EM.Illumina Tutorial Lesson 2: Computing The Radar Cross Section Of Corner Reflectors
Contents
What You Will Learn
In this tutorial you will use a wizard to create the geometry of a trihedral corner reflector. You will learn to define near-field sensors with different orientations. You will also learn how to define new variables and run a parametric sweep simulation.
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Getting Started
Open the EM.Cube application and switch to EM.Illumina. Start a new project with the following parameters:
Building a Trihedral Corner Reflector
Click on the Trihedral Reflector Wizard 
button of the Wizard Toolbar or select the menu item Tools → Component Wizards → Trihedral Reflector.
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The geometry of a trihedral structure appears in the project workspace. The corner reflector is made up of thee conjoined orthogonal metal plates.
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The side dimension of each square plate in the default corner reflector created by the wizard is 100mm. The radar cross section (RCS) of a corner reflector is much larger than its actual physical surface area. Practical corner reflectors have geometrical dimensions much larger than the operating wavelength. The trihedral reflector created by the wizard is fully parameterized. Open the Variables Dialog by clicking the 
button on the Simulate Toolbar or selecting the menu item Simulate → Functions.... You will see a variable called "side", whose value has been set to 100.
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Select and highlight this variable in the list and click the Edit button of the variables dialog to open the "Edit Variable" dialog. In the box labeled "Definition", replace the value 100 by 500. Click OK to return to the variables dialog. Note that the definition and current value of "side" have now changed.
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You can zoom to fit your structure into the screen using the keyboard shortcut Ctrl+E or by clicking the Zoom Extents 
button of View Toolbar. At the operating frequency of 3GHz, the free-space wavelength is λ0 = 100mm. The total dimensions of your trihedral corner reflector are now 5λ0 × 5λ0 × 5λ0.
Defining the Source & Observables for Your Project
The variable "side" was defined and initiated automatically by the wizard. You can define new variables of your own. Open the variables dialog once again and add a new variable called "theta". To do so, click the Add button of the variables dialog. In the "Add Variable" dialog enter the name "theta" and the numeric value "135" for the Definition of your new variable. Repeat the same procedure and define a new variable named "phi" with the numeric value "45" as its definition.
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The variables dialog with the addition of the two new variable should now look like this:
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Next, define a plane wave source just like you did in the previous tutorial lesson. In the plane wave dialog, the default numeric values of the Incident Angles are: Theta = 180° and Phi = 0°. Replace these numerical values with the names of the two variables "theta" and "phi", respectively, as shown in the figure below:
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The magenta plane wave box appears around your physical structure. Note the location and orientation of the plane wave trident at the corner of this box. Keep in mind that you kept the default Polarization type TMz.
For the simulation observables of your project, define a current distribution observable called "CD_1" and a radar cross section observable called "RCS_1" just like in Tutorial Lesson 1. Set the values of both the theta and phi angle increments equal to 1°. For this project, you need to define three orthogonal near-field sensor observables according to the table below.
| Sensor Name | Direction | Center Coordinates | Dimensions | No. Samples |
|---|---|---|---|---|
| Sensor_1 | Z | (-45mm, -45mm, 20mm) | 550mm × 550mm × (N/A) | 110, 110, (N/A) |
| Sensor_2 | X | (230mm, -45mm, 295mm) | (N/A) × 550mm × 550mm | (N/A), 110, 110 |
| Sensor_3 | Y | (-45mm, 230mm, 295mm) | 550mm × (N/A) × 550mm | 110, (N/A), 110 |
Right-click on the Near-Field Sensors item under the "Observables" section of the navigation tree and select Insert New Observable... from the contextual menu. In the sensor dialog, first set the orientation of the field sensor plane using the Direction drop-down list. For example, the Z-direction places a horizontal sensor plane parallel to the principal XY plane. Then, enter the coordinates, dimensions along the three principal axes and the number of sample along those axes for each field sensor observable.
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The three sensor planes have been arranged such that they do not intersect any of the three reflector walls.
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Running a PO Analysis of the Trihedral Corner Reflector
Before running the PO simulation, examine the mesh of your corner reflector.
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In the case of solid geometric objects, EM.Illumina's mesh generator produces triangular cells only on the outer surface of the solid object. In the case of surface geometric objects, EM.Illumina's mesh generator produces triangular cells on both sides of the surface of the object. In other words, you will get double coincident cells with opposite normal vectors. At the default mesh density of 10 cells per wavelength, your PO simulation will involve a total of 34,752 double cells, which is quite large. open EM.Illumina's mesh settings dialog and check the box labeled All Single-Sided Cells. This will reduce the number of triangular cells to a total of 17,376, that is half the original value. The dialog also provides a check box labeled "Reverse Normal" in case the single-sided cells pick the wrong normal vector.
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Run a single-frequency analysis of your structure and visualize the simulation results. This iterative physical optics (IPO) simulation converges after 4 iterations. The figure below shows the current distribution on the three walls of the corner reflector.
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Visualize the electric and magnetic field distributions on all the horizontal and vertical field sensor planes.
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The figures below show the 3D RCS pattern of the corner reflector.
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Verifying Your Simulation Results
Besides the three principal planes, EM.Illumina also saves the 2D RCS graph in a fourth custom Phi plane cut. By default, this is the φ = 45° plane cut. This happens to be the plane cut that you are most interested in because it is the plane of the maximum RCS. Open the data manager and plot the contents of the data file "RCS_1_RCS_Cart_Custom.DAT" on a dB_Power Scale. Note the bi-static RCS has two primary maxima. One happens at (θ, φ) = (135°, 45°) with a level of 23.62dBm2 and corresponds to the forward scattering. The other happens at (θ, φ) = (45°, 225°) with a level of 18.70dBm2 and corresponds to the back-scattered echo.
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There is an analytical solution for the RCS of a trihedral corner reflector, which gives the maximum value of the RCS as:
[math] \sigma_{max} = \frac{12\pi a^4 }{\lambda_0^2} = \frac{12\pi (0.5m)^4 }{(0.1m)^2} = 235.62 m^2 = 23.72dBm^2 [/math]
where a = 500mm is the side dimension of each plate. As you can see from the above RCS plot, the result predicted by EM.Illumina's iterative Physical Optics (IPO) solver is very close to the analytical value. Contrast this with the total physical surface area of the trihedral reflector, which is merely 0.25m2 or -6dBm2.
Changing the Plane Wave Polarization
So far, you have used a TM-polarized plane wave source to illuminate your target. In this part of the tutorial lesson, open the property dialog of the plane wave source and change its Polarization to TEz. Run a new PO simulation and visualize the current distribution, near-field distributions and the 3D RCS of your target as shown in the figures below:
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