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| − | {{projectinfo|Tutorial| Analyzing Scattering from a Parabolic Dish Reflector|SMOM89.png|In this project, you will build a parabolic dish reflector excited by a plane wave source and compute its radar cross section.|
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| − | *[[CubeCAD]]
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| − | *Parabolic Curve
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| − | *Object of Revolution
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| − | *Plane Wave Source
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| − | *Far Field Observable
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| − | *Radar Cross Section
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| − | |All versions|{{download|http://www.emagtech.com|EM.Libera Lesson 7|[[EM.Cube]] 14.10}} }}
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| − | ===Objective:===
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| − | To construct a parabolic dish reflector by revolving a parabola curve, excite it using plane wave source and compute its RCS.
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| − | ===What You Will Learn:===
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| − | In this tutorial lesson, you will learn more basic CAD operations like revolution of [[Curve Objects|curve objects]] and how to modify objects of revolution.
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| − | ==Getting Started==
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| − | Open the [[EM.Cube]] application and switch to [[Physical Optics Module]]. Start a new project with the following attributes:
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| − | #Name: [[SMOMLesson3]]
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| − | #Length Units: cm
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| − | #Frequency Units: GHz
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| − | #Center Frequency: 1.2GHz
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| − | #Bandwidth: 1GHz
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| − | A parabolic dish reflector can be constructed by revolving a parabola curve about its axis of symmetry. In this lesson, you will first draw a parabola and then use the Revolve Tool to create a 3D object of revolution.
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| − | ==Building a Parabolic Dish Reflector==
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| − | Draw a parabola using the "Parabola Tool" on the Object Toolbar. The first point you click on the project workspace will be the vertex of the parabola. Click at the original of coordinates (0, 0, 0) and drag the mouse along the X-axis. This will set the X-axis as the axis of symmetry of the parabola. Click at the second point to establish the focus of the parabola. Click at point (100cm, 0, 0). This will set the focal length of the parabola to 100cm. Note that at the operating frequency of 1.2GHz, the free-space wavelength is λ<sub>0</sub> = 25cm. Now drag the mouse to the right to establish the aperture diameter (or axial length). Set the "Diameter" to 250cm (10λ<sub>0</sub>). Aperture diameter and axial length are related to each other. When you set one parameter, the other is updated accordingly. At this time, you parabola is complete and shows an axial length of 39.05cm.
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| − |
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:SMOM83.png|thumb|350px|The property dialog of parabola curve.]]
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| − | </td>
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| − | <td>
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| − | [[Image:PHO101.png|thumb|350px|The drawn parabola curve.]]
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| − | </td>
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| − | <td>
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| − | [[Image:PHO102.png|thumb|350px|Hovering over the parabola object to highlight its vertex snap point.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − | Next, you will revolve the parabola object about its axis of symmetry. You can do this operation in a more formal way using [[EM.Cube]]'s "Revolve Tool" [[Image:fig-revolvetool.png]] on the CAD Toolbar. However, there is a much simpler way for revolving parabolas. Simply hover the mouse over the parabola curve to highlight its vertex snap point and then type the letter <b>V</b> on the keyboard, which is the keyboard shortcut for the Revolve Tool. The original parabola is replaced with a 3D object of revolution. A new property dialog for the object of revolution pops up at the lower right corner of the screen. Click the <b>OK</b> button to close it and accept the changes.
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| − | Your parabolic dish reflector will be illuminated using a plane wave source from the right side of the screen. Define a plane wave source with the default TMz polarization and incident angles: θ<sub>I</sub> = 90° and φ<sub>I</sub> = 180°. Also define a current distribution observable and a far field Radar Cross Section observable with an Angle Increment of 1° for both Theta and Phi angles.
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| − |
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:SMOM84.png|thumb|350px|The property dialog of the object of revolution.]]
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| − | </td>
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| − | <td>
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| − | [[Image:SMOM85.png|thumb|350px|The transformed 3D object of revolution.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − | ==Examining the Mesh of the Parabolic Dish==
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| − | Before you run the simulation, let's first take a look at the mesh of your parabolic dish reflector. Since your parabolic reflector is electrically large, [[EM.Cube]] will generate a very large mesh involving thousands of triangular cells. To make the simulation more manageable, open the Mesh Settings Dialog and reduce the Mesh Density to 6 cells per wavelength. Now generate the mesh and view it. In the "Mesh View Mode", you can rotate the view using the right mouse button and see the mesh of the dish along its parabolic contour. It may seem a bit jagged, representing the resolution with which the original parabola curve was discretized. To get a smoother variation, open the Mesh Settings Dialog again, and click on the button labeled <b>Tessellation Options</b> to open up the Tessellation Options Dialog. The default value of "Curved Edge Angle Tolerance" is 15°. Change it to 10° and regenerate the mesh once again. This time you will see a much smoother surface triangular mesh of the parabolic dish.
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:SMOM87.png|thumb|300px|The MoM3D Mesh Settings dialog.]]
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| − | </td>
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| − | <td>
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| − | [[Image:SMOM88.png|thumb|300px|THe Tessellation Options dialog.]]
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| − | </td>
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| − | <td>
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| − | [[Image:SMOM86.png|thumb|400px|The generated surface triangular mesh with a Curved Edge Angle Tolerance of 10°.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − |
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| − | ==Running the Surface MoM Analysis==
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| − | Run a Surface MoM simulation of the parabolic dish reflector. Just like the previous tutorial lesson, open the Surface MoM Engine Settings dialog, set the solver type to TFQMR, check the "Use Matrix Preconditioner" checkbox, check the "Use MPI Solver" checkbox with the maximum number of your computer's cores, and also check the "Use AIM Accleration" checkbox.
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| − | This simulation involves a total of 7,030 cells and its linear system size is N = 10,451 . The TFQMR iterative solver converges after 266 iterations with the default error tolerance of 1e-3.
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| − | Visualize the current distribution on the surface of the reflector and view its 3D RCS plots.
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| − |
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:SMOM89.png|thumb|450px|Current distribution of the parabolic dish reflector.]]
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| − | </td>
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| − | <td>
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| − | [[Image:SMOM90.png|thumb|450px|3D radiation pattern plot of the parabolic dish reflector.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − | [[Image:FDTD517.png|thumb|350px|The Edit Graph Properties dialog.]]
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| − | Note how narrow the RCS beam is on the forward scattering direction. The back-scattered RCS is hardly even visible. The 2D graphs of RCS will look better if you plot them on dB scale. To do so, open the Data Manager, select and highlight the RCS data file and click the <b>Graph Props</b> button of the dialog. In the Edit Graph Properties dialog, select the "dB-Power Scale" option from the Data Format drop-down list. This is due to the fact that RCS is a power-scale quantity as opposed to the far-field radiation patterns, which are field-scale quantities. The figures below show the 2D Cartesian and polar graphs of the RCS in the XY and ZX planes plotted in EM.Grid.
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| − | Keep in mind that the 2D Cartesian XY plane RCS or radiation pattern shows the far field quantities as a function of φ (0° ≤ φ ≤ 360°) in the azimuth plane. The 2D Cartesian YZ plane RCS or radiation pattern shows the far field quantities as a function of θ (0° ≤ θ ≤ 180°) in the elevation planes φ = 90° and φ = 270°. The 2D Cartesian ZX plane RCS or radiation pattern shows the far field quantities as a function of θ (0° ≤ θ ≤ 180°) in the elevation planes φ = 0° and φ = 180°. For convenience, the θ angle is represented by negative values in the φ = 180° and φ = 270° planes.
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:SMOM91.png|thumb|450px|2D Cartesian graph of the XY plane RCS of the parabolic dish reflector.]]
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| − | </td>
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| − | <td>
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| − | [[Image:SMOM93.png|thumb|450px|2D polar graph of the XY plane RCS of the parabolic dish reflector.]]
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| − | </td>
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| − | </tr>
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| − | <tr>
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| − | <td>
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| − | [[Image:SMOM92.png|thumb|450px|2D Cartesian graph of the ZX plane RCS of the parabolic dish reflector.]]
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| − | </td>
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| − | <td>
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| − | [[Image:SMOM94.png|thumb|450px|2D polar graph of the ZX plane RCS of the parabolic dish reflector.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − | To verify your simulation results, let's examine the RCS of a flat circular plate having the same area as the aperture of your paraboloid. The physical optics RCS of a flat circular plate of radius R is given by:
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| − | <math> \sigma = 4\pi \frac{A^2}{\lambda_0^2} = 4\pi \frac{ \left( \pi R^2 \right)^2}{\lambda_0^2} = 4\pi \left( \frac{ \pi (1.25)^2 }{0.25} \right)^2 = 4,844.73m^2 = 36.85dBm^2</math>
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| − | which is in very good agreement with [[EM.Cube]]'s computed RCS value of 4,823m<sup>2</sup> or 36.83dBm<sup>2</sup>.
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| − | ==Changing the Focal Length of the Parabola==
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| − | Next, you will change the focal length of the generating parabolic curve and see its effect on the RCS of the dish reflector. When you revolve a curve or any other object into a 3D object of revolution, you can still access the property dialog of the "Parent Object". If you open up the property of the object of revolution, you will see a button labeled "Edit Primitive". Pressing this button opens up the property dialog of the original parabola curve. In the latter property dialog, change the "Focal Length" to 50cm. Make sure that you type in 250cm for the "Aperture" diameter to update the Axial Length of the parabola. Click <b>OK</b> to close the property dialog of the parabola primitive and then click <b>OK</b> to close the property dialog of the object of revolution. You will notice that the shape of the dish reflector has now changed. The object of revolution has become deeper corresponding to an axial length of 78.13cm, which is twice as large as the previous case.
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:SMOM103.png|thumb|350px|Changing the focal length in the property dialog of the primitive parabola curve.]]
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| − | </td>
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| − | <td>
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| − | [[Image:SMOM104.png|thumb|350px|The property dialog of the modified paraboloid object of revolution.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − | [[Image:SMOM96.png|thumb|300px|The triangular surface mesh of the parabolic dish reflector with larger axial length.]]
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| − | Run a new Surface MoM analysis of this modified structure and visualize the simulation results. The mesh of the structure in this case involves a total of 8,678 cells, and the size of the linear system has increased to N = 12,923. The TFQMR solver converges after 264 iterations but after a much linger computation time due to the increased system size. Visualize the simulation results as shown in the figures below:
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:SMOM97.png|thumb|450px|Current distribution of the parabolic dish reflector with larger axial length.]]
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| − | </td>
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| − | <td>
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| − | [[Image:SMOM98.png|thumb|380px|3D radiation pattern plot of the parabolic dish reflector with larger axial length.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − | Note that the maximum RCS in the forward-scattered direction has decreased to 4,515m<sup>2</sup>. This is obviously due to the increased depth of the paraboloid, which no loner resembles a flat circular aperture in the far field zone. The figures below show the dB-scale 2D graphs of the radiation patterns in the XY and ZX planes plotted in EM.Grid. Note that the backscattered RCS has now increased to about 26dBm<sup>2</sup>, which is 10dB higher than the previous case.
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:SMOM99.png|thumb|450px|2D Cartesian graph of the XY plane radiation pattern of the parabolic dish reflector with larger axial length.]]
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| − | </td>
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| − | <td>
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| − | [[Image:SMOM101.png|thumb|450px|2D polar graph of the XY plane radiation pattern of the parabolic dish reflector with larger axial length.]]
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| − | </td>
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| − | </tr>
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| − | <tr>
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| − | <td>
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| − | [[Image:SMOM100.png|thumb|450px|2D Cartesian graph of the ZX plane radiation pattern of the parabolic dish reflector with larger axial length.]]
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| − | </td>
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| − | <td>
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| − | [[Image:SMOM102.png|thumb|450px|2D polar graph of the ZX plane radiation pattern of the parabolic dish reflector with larger axial length.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − | {{EMCUBE directory}}
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| − | [[EM.Cube | Back to EM.Cube Wiki Main Page]]
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