a traditional sector antenna. So if it's beam efficiency is 58%. The 58% is the power that the antenna radiates and that goes into the main lobe. So the remaining 42% therefore must be the side lobes. Note that we highlight all the side lobes. So beam efficiency includes all the side lobes of an antenna, not just one or a slice of the radiation pattern, but the whole package, the full 3D radiation data. Unlike front to back ratio or other side lobe parameters you might know about. So risks use a quite a wide chunk of spectrum. But in antenna textbooks, beam efficiency is defined at a single frequency and for single polarization. So this is the case for most textbook parameters actually. And again, it is up to the user and mainly actually the manufacturer to consider whether one should care about the whole bandwidth or just a single frequency point. So since the computational power is much more affordable nowadays than it was in the past, the choice between the wide band or narrow band information is really a matter of deciding of what is important rather than figuring out whether we can do it at all. Today, we can easily do both, no big deal. And with the industry, it makes perfect sense to average beam efficiency over the whole bandwidth. The antenna is working in a simply because we use their antennas in a wide frequency band. So it only makes sense that an antenna should perform well in the whole bandwidth. Therefore, we extended the definition and the textbook definition of beam efficiency to a number that is the average of the beam efficiency over the whole useful bandwidth of our antennas and over both polarizations, which turns the textbook definition of beam efficiency into sort of a super parameter, if you will. It is much more robust and more reliable measure of sideload performance than the single frequency single polarization version or anything else that is out there. So vast majority of antennas used for sectorial coverage and with networks are either patch arrays or hordes. The patch arrays have many frequency dependent sideload. So their beam efficiency values are around 60%. I mean, still, of course, there is some variation depending on the manufacturing and design quality. The horns generally have much better beam efficiency, but be careful here as well. You can see other horns in the graph as well, not only ours. So this is to highlight that it is not a given that when you have a horn antenna, it will automatically have high beam efficiency. To achieve stable and zero sideload performance takes quite a bit of effort. So beam efficiency tells you everything about the sideload performance while front-to-beam ratio or other parameters you might know almost nothing, really. So comparing front-to-beam ratio as used in the WISP industry to beam efficiency is something like comparing when looking at the world through a keyhole chain, I mean, sorry, through a keyhole in this case, which would correspond to the front-to-beam ratio and being on top of a hill and seeing the wide open space when you see everything crystal clear, which is the case of beam efficiency. The difference is simply vast. Let's continue with the strengths of the horn and now we'll look at the beam width. And the beam width we can achieve with horns. So horn technology has the flexibility needed to provide the beam widths fitting various covered scenarios. By adjusting the dimensions and the shape of the horn, you can achieve the desired performance, regardless if you need a narrow or wide sector, really. It's that flexible. This is the very powerful feature of horn technology in general, which gives you the ability to adapt to any conditions you might encounter while planning your networks. So horn technology is so flexible that you can actually choose, if you want to, to change the beam width in both horizontal and vertical planes or only one of them at a time. So when you squeeze the horn only on one side, in this case, we're showing the examples when in there it's squeezed in the horizontal plane, you change the beam width only in the elevation. So this results into an asymmetrical beam, which, again, fits particular scenarios with rather flat landscapes and adds a few decibels of gain so you can cover more distant areas. Yet another tool to your Wisp toolbox. The result of all these possibilities is a potential for wide toolset of horn sectors that you can have, which are suitable for different scenarios, obviously. So the top row shows the symmetrical horns with the gains. We can range from 9.6 to 18.5 dbi gain and large beam width spans. The second row shows the asymmetrical horn sectors with the gains from 16 to 20.5 dbi gain. For example, when we take the 90 degree asymmetrical horn, it has 16 dbi gain, whereas the symmetrical 90 degree horn has 9.6 dbi gain. So here we can see the power of shaping the aperture. In this case, it's quite intuitive. Like sort of when you imagine this, taking the symmetrical horn in your hands and squeezing the horn from both sides, you shape the aperture eventually to the oval shape and it kind of makes sense that you kind of squeeze more gain out of it. And in the same row, you can also see the example of a 24 dbi gain horn. We call it the ultra horn, which is good for the point-to-point applications or narrow sector applications. And this is, for example, a point where some which are kind of questioning. So what is this antenna good for? Is this ultra horn, is it a point-to-point antenna or is it a sector? Well, the answer is it's up to you. Whatever works for you, it can be a narrow sector. It can be a point-to-point antenna. So frequency stability. This property of horns is actually important and quite often perceived by your end customers and their service quality. So the human psychology works in a way that we're, let's say we prefer stability over, let's say occasional jolt of high-speed internet. So most people will be happier to have stable internet which achieves some decent speed over being able to do the pen of the network and see like, whoa, I can do 300 max or whatnot, right? But otherwise the network might be unstable. So for your customers, the stability of the connection is more important and that's exactly what horns actually deliver. Here is an example of our 60 degree asymmetrical horn and there is a graph of its gain depending on the frequency. So yes, of course, you can always say that, well, it's not quite flat, but then it's pretty close to be flat. And it basically shows us the maximum gain of this antenna. And this is important to have as flat the gain, it's important to have the gain as flat as possible. And that's in order to basically, be able to rely on its operation and eventually the whole performance of the network when you switch channels. So when you switch from 5.4 gigahertz, let's say, when you look at this point, the gain is somewhere around almost 16 and when you switch to 5.8 is a little bit higher, but then it's all, it's very similar. And I can guarantee you that difference between these two gains is negligible. You will get more variance of the signal received or whatever signal strength from the reflections from the surroundings. You will, I can guarantee you, you will not perceive this difference in the slightest. So in that sense, we can tell that the frequency stability of the maximum gain is really high. And there are actually two curves in this graph. So one of them is for the vertical and the other for the horizontal polarization, but because they're overlapping, you can't see the difference, which again is another good property of course. So here you see the frequency stability of the full 3D radiation pattern of the same antenna. So not just the maximum gain, because on the graph on the previous slide, we've shown the maximum, how the maximum gain changes with frequency. But here you can see how, I mean, okay, you can't see the over antenna, the numerical values of the gain at each point, but you can see how the whole radiation pattern changes with frequency. And this is another important piece of the puzzle when it comes to frequency stability of the coverage and the service you're providing eventually. So of course, you can see that the radiation pattern is breathing a little bit, but looking on the right side, how that translates to the change of the coverage. You're seeing it's negligible. And this is definitely important to the customers on the edge of the sector. I mean, of course we're not saying you should not leave any safety margin and connect even the customers, which are totally on the edge. No, of course, you need some margin, but let's say we definitely stand by the statement that the stability of the horse is uncomparably better to the traditional sectors. Here we can see a result of simulation with 60 degrees symmetrical horn. And so this is the projection on the map, but mind you, these are also results of the real physics simulation. That's why we also below the picture, we also show the parameters we used for this calculation. So we took the 3D radiation pattern off this antenna and made a quick and simple simulation to see how the coverage changes with frequency when you project it on the ground. So that's something more interesting and more close to the practical life. And there on the right side, you have the MCS scale. So the red color corresponds to the MCS level of nine or the modulation and coding scheme level of nine and more. The yellow to seven, anything between seven to nine and so on. So you can see what the coverage or what MCS range you can get depending on the distance from the AP antenna. But the takeaway from this particular image is that, okay, at the beginning, we can see that the horns, the coverage grows a little bit, but for the rest of the useful spectrum is stone stable. And this is exactly what you want from a sector antenna. Stability means reliability and this translates into a happy customer in the end. Here we show similar simulation, but for the 60 degree asymmetrical horn. And I will tell you the truth. I mean, as soon as you take asymmetrical horn and introduce some sort of asymmetry, meaning you squeeze it and you get the antenna you see on the picture, the things will change a little bit. Because of the asymmetry, the things will become a little bit less frequency stable and you can see it on the resulting coverage. It's like a nice avocado shaped pattern, which is, again, changing a little bit with the frequency, but it's definitely much more stable than anything else out there. Another component of the coverage stability is the balance between the performance of the horizontal and vertical antenna systems. Asymmetrical horns have the same radiation pattern for both polarizations, which perfectly fits this stability criteria. So you don't have to worry about the customers on the edges of the sector when you switch the polarizations, when you switch from the horizontal to vertical chain. So in comparison, the competitive battery rate sectors have unbalanced horizontal and vertical systems, which has a negative influence on the field performance, but hey, more about that in the part two. Let's not go ahead of ourselves too much so far we've shown the properties of a horn antenna, which is designed to fit all the criteria we talked about as well as possible, let's say, but do not get fooled. I mean, not all the horns are performing this way. There are many types of horns as we saw previously and even when a given type of a horn has certain advantage, it takes considerable effort to optimize the antenna so that it has the properties we are looking for when we're basically looking through its performance through the lens of the OptinWisp networks. So here's the radiation pattern of the 90-degree asymmetrical horn, no side lobes, and only one clean main lobe in both elevation and azimuth planes. So the horizontal and vertical patterns are nearly identical. So there is barely any difference between the red and blue curves. And again, these are not just some marketing images we tweaked in the Photoshop to your liking. No, these are real-world measurements. Here is an example of a so-called pyramidal horn. Now you already know that the pyramidal horn is has rectangular shape. And the inherent property of pyramidal horn is that it has some side lobes. Now, despite that, in this example, I mean, you can see that there are two wings on each of the vertical sides which are intended to suppress these side lobes. Nevertheless, this particular horn definitely doesn't have as good side lobe performance. Another problem of this antenna is the mismatch of the horizontal and vertical polarizations which results into different background noise conditions due to the side lobes when switching between the polarizations and eventually a mismatch of performance. They're like, it introduces more uncertainty in your day-to-day life. And that's why a lot of wisps are kind of like treating antennas sort of as a black magic. You can't be sure what this antenna will do when you switch the channel or when you switch the polarizations. Then this is, let's say, one of the components, why? Because of the mismatch between the two chains. There's another example of a 60-degree horn sector with similar problem of side lobes. Now we can clearly see them, they're still there. Not to say, of course, there is the mismatch between the polarizations as well causing the similar problems we just mentioned. Looking at the coverage pattern of horns, they're very, very different from the traditional sectors which might be often quite confusing to the wisps who are used to do with the traditional sectors which have a very flat radiation pattern. But let's look at the details. So with a horn, you can easily cover the null areas near the side. And this is absolutely impossible with the traditional sector arrays. Of course, you can always say that, well, but I can tilt the sector, patch erase sector so much so that it covers the null zone pretty well, which is true in the end, but you completely lose the coverage of the distant areas simply because of its shape of the radiation pattern. So horn instead illuminates the whole surface you pointed at. And you don't even need to use down tilt actually. And all this is thanks to the symmetrical radiation pattern which is really a great advantage for a sector antenna. So it's really nothing to be afraid of or skeptical, but actually it's another advantage to be used. In general, the radiation pattern of a horn with more width in the elevation allows for much better coverage of the null areas near the side. Again, that's just not possible with the traditional patch erase sectors. And here we show how it works with the asymmetrical horns when they are squeezed on either side. And yes, I can tell you that of course the asymmetrical horns cover the null zone a little bit less than the symmetrical horns, but again, later on we'll see the different scenarios for which each of these types of horns are the most suitable. So the zero silo radiation pattern is especially useful in sparsely populated areas outside the big cities and also inside the cities. The scalability of the whole combo of the symmetrical and asymmetrical horns gives you a vast flexibility when you're planning out the coverage. Yeah, so when you need more gain and have more customers close to each other and in a densely populated and urbanized area you wanna go narrow with the beam width. But when the customers are more sparse and not so far away from the site and the wide beam might be more handy in this case. So here we show how which scenario the asymmetrical horns are better for in terms of the variability of the landscape profiles. So as I mentioned before, the radiation pattern of the asymmetrical horns is flatter from the top. So it has less smaller beam width in the elevation than the azimuth. And just by this merit, it's more suitable for flat or mildly hilly landscapes. And also the areas where you actually need to, where there's additional few DBs of gain come handy because the customers might be further away from the site. The symmetrical horns on the contrary are actually suitable for any kind of landscape. It really doesn't matter where you're in in the Alps in the mountains of Colorado or in the flat lines of Louisiana, whatever it is, the symmetrical horns will do a very, very good job. And that's again, thanks to that shape of the radiation pattern, the symmetry. It's the same with the azimuth and elevation. And that enables like super easy coverage of the deep valleys. So if you live in a mountainous region, this is where the symmetrical horns are the best sectors you can use. For example, in this scenario, the patchway sectors would actually have very hard time because of how narrow their radiation pattern is in the elevation plane. But again, more of that in the second part of your webinar. So the variable beam width and gain the horns have enables an amazing scalability of network as such. So with asymmetrical horns, you have more tools to plan your networks in a sustainable way due to the lack of side lobes as well as the symmetric horns. And what does this scalability actually mean here? What do we mean by that? So scaling a network means growing a network. Meaning that sooner or later, you'll need to add more and more sectors. And with the traditional sectors, as you add with each and every new sector, you will be noticing the deterioration of the network's performance because of self-interference at the very least, not to speak of the situations if you have competition in the area, which is another source of noise and so on and so on. So you can only grow your network to a certain point where you come to a point where adding one more sector will make your network collapse altogether. So meaning that your scalability has a very low limit. Whereas on the contrary with the horns, again, thanks to the stability and the zero side low pattern and so on and so on, you can add more and more sectors. You can really cut the cookie however you want. Combine the beam weights, combine the different gains, overlap the sectors, whatever it is. Thanks to the horns properties. There is virtually no limit to your network growth. And that's actually what's actually a really nice thing to have, being able to grow when you need to and to be able to grow safely. Meaning that adding new sectors will not do anything to the infrastructure which is already in place. So every coin has two sides. And of course, so does the technology of horn antennas. So let's now look at the issues the horns might be facing. The first one we're gonna deal with is the cost of the manufacturing. So traditionally, the manufacturing of a horn antenna is a custom job, which means it's an expensive job. So these antennas are full metallic structures which are sensitive to even the slightest dimension in accuracies. So to achieve high quality product, it is not uncommon to use expensive milling machines with tools you have shown here on the slide in the picture on the right. And this is valid for high or low frequency horns without exception really. And it's probably even more so in the high frequency when things become like teeny, wey, small and it's very hard to do that precise manufacturing. Maybe some of you out there with experience in the machining can testify that these tiny, the smaller the things get, the more expensive they become because the precise machining and milling technology is quite expensive. Nevertheless, at least at our developments, we definitely put a considerable effort and energy into tweaking the design of our antennas to result into a optimized manufacturing process to a degree that actually these antennas can be mass produced while maintaining the high quality and performance standard. So definitely a large part of our effort is actually dedicated to optimize the manufacturing process so that we really meet that sweet point where the manufacturing cost is low enough to keep the pricing affordable for Wisps, but at the same time with pretty much no compromise on the quality of the performance. So in the end, it definitely is possible to make a horn antenna out of long lasting and high quality non-corrosive materials and without compromises on the quality of the art performance, but it has to be done right. So the issue with horns number two is the limit to the gain they can actually achieve in the real life. And in other words, we cannot increase the gain of horns indefinitely. So comparing a point-to-point horn with a point-to-point patch ray antenna with similar gain, the difference of the cross section is around 30 centimeters, which might not seem like much on the first glance, but mind you, these two images are in scale. So this is in the real life size comparison, let's say. But to increase the gain of the patch ray by six DBI, the area of the printed circuit board on which the antenna is etched will increase approximately fivefold. So not a big deal, honestly. I mean, the PCB technology is really well developed, to a degree that the production of the PCBs is very cheap, and the gain comes cheap. You just increase the size of the PCB, add a few more patches, and here you are. Adding the gain is actually quite easy. When scaling a horn on the other hand, you have to understand that this is not only the area, but actually the volume of the antenna that will increase and has to increase because that's based on the physics and functioning of the horn antennas as such. And for comparison, to get from 18 to 24 DBI gain, when scaling up horn, its volume will have to increase 15 times, which puts a whole lot more pressure on the mechanical engineers and designers to develop the manufacturing process that will accommodate antenna of such size while maintaining reasonable production cost. So it's really a totally different ball game, scaling the gain of a horn versus scaling the gain of the patch ray. And in the end, actually there is a definite limit to how high the gain of a horn can be. And you very rarely, if at all, can find a horn with the gain higher than 24 DBI. We really try to push the limit of what's achievable, but the physics is unrelenting and you can only do what you can do and what it allows you. So here's a short summary of the properties of horns. And the present state of the industry is that for the vast majority of whips, then the RF noise or interference, the self-interference or the competitors is the biggest issue. Where the horns actually bring in a good proposition and the zero sidelobe radiation pattern will definitely help with this issue. Not to say that because of the waveguide doesn't have any loss, you can deliver most, well, 99% of the power from your radio to the antenna, which again helps you. It's that one small additional bit of power you can transmit and provide a service to customers further away. And again, the frequency stability, we talked extensively about that and definitely an important factor when even from the point of view of the end customers of yours, which definitely appreciate the stability over some occasional high-speed performance, but then if the connection is not stable, it's definitely a lot more annoying. The bandwidth of operation of horns is quite wide. I mean, definitely wider than the battery antennas and actually the higher you go in the frequency, the wider that single-mode bandwidth becomes. So it actually only gets better the higher you go in the frequency. And not to say, of course, also the balance between the chains is important for that really high-quality performance and customer experience. But of course, the gain of the horns is moderate. I mean, it's a lot harder to achieve that high gain and there is unfortunately a hard limit on what is possible. And traditionally, they're expensive to build and manufacturing process is rather complex, but once that is hashed out, it is possible to deliver high-quality product, high-quality horn with the reasonable price. So at RF Elements, we like to challenge the industry. We like to really bring the value to customer not because the customer wants it or wants something, but because we're trying to deal with the problems. So we solve the problems which have on a daily basis through our noise rejection technology and our zero loss twist port connector, which is very easy and simple to work with and durable at the same time. And all this combined enables a massive scalability which lets your business to thrive and grow. Yeah, not like you don't have to hassle with increasing amount of your sectors. You can safely add new ones and therefore, our technology enables your business to grow. Well, and this has been me, the employee of RF Elements talking about our stuff. But I encourage you to check our YouTube channel where we have a playlist called Wisp Traveler where we have a bunch of short videos where Wisp's like yourselves, our customers share their experience with hearts. So of course, I can talk about our products all I want but as the human nature goes, we're all a lot more likely to start trusting or at least consider something when our peers who do not have a vested interest in selling their products to us to get more confidence into what's been presented. Another playlist we have on our YouTube channel is a short educational video series called Inside Wireless. And in the short videos, they're really like two, three, four minute videos. They have very quick punchy videos that go deeper into all kinds of aspects of RF engineering. So if you're still wondering what the Quad modulation is and how does it actually work or how do the polarizations work? What's noise floor? How do you actually measure the antenna beam width and so on and so on? I encourage you to check those videos. They're definitely a good resource to learn something new or refresh your knowledge. And I would definitely like to again, invite you to, if you're interested in all the details about the patch ray antennas in a similar fashion as we did today about the horns, please feel free to join us for the next webinar about the patch rays, which will happen. Actually, this is my apologies. I left this image here and that's for the central time of the United States or the Americas. So it's not the Wednesday, October 7th, but it's gonna happen. I think it will October 8th, if I'm not mistaken, at 11 a.m. central European time, but make sure you check it on our webpage. And actually, you can as well already register the registration link on our web pages. It's there and it's active. And I would also invite you to join our online community. Now we have, we call it RFELab, and it's a discussion forum where you can ask your questions or search through the questions asked by other users of our products and where we announce also our participation in all kinds of events, despite that obviously now there's not a lot of events happening, but nevertheless, it's a great resource in case you have any questions about our products and where, you know, let's say that we're not immediately available to chat or answer your questions. Personally, it's definitely a good place to start. And we're also actually putting all kinds of like recordings of webinars like this one or other videos. We're also putting them there. So feel free to check those as well. But in case you, you know, something comes to your mind, whatever it may be, you know, contact us either, you know, for example, the forum is a good one or our Facebook group or our Facebook page. So please do not hesitate to contact us if you have any questions. And I thank you for your attention. And thank you for your participation and hope you have a good rest of the day. Bye-bye.