# EM.Illumina Tutorial Lesson 2: Computing The Radar Cross Section Of Corner Reflectors

 Tutorial Project: Computing The Radar Cross Section of Corner Reflectors Objective: In this project, you will build a very large multi-faced PEC structure and compute its radar cross sections. Concepts/Features: Wizard PEC Surface Plane Wave Source Current Distribution Field Sensor Radar Cross Section Minimum Version Required: All versions ' Download Link: EMIllumina_Lesson2

## 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.

## Getting Started

Open the EM.Cube application and switch to EM.Illumina. Start a new project with the following parameters:

 Name EMIllumina_Lesson2 Millimeters GHz 3GHz 1GHz

## 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.

 EM.Illumina's wizard toolbar.

The geometry of a trihedral structure appears in the project workspace. The corner reflector is made up of thee conjoined orthogonal metal plates.

 The geometry of the trihedral corner f=reflector created by the wizard.

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.

 The Variables dialog showing the original definition of the variable "side".

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.

 Changing the definition of the variable "side".
 The Variables dialog showing the modified definition of the variable "side".

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.

 Defining a new variable called "theta".

The variables dialog with the addition of the two new variable should now look like this:

 The variables dialog showing the newly added variables "theta" and "phi".

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:

 Setting the incidence angles in the plane wave dialog.

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.

 The field sensor dialog.

The three sensor planes have been arranged such that they do not intersect any of the three reflector walls.

 The geometry of the trihedral corner reflector with an obliquely incident TM-polarized plane wave and three orthogonal field sensor planes.

## Running a PO Analysis of the Trihedral Corner Reflector

Before running the PO simulation, examine the mesh of your corner reflector.

 The surface mesh of the trihedral corner reflector.

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.

 EM.Illumina's mesh settings dialog.

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.

 The Total current distribution on the three walls of the trihedral corner reflector with TMz plane wave polarization. The geometric object is in the freeze state.

Visualize the electric and magnetic field distributions on all the horizontal and vertical field sensor planes.

 Electric field distribution on the horizontal sensor plane Sensor_1 with TMz plane wave polarization. Magnetic field distribution on the horizontal sensor plane Sensor_1 with TMz plane wave polarization. Electric field distribution on the vertical sensor plane Sensor_3 with TMz plane wave polarization. Magnetic field distribution on the vertical sensor plane Sensor_3 with TMz plane wave polarization.

The figures below show the 3D RCS pattern of the corner reflector.

 The 3D radar cross section plot of the trihedral corner reflector on a dB scale with TMz plane wave polarization.

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.

 The dB-scale 2D Cartesian graph of the RCS of the trihedral corner reflector in the custom φ = 45° plnae.

There is an analytical solution for the RCS of a trihedral corner reflector, which gives the maximum value of the RCS as:

$\sigma_{max} = \frac{12\pi a^4 }{\lambda_0^2} = \frac{12\pi (0.5m)^4 }{(0.1m)^2} = 235.62 m^2 = 23.72dBm^2$

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:

 The Total current distribution on the three walls of the trihedral corner reflector with TEz plane wave polarization. The geometric object is in the freeze state.
 Electric field distribution on the horizontal sensor plane Sensor_1 with TEz plane wave polarization. Magnetic field distribution on the horizontal sensor plane Sensor_1 with TEz plane wave polarization. Electric field distribution on the vertical sensor plane Sensor_3 with TEz plane wave polarization. Magnetic field distribution on the vertical sensor plane Sensor_3 with TEz plane wave polarization.
 The 3D radar cross section plot of the trihedral corner reflector on a dB scale with TEz plane wave polarization.

## Running a Parametric Sweep of the Elevation Plane Wave Incident Angle

In this part of this tutorial lesson, you will vary the theta incident angle of the plane wave source and see how it affects the RCS of your target. As the previous part of this lesson, use a TE-polarized plane wave source to illuminate your target. In a sweep simulation, one or more parameters are varied, and the simulation engine is run for each parameter set. Open the Simulation Run dialog and choose the Parametric Sweep option from the Simulation Mode drop-down list. Click on the Settings button next to this drop-down list to open the Parametric Sweep Settings dialog.

 Selecting parametric sweep as the simulation mode in EM.Illumina's run dialog.

The sweep variables list is initially empty. On the left side of this dialog, you see a list of all the available independent variables. Select "theta" from the left table and use the right arrow --> button to move it to the right table. Another dialog titled "Sweep Variable" opens up. You have to set the start, stop and step values of your sweep variable. By default, the sweep variable is of uniform type. Enter 90, 180, and 15 for the start, stop and step values, respectively. This will create a value list of {90, 105, 120, 135, 150, 165, 180}. Note that θ = 90° corresponds to lateral plane wave incidence, while θ = 180° corresponds to downward normal plane wave incidence. Close the sweep variable dialog and then close the sweep settings dialog to return to the simulation run dialog.

 Parametric sweep settings dialog.
 Sweep variable settings dialog.
 Setting variable "theta" for parametric sweep.

Run the sweep simulation. It may take a while as a total of seven individual PO simulations must be completed. At the end of the parametric sweep, you will see a total of seven 3D RCS plots in the navigation tree. The figures below shows some of these plots.

 The 3D bistatic RCS plot of the corner reflector for theta = 90°. The 3D bistatic RCS plot of the corner reflector for theta = 135°. The 3D bistatic RCS plot of the corner reflector for theta = 180°.

Open the data manager and plot the data files "BRCS_Sweep.DAT" and "FRCS_Sweep.DAT". You should see graphs like the figures below. They shows that the forward-scatter RCS is maximized at θ = 120° as you would have expected.

 The graph of variation of back-scatter RCS as a function of theta incident angle. The graph of variation of forward-scatter RCS as a function of theta incident angle.

## Running a Parametric Sweep of the Azimuth Plane Wave Incident Angle

In the last part of this tutorial lesson, you will vary the phi incident angle of the plane wave source and see how it affects the RCS of your target. Open the Simulation Run dialog and then open parametric sweep settings dialog. In the last part, "theta" was designated as the sweep variable. Select and highlight this variable in the table on the right and use the left arrow <-- button to move it to the right table. This time select "phi" from the left table and use the right arrow --> button to move it to the right table. The sweep variable settings dialog opens up again. Set the start, stop and step values of your new sweep variable to 0, 90, and 15, respectively. This will create a value list of {0, 15, 30, 45, 60, 75, 90}. Note that φ = 0° and φ = 90° correspond to head-on plane wave incidence on the left and right vertical walls, respectively. Return to the simulation run dialog.

 Changing the sweep variable in the parametric sweep settings dialog.
 Defining the bounds of "phi" in the sweep variable settings dialog.

Run the new parametric sweep simulation. The figures below show some of the 3D RCS plots.

 The 3D bistatic RCS plot of the corner reflector for phi = 0°. The 3D bistatic RCS plot of the corner reflector for phi = 45°. The 3D bistatic RCS plot of the corner reflector for phi = 90°.

Open the data manager and plot the data files "BRCS_Sweep.DAT" and "FRCS_Sweep.DAT". As you expected, both back-scatter and forward-scatter RCS reach their maximum value for φ = 45°.

 The graph of variation of back-scatter RCS as a function of phi incident angle. The graph of variation of forward-scatter RCS as a function of phi incident angle.