View source for EM.Illumina Tutorial Lesson 2: Computing The Radar Cross Section Of Corner Reflectors

{{projectinfo|Tutorial| Computing The Radar Cross Section of Corner Reflectors|Illumina L2 Fig title.png|In this project, you will build a very large multi-faced PEC structure and compute its radar cross sections.|

*Wizard
*PEC Surface
*Plane Wave Source
*Current Distribution
*Field Sensor
*Radar Cross Section
|All versions|{{download|http://www.emagtech.com/downloads/ProjectRepo/EMIllumina_Lesson2.zip 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. 

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==Getting Started==

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

<div class="noprint" style="float:left;margin-right:10px">
{| border="1" class="wikitable"
|+ Starting Parameters
|-
! Name
| EMIllumina_Lesson2
|-
! Length Units
| Millimeters
|-
! Frequency Units
| GHz
|-
! Center Frequency
| 3GHz
|-
! Bandwidth
| 1GHz
|}
</div>

<div class="noprint" style="clear:both"></div>

==Building a Trihedral Corner Reflector==

Click on the <b>Trihedral Reflector Wizard</b> [[Image:TrihedralReflectorWizardIcon.png]] button of the Wizard Toolbar or select the menu item '''Tools &rarr; Component Wizards &rarr; Trihedral Reflector'''.

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<td> [[Image:Illumina L2 Fig1.png|thumb|720px|EM.Illumina's wizard toolbar.]] </td>
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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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<td> [[Image:Illumina L2 Fig5.png|thumb|720px|The geometry of the trihedral corner reflector created by the wizard.]] </td>
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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 [[File:Variable icon tn.png]] button on the '''Simulate Toolbar''' or selecting the menu item '''Simulate &rarr; Functions...'''. You will see a variable called "side", whose value has been set to 100. 

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<td> [[Image:Illumina L2 Fig2.png|thumb|550px|The Variables dialog showing the original definition of the variable "side".]] </td>
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Select and highlight this variable in the list and click the {{key|Edit}} button of the variables dialog to open the "Edit Variable" dialog. In the box labeled "Definition", replace the value 100 by 500. Click {{key|OK}} to return to the variables dialog. Note that the definition and current value of "side" have now changed.   

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<td> [[Image:Illumina L2 Fig3.png|thumb|480px|Changing the definition of the variable "side".]] </td>
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<td> [[Image:Illumina L2 Fig4.png|thumb|550px|The Variables dialog showing the modified definition of the variable "side".]] </td>
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You can zoom to fit your structure into the screen using the keyboard shortcut <b>Ctrl+E</b> or by clicking the Zoom Extents  [[Image:fdtd_zoomextents.png]] button of View Toolbar. At the operating frequency of 3GHz, the free-space wavelength is &lambda;<sub>0</sub> = 100mm. The total dimensions of your trihedral corner reflector are now 5&lambda;<sub>0</sub> &times; 5&lambda;<sub>0</sub> &times; 5&lambda;<sub>0</sub>.

== 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 {{key|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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[[Image:Illumina L2 Fig6.png|thumb|left|450px|Defining a new variable called "theta".]]
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The variables dialog with the addition of the two new variable should now look like this:

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[[Image:Illumina L2 Fig7.png|thumb|left|550px|The variables dialog showing the newly added variables "theta" and "phi".]]
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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&deg; and Phi = 0&deg;. 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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[[Image:Illumina L2 Fig8.png|thumb|left|480px|Setting the incidence angles in the plane wave dialog.]]
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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&deg;. For this project, you need to define three orthogonal near-field sensor observables according to the table below. 

{| class="wikitable" 
|-
! Sensor Name !! Direction !! Center Coordinates !! Dimensions !! No. Samples
|-
| Sensor_1 || Z || (-45mm, -45mm, 20mm) || 550mm &times; 550mm &times; (N/A) || 110, 110, (N/A) 
|-
| Sensor_2 || X || (230mm, -45mm, 295mm) || (N/A) &times; 550mm &times; 550mm || (N/A), 110, 110  
|-
| Sensor_3 || Y || (-45mm, 230mm, 295mm) || 550mm &times; (N/A) &times; 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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[[Image:Illumina L2 Fig10.png|thumb|left|480px|The field sensor dialog.]]
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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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[[Image:Illumina L2 Fig9.png|thumb|left|720px|The geometry of the trihedral corner reflector with an obliquely incident TM-polarized plane wave and three orthogonal field sensor planes.]]
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</table>

==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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[[Image:Illumina L2 Fig11.png|thumb|left|640px|The surface mesh of the trihedral 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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[[Image:Illumina L2 Fig11A.png|thumb|left|480px|EM.Illumina's mesh settings dialog.]]
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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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[[Image:Illumina L2 Fig12.png|thumb|left|640px|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.]]
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Visualize the electric and magnetic field distributions on all the horizontal and vertical field sensor planes.

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[[Image:Illumina L2 Fig13.png|thumb|left|640px|Electric field distribution on the horizontal sensor plane Sensor_1 with TMz plane wave polarization.]]
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[[Image:Illumina L2 Fig14.png|thumb|left|640px|Magnetic field distribution on the horizontal sensor plane Sensor_1 with TMz plane wave polarization.]]
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<td> 
[[Image:Illumina L2 Fig15.png|thumb|left|640px|Electric field distribution on the vertical sensor plane Sensor_3 with TMz plane wave polarization.]]
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[[Image:Illumina L2 Fig16.png|thumb|left|640px|Magnetic field distribution on the vertical sensor plane Sensor_3 with TMz plane wave polarization.]]
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The figures below show the 3D RCS pattern of the corner reflector. 

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[[Image:Illumina L2 Fig17.png|thumb|left|640px|The 3D radar cross section plot of the trihedral corner reflector on a dB scale with TMz plane wave polarization.]]
</td>
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</table>

== 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 &phi; = 45&deg; 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 (&theta;, &phi;) = (135&deg;, 45&deg;) with a level of 23.62dBm<sup>2</sup> and corresponds to the forward scattering. The other happens at (&theta;, &phi;) = (45&deg;, 225&deg;) with a level of 18.70dBm<sup>2</sup> and corresponds to the back-scattered echo.  

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[[Image:Illumina L2 Fig18.png|thumb|left|480px|The dB-scale 2D Cartesian graph of the RCS of the trihedral corner reflector in the custom &phi; = 45&deg; plnae.]]
</td>
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</table>

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 0.25m<sup>2</sup> or -6dBm<sup>2</sup>.

== 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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[[Image:Illumina L2 Fig20.png|thumb|left|640px|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.]]
</td>
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</table>

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[[Image:Illumina L2 Fig21.png|thumb|left|640px|Electric field distribution on the horizontal sensor plane Sensor_1 with TEz plane wave polarization.]]
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[[Image:Illumina L2 Fig22.png|thumb|left|640px|Magnetic field distribution on the horizontal sensor plane Sensor_1 with TEz plane wave polarization.]]
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<td> 
[[Image:Illumina L2 Fig23.png|thumb|left|640px|Electric field distribution on the vertical sensor plane Sensor_3 with TEz plane wave polarization.]]
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[[Image:Illumina L2 Fig24.png|thumb|left|640px|Magnetic field distribution on the vertical sensor plane Sensor_3 with TEz plane wave polarization.]]
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[[Image:Illumina L2 Fig25.png|thumb|left|640px|The 3D radar cross section plot of the trihedral corner reflector on a dB scale with TEz plane wave polarization.]]
</td>
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<p>&nbsp;</p>
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