EM.Libera Tutorial Lesson 3: Computing The Radar Cross Section Of Metallic, Dielectric & Composite Targets
Contents
What You Will Learn
In this tutorial you will learn how to build and analyze solid geometric objects made of metal and dielectric materials. You will also build and analyze a composite target with conjoined metal and dielectric parts.
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Getting Started
Open the EM.Cube application and switch to EM.Libera. Start a new project with the following parameters:
Drawing a Metal Sphere
When you start drawing in EM.Libera for the first time in a blank project, a default PEC group called "PEC_1" is created in the navigation tree to hold your CAD objects. In other words, all the objects you draw are assumed to be perfect electric conductors by default. Click on the Sphere 
button of the Object Toolbar or select the menu item Object → Solid → Sphere.
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With the sphere tool selected, click at the origin (0,0,0) of the project workspace to start your drawing, and drag the mouse to draw a sphere. Set the Radius of the sphere to R = 150mm. When you drew a very large object, it may fill up the entire screen. 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.
Note that at the center frequency fo = 1GHz, the operating wavelength is λ0 = 300mm, and your sphere has a diameter of one wavelength.
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Defining the Plane Wave Source
In order to analyze electromagnetic scattering from targets, you illuminate them with a plane wave source and compute the scattered (or reflected) fields. To define a plane wave source, right click on the Plane Waves item of the Sources section in the navigation tree and select Insert New Source… from the contextual menu. The Plane Wave Dialog opens up with a number of default settings. Your plane wave source will have an "Amplitude" of 1V/m and a zero "Phase". You will keep the default TMz polarization. In the “Incident Angle” section of the dialog you need to enter the elevation θ and azimuth φ angles in the standard spherical coordinate system. Accept the default values: θ = 180° andφ = 0°, which represent an X-polarized normally incident plane wave. Note that In EM.Cube, plane waves are characterized by their unit propagation vector. Therefore, for a downward-looking normally incident plane wave, θ = 180°, and for an upward looking wave (along the positive Z-axis), θ = 0°.
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After you define the plane wave source, a magenta box appears around your physical structure. A trident also appears at the boundary of the box showing the propagation vector in magenta, the electric polarization vector in dark blue and the magnetic polarization vector in turquoise.
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Defining the Simulation Observables
Define a default current distribution observable called "CD_1". Then, define a Radar Cross Section (RCS) observable. Right-click on the Radar Cross Sections item in the navigation tree and select Insert New RCS... from the contextual menu. The Radar Cross Section dialog opens up. In the "RCS Type" section of the dialog, select the default Bistatic RCS option. Change the values of Angle Increment for both Theta and Phi from the default value of 5° to 3°, and close the dialog.
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Running a Surface MoM Simulation of the Spherical Metal Target
EM.Libera uses a triangular surface mesh generator to discretize the surface and solid geometric objects. The triangular cells are usually generated to be as regular as possible with almost equal surface areas throughout the entire mesh. Keep the default mesh density of 10 cells per wavelength and generate the mesh of your spherical target.
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At this time, your project is ready for the simulation of your metal target structure. Open the simulation run dialog. You will notice that the Surface Method of Moments (SMOM) solver has been selected as the simulation engine type. This is EM.Libera's default solver and will be used for the analysis of your solid target.
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Run a single-frequency SMOM simulation. The output message window reports some simulation statistics:
Number of mesh nodes: 325
Number of mesh cells: 646
MPI Enabled: Running using 4 Processor(s)...
Size of linear system (J's and M's): 969
3D simulation data are visualized in EM.Cube’s project workspace, and the plots are usually overlaid on the physical structure. For this reason, it might be necessary to hide the geometric objects which might obstruct the plots. You can also freeze the geometric objects. In that case, you will see a wireframe outline of the frozen object and you cannot select it. To freeze an object, right-click on its surface in the project workspace or right-click on its name in the navigation tree and select Freeze from the contextual menu.
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It is recommended that you freeze objects with curved surfaces in the project workspace before 3D data visualization. |
First, visualize the three components of the electric surface currents as well as the total current distribution on the metal sphere. Since you have only a PEC surface, M = 0.
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Next, visualize the theta and phi components of the RCS as well as the total 3D RCS of your spherical target.
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Next, open the data manager and plot the 2D data files "RCS_1_RCS_Polar_YZ.CPX" and "RCS_1_RCS_Polar_ZX.CPX".
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Simulating a Spherical Dielectric Target
In order to create a dielectric object, first you have to define a dielectric material group in the navigation tree. Right-click on the Dielectric item in the Physical Structure section of the navigation tree and select Insert New Dielectric... from the contextual menu. The New Dielectric Dialog opens up. Besides a name and a color, dielectric objects have other properties like the permittivity εr and conductivity σ. You can enter these values manually or you can use EM.Libera's material list.
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Click on the Material button of the dialog to open the "Material List" dialog. You can type any letter on your keyboard and move the selection to the first material starting with that letter. Select "PVC" with εr = 4.
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Click the OK button of the materials list to return to the dielectric material dialog. You will now see the material properties of PVC copied to this dialog. Close this dialog and return to the project workspace.
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When you create a new material group, it becomes the active group in the navigation tree. This means that all the new objects your draw in the project workspace will belong to this active group. You can change the active group to any group in the navigation tree by right-clicking on the group's name and selecting Activate from the contextual menu.
You can delete the PEC sphere you drew earlier and draw a new dielectric sphere. Or alternatively, you can move the object "Sphere_1" from the group "PEC_1" to the new dielectric group. To do the latter, right-click on the name of "Sphere_1" in the navigation tree and select Move To → EM.Libera → Dielectric_1 from the contextual menu. The color of the sphere turns into light green, that of the dielectric group.
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Run a single-frequency SMOM simulation. The output message window reports some simulation statistics:
Number of mesh nodes: 325
Number of mesh cells: 646
MPI Enabled: Running using 4 Processor(s)...
Size of linear system (J's and M's): 1938
Note that the size of the linear system has been doubled as the dielectric object involve both electric and magnetic current unknowns. The current distribution section of the navigation tree now has both J and M plots. The total electric and magnetic current distribution maps are shown in the figures below:
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Next, visualize the total 3D RCS of your spherical target.
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Next, open the data manager and plot the 2D data files "RCS_1_RCS_Polar_YZ.CPX" and "RCS_1_RCS_Polar_ZX.CPX".
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Building & Simulating a Composite Target
In this part of the tutorial lesson, you will construct a physical structure that contains both PEC and dielectric parts. First, open the property dialog of your dielectric object "Sphere_1" and change its Stop Angle from its default value of 360° to 180°. This turns your object into a hemisphere.
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Next, activated your PEC_1 group from its contextual menu and draw a PEC rectangle strip object. To draw a rectangle, click the Rectangle Strip 
button of the Object Toolbar or select the menu item Object → Surface → Rectangle Strip.
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With the rectangle strip tool selected, click on a blank space in the project workspace and drag the mouse to draw the planar rectangle object. A property dialog pops up at the lower right corner of your screen. As you drag the mouse, you will see that the X-dimension and Y-dimension of your new object continuously change. Draw a rectangle with side dimensions of 600mm × 600mm centered at (0, 0, 0).
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The table below summarizes the properties of the two geometric objects in your project workspace:
| Part | Object Type | Material Type | Dimensions | Coordinates | Rotation Angles | Other Parameters |
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| Rect_Strip_1 | Rectangle Strip | PEC_1 | 600mm × 600mm | (0, 0, 0) | (0°, 0°, 0°) | None |
| Sphere_1 | Sphere | Dielectric_1: PVC | R = 150mm | (0, 0, 0) | (0°, 0°, 0°) | Start Angle = 0°, End Angle = 180° |
Your physical structure at this time should look like this:
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Generate and examine the mesh of your composite structure using the default mesh density.
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Run a single-frequency SMOM simulation. The output message window reports some simulation statistics:
Number of mesh nodes: 644
Number of mesh cells: 1236
MPI Enabled: Running using 4 Processor(s)...
Size of linear system (J's and M's): 2536
At the end of the SMOM simulation, visualize the total electric and magnetic current distribution maps:
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Next, visualize the total 3D RCS of your composite target. Note that there is a significant back-scatter lobe due to the presence of the metal plate.
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Next, open the data manager and plot the 2D data files "RCS_1_RCS_Polar_YZ.CPX" and "RCS_1_RCS_Polar_ZX.CPX".
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