in this video I want to introduce the concept of phased arrays and actually the name kind of says it all an array just means that there are multiple sensors arranged in some configuration that act together to produce a desired sensor pattern and with a phased array we can electronically steer that pattern without having to physically move the array simply by adjusting the phase of the signals to each individual element now commonly an array is made up of antennas like for Wireless Communications and for radar but the general concept can be applied to different sensors as
long as they measure or emit waves such as microphones which are used for sonar and acoustic Imaging in each of these applications we have to form a beam and we have to be able to move that beam around and we can do that with phased array systems so I hope you stick around for this introduction I'm Brian and welcome to a Matlab Tech talk to begin let's start with a single antenna instead of an array let's assume this is an isotropic antenna which means that it radiates equally in all directions in the basics of radar
Tech talk series which is linked below we talked about how this is not an ideal pattern for a lot of radar applications and we would rather have a narrow beam and one way to create a narrow beam is to redirect the energy with a dish and radar dishes are a great design and there are many applications where they are the ideal solution like for example the rotating dishes that you find for weather radar and the commercial dishes that are on people's roofs for satellite TV and internet however they aren't ideal for all applications and specifically
for fast steering applications steering the beam requires the dish to physically rotate and not only does this require gimbals and joints that need to be maintained over time but having to move Mass around is relatively slow you could probably imagine that you're not going to gimbal the dish back and forth between two Targets in a few milliseconds but this is one area where an array of smaller antennas is beneficial with phased arrays the beam steering is done electronically so not only does this mean that there are no moving Parts but we can steer the beam
to a new Target in a fraction of a second and not just this but phased arrays can also be used to generate multiple beams each that are steered independently from the other and this is all done using a single array so with that being said let's look at how we can actually form a narrow Beam with an antenna array and how we can steer that beam through phase shifting let's go back to our single isotropic antenna and we'll just look at half of the pattern the antenna is radiating out a sine wave where the dark
lines are where the signal is high and the light lines are where the signal is low now this antenna has no directivity since it radiates equally in all directions but imagine we have a second antenna that is placed half a wavelength away that is also radiating out the exact same sine wave now I know that this is a bit hard to see like this but I want to explain a few parts of this image because it's important for understanding how the array works along the horizontal axis we can see that the two waves are exactly
out of phase with each other since the light part of one overlaps with the dark part of the other this means that when one signal is high the other is low and when we combine those two signals they cancel out and we're left with very little energy in these directions however if we look up in this direction we can see that the two signals are almost perfectly in Phase with each other the light lines up with the light and the dark with the dark this means that both signals are high or low at the same
time and they constructively add in that direction this means that the interference pattern that results from these two antennas looks something like this in this image the dark areas are where the signal is canceled out off to the side and the colored portion is where the signal is stronger so we can see that even with just two antennas we already have a more directional beam than we did with a single antenna now this isn't a very sharp beam and we can see that a little more clearly if I zoom out a little bit so if
we want a sharper beam we need to increase the aperture of the antenna or the width of the array and one way to do that is by simply moving these two antennas apart notice how the main beam gets narrower as I move the two antennas from half a wavelength apart out to 1.5 wavelengths however this has created some additional unwanted effects like these two grading lobes a grading lobe has a gain that is comparable to the main lobe which can cause some trouble determining which beam a detection is coming from so instead of spreading out
the antenna elements we can increase aperture by adding more antenna elements each at a spacing of half a wavelength with three antennas notice the main beam is narrower but we also have two weaker side lobes that appear again they're not grading lobes since they are much lower gain than the main lobe all right let's add more here is four elements and the main beam is even more narrow here is six elements and then eight elements each time the beam gets narrower and we get more weak side lobes now look at this beam it's like a
spotlight shining up into the sky and what's kind of amazing about this is that all we've done is line up eight isotropic antennas in a linear array and the interference pattern between them results in this really directed Central beam and that's pretty cool okay so that is the basic principle behind how an array of antennas can create a directed beam it is just the pattern that is Created from the constructive and destructive interference between the different antenna elements and as you can probably infer at this point this pattern depends on things like the number of
elements the spacing between the elements and the geometry of the array layout these parameters contribute to the so-called array factor which we're going to talk about later but the array pattern is also a function of the radiation pattern of each of the individual antennas now I chose isotropic antennas for this pattern but we could also have an array of antennas with other radiation patterns as well and all of these different variables can be adjusted to modify the beam in a number of different ways and to see this more clearly let's jump over to Matlab and
open the sensor array analyzer app now this app can do a lot and I've linked to information in the description below if you want to check everything out but all I'm going to use it for here is to visualize some radiation patterns and to start let's duplicate the array we had earlier we have eight isotropic antenna elements arranged in a linear array each half a wavelength apart and now let's plot the 2D array pattern so this is showing the antenna gain as a function of Azimuth angle at an elevation of zero degrees so it's just
the gain around the Horizon and notice that there is a high gain lobe that's in the direction of the bore side of the antenna array and several lower gain side lobes exactly what we saw before in fact let's take this game plot and overlay it on the other pattern and we can see that they nicely line up now there must be some side lobes here that are just too dim to see but that's how low gain they are anyway I just wanted to show you that these are two different ways of visualizing the radiation pattern
but I think the gain in Azimuth plot is easier to interpret so we're going to stick with it for now and just go back to the app all right so something that I think is really important to remember is that this is the gain for a two-dimensional slice at zero elevation however antennas send out radiation in three dimensions and we can see what the actual radiation pattern looks like in 3D with this plot and notice that instead of a nice sharp main beam the pattern is really this sort of snail shape where the main lobe
extends both up and down from the horizon so in order to create a sharper beam in two Dimensions you know like a cone-shaped beam then instead of a linear array we need a planar array MathWorks has a nice Gallery here of different types of array geometries there are the linear arrays that we started with and we can bend a one-dimensional array to conform around a curved surface like we have here with a circular array but if we want the interference pattern to create a cone-like beam and if we want to be able to steer that
beam in two dimensions then we need a planar array like this rectangular array or really any other 2D shape like a circle or an oval or a hexagon and to show you what I mean let's go back to the sensor array analyzer app and change our geometry from a linear array to an eight by eight element rectangular array see now how the main beam is shaped in two dimensions and we have a number of smaller side lobes all around it and what's really interesting still about this is that this pattern simply comes from how each
of the individual antennas in the array interfere with each other if you build an eight by eight array of isotropic antennas each spaced half a wavelength from each other and send the same signal to each one of them this is the radiation pattern that will emerge this is a good time to explain the pattern of the entire array that we see here is the product of the array factor and the pattern of each individual element the array factor is a function of how the array is set up that is how many elements there are what
their spacing is and in which way they are oriented and given those parameters an antenna array has a specific gain pattern which we call the array Factor for example this is the array factor for a two element array spaced half a wavelength apart and with the same signal sent to both elements now I'm showing a back baffled array which is why the pattern is only radiating out in the forward Direction and it's not mirrored in the backward Direction so that's just something to be aware of here all right so this Two element array that's spaced
half a wavelength apart is going to provide 6 DB of gain or twice the power in the boresight direction which makes sense since there are two antennas contributing to it and then because of the interference pattern that we saw earlier the gain is going to drop as the angle off boresight increases okay so that is the array Factor now let's talk about the element pattern if the antenna elements are isotropic then the element pattern has a gain of 0 DB in every direction so the multiplication of the array factor and this element pattern produces an
array pattern that looks like this but what if we switch out the individual elements with say two ideal sync pattern elements instead well what's interesting about this is that the array factor is the same since it's the same array geometry but the element pattern is different and when we multiply the array Factor by this new element pattern we can see that the total pattern for the new array is a much more directed beam so hopefully you can start to see how the array geometry impacts the array pattern as well as the pattern of the individual
elements and to sort of see this in action let's go back to the center array analyzer app and switch the element from isotropic to an ideal sync pattern element now the array Factor has stayed the same but since the sync elements are a more focused beam the overall array pattern is more focused too okay so we know we can form a static beam but we want to steer this beam electronically so how do we do that well let's go back to the Two element linear array and try to develop some intuition recall that this setup
caused a cancellation of the two signals off to the side and a doubling of the signal along the bore site and if we separate the two signals we can see clearly that they are in Phase with each other both of these patterns are identical now instead of in-phase signals let's change the phase of the second antenna by exactly half a wavelength so now the two antennas are sending signals that are exactly out of phase and now if we bring them back to half a wavelength apart we can see that we've changed how these two radiated
patterns line up now the signals are doubled along the tangential axis where the light Parts overlap and the dark Parts overlap and are more canceled along the perpendicular axis where they are out of phase and if we look at the combined radiation pattern for these two antennas we see now that the strongest signal is off to the side and not in the direction of the bore sight so by phase shifting one signal by half a wavelength we've essentially rotated the main Beam by 90 degrees of course we can delay the signal by any amount and
by sweeping through different phase shifts we can see how the main beam sweeps back and forth and to see this effect more strongly let's go back to our eight element array in this case each antenna element is Phase shifted compared to the element right next to it so in this eight element array there is a total of seven phase shifts between the first and last element all right hopefully it's starting to make sense that the array creates the beam pattern and the phase shifting steers that beam and to see what all of this looks like
in 3D with a planar array let's go back to the sensor array analyzer app we'll go back to the pattern for an 8x8 planar array with isotropic antennas and notice that the main lobe is aligned along the x-axis or the bore side of the array but now under the steering tab I can change the steering angle for the beam to something like 10 degrees in azimuth and then the 3D plot shows what the beam pattern would look like and notice that the main lobe has rotated by 10 degrees and now I'll change the elevation angle
to 10 degrees as well and let me spin this around a bit and you can see that the main lobe is shifted both in Azimuth and elevation so hopefully we can start to picture what the radiation pattern looks like for the array if we shift the phase to each element in such a way that it produces these steering angles now I want to show you how the main lobe changes and distorts as the steering angle increases well past 10 degrees and to do that I created a script that Loops through and changes the steering angle
from minus 90 degrees to positive 90 degrees and this is the result watch the main beam as I slowly increase Azimuth angle the beam rotates further from the bore sight but watch how right about here it really starts to widen out and get distorted now when the beam is near the bore sight it's a sharper beam than it is when it's steered further away again all we're changing here is the phase to each element and not the array geometry itself anytime you try to steer too far from the bore sight the main beam gets a
little more Blobby and less Sharp because of this there really is only about 120 degrees of usable steering angle in both Azimuth and elevation directions instead of the full 180 degrees so if you need a larger steering range this is where things like multiple arrays oriented in different directions or conformal arrays that physically curve can become beneficial now this is by no means the whole story of phased array antennas and in the next video we're going to continue talking about the larger concept of beam forming we'll cover how we can go further than just transmitting
and receiving a signal from a certain direction by doing things like forming multiple beams for multi-function radar and adapting the beam real time to maximize signal and minimize noise and other interferences so if you don't want to miss that or any other future Tech talk videos don't forget to subscribe to this channel also if you want to check out my channel control system lectures you can find more control theory topics there as well thanks for watching and I'll see you next time
