Dielectric Shielding Comparison

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Dielectric Shielding Comparison

The dielectric shielding boundary condition is meant to approximate a thin layer of material with high relative permittivity compared to its surroundings. This boundary condition is available for electrostatic field modeling. This example compares the dielectric shielding boundary condition to a full-fidelity model and discusses the range of applicability of this boundary condition.

Figure 1: A two-dimensional parallel plate capacitor in free space. A thin-walled circular inclusion between the plates distorts the electric field.

Model Definition

The situation being modeled is shown in Figure 1. Two parallel plates in free space (relative permittivity, εr = 1) have a voltage difference applied to them, forming a capacitor. Between these plates there is a 1 cm outer diameter circular inclusion with a wall thickness of 1mm. The walls are made of a high dielectric (εr = 20) material.

The walls of this inclusion are modeled two ways, first using a full fidelity model that includes the thickness of the walls, and also using the dielectric shielding boundary condition. The inside of the inclusion has the same properties as free space. The two models are separate, but are being modeled simultaneously for comparison.

The location of the dielectric shielding condition is at the centerline, midway between the inner and outer radii of the full fidelity model. Note that, when using the dielectric shielding condition, the total volume of the surrounding material is slightly larger, since the thickness of the wall is not being explicitly modeled.

Results and Discussion

The electric field and isolines of the voltage is plotted in Figure 2. The field lines can be observed to deform toward the inclusion. The solutions for the full fidelity and electric shielding model agree well.

Figure 2: Isolines of the voltage field, and streamlines of the electric field are plotted. The lines are colored according to the strength of the electric field, and the background gray-scale plot is of the electric field. The full fidelity (left) and dielectric shielding (right) solutions are almost identical.

The dielectric shielding boundary condition can be used in cases where the thickness of the boundary being approximated is much smaller than the characteristic size of the model domain, and when the relative permittivity of the layer is greater than the surrounding medium. When this boundary condition can be used, the resulting mesh size is much smaller, saving solution time and memory.

ACDC_Module/Capacitive_Devices/dielectric_shielding_comparison

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select .

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4

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In the tree, select .

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

Global Definitions

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In the window, under click .

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Value	Description
er_a	1	1	Relative permittivity, free space
er_b	20	20	Relative permittivity, dielectric
V0	1[V]	1 V	Applied voltage

Rectangle 1 (r1)

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 8.

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In the text field, type 10.

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Locate the section. In the text field, type 0.1.

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In the text field, type -5.

Rectangle 2 (r2)

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 3.5.

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Locate the section. In the text field, type 0.1.

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In the text field, type 2.

Fillet 1 (fil1)

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In the toolbar, click

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On the object , select Points 2 and 3 only.

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In the window for , locate the section.

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In the text field, type 0.5.

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In the toolbar, click

and choose .

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Select the object only.

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In the window for , locate the section.

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In the text field, type -5.

Mirror 1 (mir1)

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In the toolbar, click

and choose .

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Click in the window and then press Ctrl+A to select all objects.

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In the window for , locate the section.

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Select the check box.

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.

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button in the toolbar.

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 0.95.

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In the text field, type 180.

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Locate the section. In the text field, type 0.1.

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Locate the section. In the text field, type -90.

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 180.

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Locate the section. In the text field, type -0.1.

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Locate the section. In the text field, type 90.

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Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (cm)
Layer 1	1[mm]

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The geometry on the left side describes the full fidelity model. The geometry on the right side replaces the thin layer with a boundary in order to use the feature.

Create a set of selections to use when setting up the physics. First, create a selection for the wall of the inclusion in the full fidelity model.

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In the toolbar, click

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Select Domains 4 and 5 only.

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Right-click and choose .

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In the dialog box, type Full fidelity in the text field.

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Add a selection for the dielectric shielding boundaries.

Dielectric shielding

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In the toolbar, click

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In the window for , locate the section.

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From the list, choose .

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Select Boundaries 42 and 43 only.

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Right-click and choose .

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In the dialog box, type Dielectric shielding in the text field.

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Add a selection for the bulk area. This is the modeling domain for the interface.

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In the toolbar, click

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Select Domains 1, 4–7, and 9 only.

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Right-click and choose .

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In the dialog box, type Model domain in the text field.

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Electrostatics (es)

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In the window for , locate the section.

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From the list, choose .

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Right-click and choose .

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Select Boundaries 22, 24, 44, and 45 only.

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In the toolbar, click

and choose .

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Select Boundaries 4, 5, 34, and 35 only.

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In the toolbar, click

and choose .

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Select Boundaries 29, 31, 46, and 47 only.

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In the window for , locate the section.

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From the list, choose .

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In the V0 text field, type V0.

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In the toolbar, click

and choose .

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Select Boundaries 6, 7, 36, and 37 only.

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In the window for , locate the section.

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From the list, choose .

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In the V0 text field, type V0.

Dielectric Shielding 1

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the ds text field, type 1[mm].

Material 1 (mat1)

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In the window, under right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	er_a	1	Basic

Material 2 (mat2)

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Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	er_b	1	Basic

Material 3 (mat3)

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Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

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Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	er_b	1	Basic

In the window, under right-click and choose .

In the toolbar, click

.

Electric Potential (es)

The default plot shows the surface plot of the electric potential. Change the expression to show the norm of the electric field.

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In the window, expand the node, then click .

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In the window for , click in the upper-right corner of the section. From the menu, choose .

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Locate the section. From the list, choose .

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Clear the check box.

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Select the check box.

Electric Potential (es)

Next, add a contour plot showing the electric potential.

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In the window, right-click and choose .

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In the window for , locate the section.

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In the text field, type 21.

Color Expression 1

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose .

Electric Potential (es)

Then, add a streamline plot of the electric field.

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In the window, right-click and choose .

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Select Boundaries 6, 29, 36, 37, 46, and 47 only.

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In the window for , locate the section.

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In the text field, type 40.

Color Expression 1

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose .

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Locate the section. Clear the check box.

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button in the toolbar.

Compare the plot with Figure 2.

Finish the result analysis by evaluating the capacitance of the system.

Global Evaluation 1

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In the toolbar, click

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
es.Q0_1/V0	F

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Global Evaluation 2

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In the toolbar, click

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
es.Q0_2/V0	F

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The capacitance should be about 13 pF in both cases.