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HOME / Applications / Computing capacitance of a multi-material capacitor

Computing capacitance of a multi-material capacitor

Used Tools:

Physics

The capacitance is defined as the ratio of the amount of charge stored in the capacitor and the potential difference between the electrodes.
The example of a parallel-plate capacitor, in Figure1, is constructed by filling the space between two square plates with blocks of three dielectric materials.

The capacitance of each dielectric block is given by equations (1), (2) and (3):

(eq.1)

(eq.2)
(eq.3)

, and are the dielectric constants of individual dielectric materials,  is the permittivity of free space,  is the capacitor plate area and  is distance betweenthe plates. Figure1 shows that the total capacitance is formed by connecting a capacitance of the dielectric block  in parallel with a series connection of blocks and . Therefore, the equivalent capacitance is given by equation (4) as:

(4)

Figure1 - parallel plate capacitor with three dielectrics

With the following parameters:

The equivalent capacitance is:

Model

The following instructions show how to prescribe material to individual parts of your model and compute capacitance between two elements.
Model of the capacitor with multipledielectrics has been created in Solidworks. The space betweenthe parallel plates is filled by 3 different dielectric materials.Plate surface is , whilethe thickness of each plate is 1mm.Thickness of dielectric block is the same as the distance between the plates: 2mm; thickness of blocks and  is half of that:1mm (Figure 2).

The simulation is performed in the EMS Electrostatic study  . Aluminum is used as a material for the electrode plates, Teflon, polyimide and nylon are used for dielectric,and  , respectively. All these materials with their electromagnetic properties can be found in the EMS material library.

Assign material

To define material for the Dielectric 1:
1. Under Materials in the EMS manager tree, right click on the Dielectric 1.
2. Select Apply Material
3. The Material Browser folder appears
4. Under “Cables” folder, choose Teflon
5. Click Apply and Close
This procedure is repeated to assign Polyimide and Nylon to Dielectrics 2 and 3, as well as to assign Aluminum to the plates.

Figure 2 - Solid works model of a capacitor with 3 dielectrics

Compute capacitance

To obtain capacitance results from EMS:

1. In the EMS manger tree, Right-click on the Electrostatic study  folder.
2. Select Properties
3. Under General Properties, check Compute Capacitance box
4. Click OK.

Boundary Conditions

To account for the capacitance, a Floating conductor boundary condition is assigned to both plates.
To do so:
1. In the EMS manger tree, Right-click on the Load/Restraint folder.
2. Select Floating Conductor .
3. Click inside the BodiesSelection box and then select the Topplate.
4. Click OK.
For the bottom plate:
1. In the EMS manger tree, Right-click on the Load/Restraint folder.
2. Select Floating Conductor .
3. Click inside the BodiesSelection box and then select the Bottom plate.
4. Click OK.

Results

In the EMS manger tree, under Results , open the Results Table to find Capacitance matrix. EMS solution for total capacitance is F (Figure 3) and it matches the theoretical result very closely.

Figure 3 - EMS results for Capacitance