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{{projectinfo|Tutorial| Analyzing A Parallel Plate Capacitor|Ferma L2 Fig title.png|In this project, you will analyze parallel plate capacitor structures made up of metal and dielectric parts.|
*[[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]
*PEC Objects
*Dielectric Objects
In this tutorial you will construct structures involving metal and dielectric objects in [[EM.Ferma]], visualize their electric field and potential and calculate their capacitance. Specifically, you will build and analyze air-filled and dielectric-filled parallel plate capacitors.
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== Getting Started ==
Activate each PEC group by right-clicking on their name in the navigation tree and selecting '''Activate''' from the contextual menu. Then draw two rectangle objects with the location and dimensions given in the table below.
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[[Image:Ferma_L2_Activate.png|thumb|left|480px|Activating PEC group in the navigation tree.]]
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To draw a rectangle, click the '''Rectangle Strip''' [[Image:RectangleStripIconx.png]] button of the Object Toolbar or select the menu item <b>Object → Surface → Rectangle Strip</b>.
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== Computational Domain, Boundary Conditions & Observables ==
You saw in the previous tutorial lesson that [[EM.Ferma]] automatically places a domain box around your objects. By default, this is a PEC box consisting of six perfect metal plates held at zero potential. In other words, the Dirichlet boundary conditions are applied to your boundary-value problem. The default domain box is placed at a certain offset distance from the largest bounding box enclosing all of your geometric objects in the project workspace. [[EM.Ferma]]'s default domain offset is 20 project units. You can change this offset value individually along the six axial directions. Open the Domain Settings Dialog by clicking the <b>3D Static Domain Settings</b> [[Image:fdtd_domainsettings2.png]] button of Simulate Toolbar or by selecting the menu item <b>Simulate → Computational Domain → Domain Settings…</b> or using the keyboard shortcut {{key|Ctrl+A}}).
In this project, the bottom capacitor plate is held at zero potential, the same as the six domain boundary walls. On the other hand, the top capacitor plate has a potential of 1V. If the domain walls are placed too close to the top plate, strong field lines will establish between them. You need to place the domain walls far enough from the top plate to make them "invisible". Set the six offset values according to the table below:
== Running an Electrostatic Analysis of Your Capacitor ==
At this time, your project is ready for simulation. Open the mesh settings dialog and change the '''Fixed Mesh Cell Size''' to Δx = Δy = Δz = 0.5mm, <i>i.e. </i> a uniform mesh along all the three principal directions. The mesh resolution was chosen so that four cells are placed between the two metal plates across the gap region.
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[[Image:Ferma L2 Fig9.png|thumb|left|640px|The electric field distribution on the vertical Sensor_1 Sensor_2 (YZ) plane.]]
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[[Image:Ferma L2 Fig10.png|thumb|left|640px|The electric potential distribution on the vertical Sensor_1 Sensor_2 (YZ) plane.]]
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Also, open the Data Manager and plot the data file in EM.Grid. As you should have expected, the results show a quite uniform electric field at the center of the parallel plate capacitor.
== Verifying the Simulation Results ==
<math> E_z = -\nabla \Phi = -\frac{d\Phi}{dz} = -500 V/m </math>
Open the Data Manager and plot the data files “Sensor_1_X_ETotal.DAT” and “Sensor_1_X_EPotential.DAT” in EM.Grid as shown below. You can clearly see a wide region of constant potential Ψ = 0.5V and of constant electric field strength |E| = 500V/m under the two metal plates.
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[[Image:Ferma L2 Fig20.png|thumb|left|720px|The voltage line and flux box defined for the parallel plate capacitor structure.]]
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You can freeze any geometric objects to see other objects hidden behind, beneath or inside it. 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 <b>Freeze </b> from the contextual menu. To unfreeze, repeat the same procedure. In the figure below, the two plates have been shown in freeze state.
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[[Image:Ferma L2 Fig13.png|thumb|left|480px600px|The new dielectric dialog.]]
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With the Box tool selected, click on a blank space in the project workspace and drag the mouse to draw the rectangular base of your box 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. When the base reaches the desired size or something close to that, click the mouse. Next, you have to give the right height to your box. Drag the mouse upward until you reach the desired height (Z-dimension). Then, click once more (<i>i.e. </i> drop the mouse). At this time, the drawing of your box is complete. You can always enter values for the dimensions or LCS coordinates at any time. While the new Dielectric_1 group is active, draw a box object according to the table below:
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