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| − | {{projectinfo|Tutorial| Modeling Periodic Frequency Selective Surfaces|PMOM255.png|In this project, you will build and analyze a periodic planar structure illuminated by a plane wave source.|
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| − | *[[CubeCAD]]
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| − | *Periodicity
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| − | *Plane Wave Source
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| − | *Reflection Coefficient
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| − | *Transmission Coefficient
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| − | *Oblique Incidence
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| − | |All versions|{{download|http://www.emagtech.com/downloads/ProjectRepo/EMPicasso_Tutorial_5.zip EM .Picasso Lesson 5}} }}
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| − | ===Objective:===
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| − | To construct a periodic planar structure in [[EM.Cube]]’s [[Planar Module]], excite it with a plane wave source and compute its reflection and transmission characteristics.
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| − |
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| − | ===What You Will Learn:===
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| − | In this tutorial lesson you will use [[EM.Cube]]'s spectral domain periodic Planar MoM simulation engine and will learn how to define plane wave sources.
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| − |
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| − | ==Getting Started==
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| − | Open the [[EM.Cube]] application and switch to [[Planar Module]]. Start a new project with the following attributes:
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| − | *Name: EMPicasso_Lesson_5
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| − | *Length Units: mm
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| − | *Frequency Units: GHz
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| − | *Center Frequency: 9GHz
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| − | *Bandwidth: 14GHz
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| − | *Number of Finite Substrate Layers: 1
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| − | **Top Half-Space: Vacuum
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| − | **Middle Layer: ROGER RT/Duroid 5880, ε<sub>r</sub> = 2.2, μ<sub>r</sub> = 1, σ = σ<sub>m</sub> = 0, thickness = 6mm
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| − | **Bottom Half-Space: Vacuum
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| − |
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| − | ==Drawing the Periodic Unit Cell==
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| − | Define a PEC group called PEC_1 and draw a rectangle strip of dimensions 3mm × 12mm. Open the Periodicity Dialog of the [[Planar Module]] by right-clicking on the <b>Periodicity</b> item of the Navigation Tree and selecting <b>Periodicity Settings...</b> from the contextual menu. Check the box labeled <b>Periodic Structure</b> and set the <b>Spacing</b> equal to 15mm along both X and Y directions. Leave the "Offset" boxes with their default zero values.
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| − |
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:PMOM250.png|thumb|400px|Periodicity Settings.]]
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| − | </td>
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| − | <td>
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| − | [[Image:PMOM251.png|thumb|460px|The geometry of the periodic model.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − |
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| − | [[Image:PMOM252A.png|thumb|350px|The Plane Wave Source dialog.]]
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| − |
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| − | ==Defining a Plane Wave Source==
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| − | Plane wave source are used to illuminate and excite periodic surfaces and compute their reflection and transmission characteristics. To define a plane wave source, right-click on the <b>Plane Waves</b> item of the Navigation Tree and select <b>Insert New Source...</b> from the contextual menu. This opens up the Plane Wave Source dialog. By default, a downward-looking normally incident plane wave source is assumed. This corresponds to incident Theta and Phi angles of 180° and 0°, respectively. Also, the default polarization of plane wave source is "TMz". You can also choose "TEz" or circular polarizations RCPz and LCPz.
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| − |
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| − | {{Note|In [[EM.Cube]], the incident angles of a plane wave source correspond to its propagation vector.}}
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| − |
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| − | For this part of the tutorial lesson, you will start with the default plane wave source and then change its polarization as well as its incident Theta and Phi angles.
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| − | [[Image:PMOM252.png|thumb|350px|Meshed printed dipole with Planewave excitation.]]
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| − | ==Running a Periodic Planar MoM Analysis==
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| − | Set the planar mesh density to 30 cells per effective wavelength. View and inspect the generated mesh. Also define a default current distribution observable.
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| − |
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| − | {{Note|If your structure is periodic and excited by a plane wave source, [[EM.Cube]] always computes its reflection and transmission coefficients without a need to define an observable.}}
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| − | Run a quick planar MoM analysis of your periodic planar surface. At the end of the simulation, read the values of the computed reflection and transmission coefficients in the output message window. Also visualize the current distribution on the surface of the strip. Repeat this procedure for the following combination of source polarization and incident Theta and Phi angles:
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| − |
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| − |
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| − | {| border="0"
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| − | |-
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| − | | valign="top"|
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| − | | valign="bottom"|
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| − | {| class="wikitable" style="text-align: center;"
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| − | |-
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| − | ! scope="col"| Source Case
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| − | ! scope="col"| Polarization
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| − | ! scope="col"| Theta
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| − | ! scope="col"| Phi
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| − | ! scope="col"| Reflection Coefficient
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| − | ! scope="col"| Transmission Coefficient
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| − | |-
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| − | ! scope="row"| 1
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| − | | TMz
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| − | | 180°
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| − | | 0°
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| − | | -0.369501 + 0.0143261j
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| − | | -0.124906 - 0.920686j
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| − | |-
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| − | ! scope="row"| 2
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| − | | TEz
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| − | | 180°
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| − | | 0°
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| − | | -0.908299 - 0.222347j
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| − | | -0.344712 - 0.0820254j
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| − | |-
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| − | ! scope="row"| 3
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| − | | TEz
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| − | | 135°
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| − | | 0°
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| − | | -0.963313 + 0.103053j
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| − | | 0.0409091 - 0.11252j
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| − | |-
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| − | ! scope="row"| 4
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| − | | TEz
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| − | | 135°
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| − | | 45°
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| − | | -0.781353 - 0.0441467j
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| − | | -0.165279 - 0.48628j
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| − | |-
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| − | |}
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| − |
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| − |
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:PMOM253.png|thumb|400px|Electric field distribution on periodic strip with a TMz-polarized plane wave source: θ = 180° and φ = 0°.]]
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| − | </td>
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| − | <td>
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| − | [[Image:PMOM254.png|thumb|400px|Electric field distribution on periodic strip with a TEz-polarized plane wave source: θ = 180° and φ = 0°.]]
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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:PMOM255.png|thumb|400px|Electric field distribution on periodic strip with a TEz-polarized plane wave source: θ = 135° and φ = 0°.]]
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| − | </td>
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| − | <td>
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| − | [[Image:PMOM256.png|thumb|400px|Electric field distribution on periodic strip with a TEz-polarized plane wave source: θ = 135° and φ = 45°.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − |
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| − | ==Running an Adaptive Frequency Sweep==
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| − | In this part of this tutorial lesson, let's run a frequency sweep of your periodic surface to examine its frequency response. But first open the property dialog of the plane wave source and set its polarization to "TEz" with normal incidence, i.e. θ<sub>s</sub> = 180° and φ<sub>s</sub> = 0°. Run an adaptive frequency sweep with the following [[parameters]]:
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| − | Frequency Sweep Type: Adaptive
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| − | *Start Frequency: 2GHz
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| − | *End Frequency: 16GHz
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| − | *Min No. of Frequency Samples: 5
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| − | *Max No. of Frequency Samples: 15
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| − | *Convergence Criterion: 0.02
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| − | Start the adaptive frequency sweep simulation and wait until it convergence. You may get a message asking if you want to continue as the required error criterion was not met within the specified maximum number of samples. Let the program continue until converges successfully. Open the Data Manager and plot the data files "REFLECTION_RationalFit.CPX" and "TRANSMISSION_RationalFit.CPX" in EM.Grid. The figures below show the computed reflection and transmission coefficients as a function of frequency for normal plane wave incidence with a TEz polarization.
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| − |
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:PMOM260.png|thumb|400px|Plot of the magnitude and phase of the reflection coefficient of the strip FSS with normal TEz incidence.]]
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| − | </td>
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| − | <td>
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| − | [[Image:PMOM261.png|thumb|400px|Plot of the magnitude and phase of the transmission coefficient of the strip FSS with normal TEz incidence.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − |
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| − |
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| − | Finally, run an adaptive frequency sweep for a case of oblique plane wave incidence. Keep the TEz polarization and set the incident angles to θ<sub>s</sub> = 135° and φ<sub>s</sub> = 0°. This represent a plane source propagating downward with an angle of 45°off the normal to the surface. Note how the frequency response changes with the angle of incidence.
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| − |
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:PMOM262.png|thumb|400px|Plot of the magnitude and phase of the reflection coefficient of the strip FSS with oblique TEz incidence.]]
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| − | </td>
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| − | <td>
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| − | [[Image:PMOM263.png|thumb|400px|Plot of the magnitude and phase of the transmission coefficient of the strip FSS with oblique TEz incidence.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − |
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| − | ==The Special Case of a Periodic Screen==
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| − | In the last part of this tutorial lesson, you will see what happens if you set the length of the strip equal to the Y-period. Open the property dialog of Rect_Strip_1 and set its Y Dimension equal to 15mm. Generate and view the planar mesh of the modified structure. As you can see from the figures below, in this case, the metal strip is considered to be extended to infinity along the Y direction. As a result, an extra row of rectangular cells are placed at the top of the unit cell beyond the periodic boundary to ensure current continuity from this unit cell to the adjacent one.
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| − |
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| − | {{Note|If an object touches the periodic boundary, it is assumed to extend to the neighboring unit cell. In that case, [[EM.Cube]] extends the planar mesh beyond the periodic boundary to ensure the current continuity. It is the user's responsibility to enforce the symmetry of the unit cell structure at the left and right boundary walls or at the top and bottom boundary walls to accommodate the geometric continuity across the neighboring unit cells.}}
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| − |
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:PMOM264.png|thumb|400px|The geometry of the periodic infinite metal strip.]]
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| − | </td>
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| − | <td>
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| − | [[Image:PMOM265.png|thumb|400px|The extended mesh of the periodic infinite metal strip.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − | Keep the TEz polarization and set the incident angles to θ<sub>s</sub> = 180° and φ<sub>s</sub> = 0°. Then run a quick planar MoM analysis of the new periodic planar surface. At the end of the simulation, read the values of the computed reflection and transmission coefficients in the output message window:
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| − | Reflection Coefficient: -0.516582 + 0.266943j
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| − | Transmission Coefficient: 0.276652 - 0.765081j
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| − | Also visualize the current distribution on the surface of the infinite metal strip. As you can see from the figure below, there is no field variation along the Y direction, because the strip has an infinite extent along that direction.
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:PMOM266.png|thumb|400px|Electric field distribution on the infinite strip FSS with normal TEz incidence.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − | Finally, run an adaptive frequency sweep of the infinite metal strip FSS with the same frequency settings as in the previous case and plot the R/T coefficients vs. frequency. You can see that the frequency response in this case is entirely different than the previous case with a finite-sized periodic strip.
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| − | <table>
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| − | <tr>
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| − | <td>
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| − | [[Image:PMOM267.png|thumb|400px|Plot of the magnitude and phase of the reflection coefficient of the infinite strip FSS with normal TEz incidence.]]
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| − | </td>
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| − | <td>
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| − | [[Image:PMOM268.png|thumb|400px|Plot of the magnitude and phase of the transmission coefficient of the infinite strip FSS with normal TEz incidence.]]
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| − | </td>
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| − | </tr>
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| − | </table>
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| − |
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| − | {{Picasso Details}}
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| − | [[EM.Cube | Back to EM.Cube Wiki Main Page]]
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