## Electronics

#### Using periodic boundary conditions for simulating parallel plate capacitance in Ansys Maxwell

• ganand
Subscriber

Hi,

I have been using Ansys Maxwell (Electrostatics) for a while. I have been successfully able to model and calculate capacitances for parallel plate configuration. However, as I am moving towards complicated geometries, I need to decrease the simulation time and hardware requirements. Hence, I have been thinking about using periodic boundary conditions for parallel plate capacitance estimation. My queries are:

• How can we correctly use Symmetry boundary conditions in a parallel plate scenario?

• How can we use Master/Slave BCs to estimate the overall capacitance of the model

I am specifically looking to know which faces/surfaces do the boundary conditions have to be applied. Also, what is the correct orientation of the u-v vectors for E-field and how would that be applied.

For the purspose of this query, the model will look as in the attached image.

• akaktto
Subscriber

Hi, I have been able to model for parallel plate configuration, but I can't calculate capacitances successfully. I have already assgined voltages on each two surface. And I assign the parameter of matrix, selected two voltages. Could you pleas tell me how do you calculate the capacitance successfully? Thank you.

• Paul Larsen
Ansys Employee

For symmetry conditions, you can use them whenever both geometric and electrical symmetries are consistent.  Geometric symmetries are easy to tell, but electrical symmetries might not be permitted in all conditions.  For example, if you have 4 spheres located on the corners of a square, then there is an easy quarter geometric symmetry due to the box geometry, but the electrical symmetry would depend on the voltages applied to each sphere, and would only be true for certain combinations of equal and/or opposite voltages on the 4 objects.

Similarly for periodic structures, you could use symmetry boundaries when there is appropriate electrical symmetry conditions (fields either completely tangential or perpendicular to a plane). If the fields are not parallel/perpendicular to any periodic plane, then you can use master/slave BCs on planes where the geometry repeats.  If the electric fields are completely between the two parallel plates (no fringing), then you only need to model the area between the plates with the top/bottom faces assigned as 2 different voltages, and the side faces of the vacuum assigned as symmetry/periodic.  If you do have fringing on the sides, then you would have a larger region object, and you can assign the symmetry/periodicity directly the larger region face.

The U-V vectors for master/slave boundaries just need to be consistent from master to slave boundaries.  They can be defined in arbitrary was on the first face, but need to be reproduced exactly on the second face.  They would define if the symmetry is translational or if there is a rotation.

Once you define the voltages, then you can define the capacitance matrix definition (select all voltage assignments).  Once you solve the model, make sure to scale the result by the symmetry factor, and (in 2D) also by the model depth (default 2D assumption is 1meter).  The solutions are found in the Solution Data or in the Result Plots sections.

• ganand
Subscriber

Thanks for the info, pblarsen. Your are right, it's the electrical symmetry that concerns me. For my case (as shown in the diagram). I divided my parallel plate setup into 36, 10degree sections and I would like to define a rotational symmetry. However, I am not sure how to do that accurately. My case is such that I have not been using a region to calculate capacitance till now, assuming it would include all the fringing effects from any direction in its calculation. Specifically, I have the following concerns:

• Now, when I take a 10 degree section (without any boundary conditions) the capacitance for that section is not exactly 1/36th of the total, but very close. As a comparison, the cap of the full setup is 112.04pF, whereas for each section it calculates to be 3.0494pF. If this difference is considered negligible and common, do I even need to consider any boundary conditions for my case?

• Secondly, when I do consider Master/Slave boundary condition (firstly, I have to define three sets of Master/Slave - for the two plates and the dielectric, since I have no region), the result is different but again not exactly 1/36th of the total.

I am just trying to figure out how to proceed with this. I can provide my model If someone is willing to test this out.

Your help is much appreciated. Thanks

• ganand
Subscriber

Hi akaktto,

If you know you have been able to model the configuration, what makes you think the capacitances you have calculated are not correct. I would like to highlight that the value of the capacitance will not only depend on the absolute dimensions of the plates but also their relative dimensions to each other and the dielecric (aspect ratio). Beyond a certain limit, this causes fringing effects which may or may not substantially affect your capacitance. For more info, refer to this article:

https://nvlpubs.nist.gov/nistpubs/jres/22/jresv22n6p747_A1b.pdf

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