The lumped element (Capacitance) has no influence on the S11 response of the unit cell simulated using Floquet ports.

[jokincifu]

Hello everyone,
To give you a context of what I am simulating and why, the ultimate goal is to build a Reconfigurable Intelligent Surface with multiple unit cells to reflect the signal in different directions. I am using the CST Studio 2019 tool for the simulations, using Frequency Domain Solver simulations with Floquet ports.

I am simulating a rectangular unit cell at the frequency of 9.6 GHz where the reactance value can be changed to modify the phase of the reflection coefficient.
For this, I have designed a unit cell of 5x5mm, with a substrate (MT-40) height of h=1.5mm, and a top metal (Annealed Copper) reflector of 4x4mm, as shown in the following image:

To modify the reactance of the unit cell, I inserted a finite element (RLC serial type element, but only giving value to the C parameter, in order to have a capacity) into the cell. As an ideal first step (to see if the element has effect on the response), I placed the element between the upper and lower metals (Ground), as shown below:

In the image above it can be seen the values of the phase of the S11 (refering to reflection from the cells) by modifying the value of the capacitor, proving that the capacitance has an influence on the reactance of the unit cell.

In order to design a more realistic unit cell (for future implementation of the cells), I inserted a metallic via from the metal top patch to the bottom patch, in which I drilled a hole (0.2mm radius) so that the via goes through both the substrate and the bottom patch, thus connecting the capacitor between the via and the bottom patch, as shown in the following image:

To give more information:
-The via and the top patch are a complete component (created with the Boolean>Add tool).
- The hole in the bottom patch was created by using a cylinder of vacuum material and subtracting it (Boolean>Substract) from the bottom metal.
- The capacitor has been placed by selecting the circular edges of the via and the hole:

The following figure shows how the value of S11 changes with the capacitor values. It can be seen that the capacitor has no effect on the response of S11, as if it does not generate any capacitance in the unit cell.

The S11 response that should be achieved with the via should be very similar to the previous case, it should vary a little (due to the inductance introduced by the via in the cell), but for practical purposes it should be similar. However, it is observed in the image that the results are not similar, and that no matter the value introduced in the capacitance, this has no effect on the response of the cell.

I have been thinking a lot about the problem, I deduce that it may be related to the way of simulating, but I don't know where exactly the failure may be. Thank you in advance.

P.D. I attach also the .cst files (the capacitance connected in an ideal way (_Varicap) and using the via (_Via)), in case someone wants to simulate it/change some things.

 

[PlanarMetamaterials]

The S11 response that should be achieved with the via should be very similar to the previous case, it should vary a little (due to the inductance introduced by the via in the cell), but for practical purposes it should be similar. However, it is observed in the image that the results are not similar, and that no matter the value introduced in the capacitance, this has no effect on the response of the cell.

Are you sure? Have you examined the field symmetries of the modes you are trying to excite? Based on these results it looks like your excited mode my have a null at the center of your unit cell. Please:

a) Offset the via slightly and resimulate.
b) Post some images of the field distributions.

 

[jokincifu]

Thank you for your quick response.
First of all, the boundary conditions are as follows: Unit cell in X and Y plane and open in the Z one (plane through which the unit is excited).

I have moved the via, as you said, 0.5mm in the x-plane, as shown here:

However, the results I get are the same: no influence from the capacitor.

On the other hand, when referring to the distribution of the fields, I understand that you are referring to the electric and magnetic fields. In addition, I also attach the surface current. (All images correspond to the unit cell with the via moved 0.5mm on the X-axis.)

E-FIELD:

H-FIELD

SURFACE CURRENT

If you need anything else, please feel free to contact me. On the other hand, the.cst projects are in the first post, in case you need more information about the project.

 

[PlanarMetamaterials]

Depending on the modes excited (which it appears to be a y-directed variation in electric field), there are a few possibilities here that I can see:

1) The resonant mode you are looking for is insensitive to changes in the X-position (perhaps only Y?)
2) The resonant mode does not exist at a sufficiently low frequency for such a small change in X-position, and you need to sweep to a higher frequency to see it (or adjust the capacitance).
3) There is an error in your setup somewhere (although based on what you've posted, it seems correct [I don't have access to CST]).

The resonant frequency is likely a complicated function of position and loading capacitance. Most likely, the magnitude of the resonance diminishes as the capacitor approaches the center of the unit cell; symmetry is likely to blame here.

You can rule out the first two by doing an extended parametric sweep on the location of the pin. Sweep the X and Y position around the unit cell and see how the results vary. For each step, simulate over a wider frequency range, or adjust capacitance to find the resonance you're looking for. If you don't see any variations, likely point #3 is to blame.