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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:

(4)

With the following parameters:

The equivalent capacitance is:

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.

To define the material for the Dielectric 1:

- Under Materials in the EMS manager tree, right-click on Dielectric 1.
- Select
**Apply Material** - The
**Material Browser**folder appears - Under “Cables” folder, choose Teflon
- 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.

To obtain capacitance results from EMS:

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

To account for the capacitance, a Floating conductor boundary condition is assigned to both plates.

To do so:

- In the EMS manager tree, Right-click on the
**Load/Restraint**folder. - Select
**Floating Conductor**. - Click inside the
**BodiesSelection**box and then select the**Topplate**. - Click OK.

For the bottom plate:

- In the EMS manger tree, Right-click on the
**Load/Restraint**folder. - Select
**Floating Conductor**. - Click inside the
**BodiesSelection**box and then select the**Bottom plate**. - Click OK.

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

This application note explores the concept of capacitance through the simulation of a parallel-plate capacitor filled with three different dielectric materials in EMS. By employing the superposition principle, the study calculates the capacitance contributed by each dielectric block and the total equivalent capacitance of the system, showcasing the impact of dielectric constants on the capacitor's overall capacitance. The simulation, created in SolidWorks and analyzed in an EMS Electrostatic study, utilizes materials like aluminum for electrodes and Teflon, polyimide, and nylon for the dielectrics. The process involves assigning materials, computing capacitance, and setting boundary conditions to accurately model the capacitor's behavior.

The findings from EMS closely align with theoretical calculations, demonstrating the software's effectiveness in predicting the capacitor's performance. The total capacitance obtained from the simulation is 6.1056 x 10^-11 F, validating the theoretical approach. This study not only reinforces the fundamental principles of capacitance but also illustrates the practical application of simulation tools in understanding and analyzing complex electrical systems. Through detailed modeling and precise simulations, EMS proves to be a valuable tool in the design and analysis of capacitive systems, offering insights that bridge theoretical physics with practical engineering solutions.

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