Capacitance of Multi-Layer Capacitors: Insights and Simulations

Physics

Capacitance is a fundamental concept in physics, defined as the ratio of the amount of charge stored in a capacitor to the potential difference between its electrodes. Let's consider an example of a parallel-plate capacitor, as shown in Figure 1. In this example, the capacitor is constructed by filling the space between two square plates with blocks of three different dielectric materials.
The capacitance of each dielectric block is determined by the 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 the distance between the plates. Figure 1 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: 
 

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.
A model of the capacitor with multiple dielectrics has been created in Solidworks. The space between the parallel plates is filled by 3 different dielectric materials. The plate surface is , while the thickness of each plate is 1mm. The thickness of the dielectric block is the same as the distance between the plates: 2mm; the thickness of the 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

1. Under Materials in the EMS manager tree, right-click on Dielectric 1.
2. Select Apply Material
3. The Material Browser folder appears
4. Under “Cables” folder, choose Teflon
5. Click Apply and Close 

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 manager 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 manager tree, under Results , open the Results Table to find the 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

Conclusion