Embedded Element Pattern for Antenna Array Pattern Calculation

Hello, this is Ibrahim Nassar with Ozen Engineering, and in this demo, we will be using the Ansys HFSS 2025 R2 release to simulate the embedded antenna element radiation pattern based on unit cell analysis.

The simulation method can be used to calculate the embedded element pattern, which accounts for mutual coupling between the array elements and creates a more accurate overall array pattern based on unit cell analysis.

We will start this demo by using this antenna element, which is a simple probe-fed patch antenna designed to operate at 2.5 GHz. This antenna was created using the antenna toolkit, which can be accessed from the automation, show, act extension, launch wizard, and the HFSS antenna toolkit.

So, how do we set it up? First, we want to set the model for a unit cell analysis. The way to do that is to create a region, first an airbox to enclose the unit cell. Let's change the absolute offset and keep it 0 cm.

And now, let's change it from the positive and negative Z-axis to be about 4 cm, which is nearly like lambda over 3, and 1 cm from the bottom side. Now, we want to assign the periodic boundary conditions. To do that, we're going to right-click and go to the selection mode faces.

We're going to select this face and this face, right-click, and assign boundary coupled lattice pair, and hit next. We need to define scan angles, but let's keep it now at zero degrees, and we will define it later. Next, we're going to assign it to the other side.

By using the Ctrl key, we select these two faces, right-click, and assign boundary coupled lattice pair. Similarly, next and finish. Now, from the top side and from the bottom side, and the top side, when assigned radiation boundary, and hit OK.

So now, we have the model ready to simulate, so we can right-click and analyze it. While the simulation is running, now we can define the far-field setup to be able to look at the far-field.

By right-clicking on Radiation, insert Far-field Setup, Infinite Sphere, just call that the 3D Sphere, and Phi from 0 to 360, and Theta from minus 180 to 180. Okay, so now the conversion passes are done, so we can look at the far field.

Right-click on results, create far field report, 3D polar plot, and let's plot the gain in dB. Okay, and here's S11 of the antenna, so it resonates about 2.55 GHz.

Let's create a radiation pattern plot, so create Far Field Report, Radiation Pattern, Realize Gain here in dB, and let's look at it at V 0. Okay, so now this is the radiation pattern of the unit cell. Now, we want to create the embedded element pattern.

So, for the embedded element pattern, we need to steer the beam and look at the far-field data in the unit cell analysis only in the direction of the scan angle in theta and phi. The pattern based on the regular infinity sphere is only valid at one point.

To do that, we first need to define the scan angles, so we can go here to the lattice pair and define a variable for the scan angle. So, let's call it phiScan, and this one is thetaScan.

By default, it will be defined for the other one, and the default values here were defined to be 0, 0. Now, we define the scan angles; we need to make a coordinate system so we can look at the far field only at the point where the scan angle is pointing to.

To do that, let's go here, Modular, Coordinate System, Create, and create an offset one. Let's just place it somewhere, and then we can modify its properties. So, let's keep it as 0, 0, 0. The x-point will be cosine theta scan times cosine phi scan.

Okay, and now let's copy it, comma, now the Y point is, will be also sine phi scan. So, we define, take the projection on the Y, and the Z axis will be minus sine theta scan. Okay, so that's the x-axis. For the y-axis, let's copy this and then modify it.

It will be minus sine phi scan, and the y-point is cosine theta scan times cosine phi scan. So, we need to modify this, and for the Z point will be 0. So, now we created a coordinate system called RelativeCS1, so let's change that to embedded.

So, this is the coordinate system that we will be using to plot the far field as we steer the beam, so we can look at the far field data only in the direction where we steer the beam at, and hit OK. So, now we defined this coordinate system. Next, we want to define an infinite sphere for that.

We're going to create a new far setup infinite sphere, and we want to be looking only at one point now, so 0, 0 to 1, and 0, 0 to 1, and we want to change it to be looking at the embedded coordinate system. And let's call this also Embedded. And we hit OK.

Now, we want to define an optiSLang parametric sweep to do the different scan angle for steering the beam. So, right-click on optiSLang, add parametric sweep, click on add, and let's just change for now the theta scan. And similarly, you can do it for any scan angle needed.

So, let's do it like from 0 to 90, and let's just do it by 10 degrees. You can do more points. Okay, so these are 10 points, and let's copy the mesh here and solve just with the copied mesh, give it okay, and now we can start the simulation.

Okay, so now, after the simulation is done, we can look at create the plot of the embedded element pattern. To do that, right-click on results, create far field report. The first change we need to make is the geometry here. We want to change it to be the embedded radiation sphere we defined.

And let's keep it, just look at the gain here in dB. And we want to change the primary sweep, but first, we have to go to families and make a selection of all the variables, all the variations of the theta scan we simulated. And now it will be an option under primary sweep, so we select theta scan.

And now we click on the report.

So, this is now the plot of the embedded element pattern, which is a more accurate representation of the actual pattern as the beam is steered, which can be then used to approximate the far-field pattern of the entire array by multiplying it with the array factor calculation.

That's all for this demo, and thank you for watching. Please contact us at https://ozeninc.com/contact for more information.