Are you sure you want to have a perfect electrical conductor (PEC) directly behind the ring? You have Et=0 at zmin. Thios is a PEC. I expected an open boundary condition, with an air gap perhaps as well.

Having a PEC behind the ring will vastly reduce its inductance, and increase the resonant frequency. The magnetic fields can't go through the PEC, so have to squeeze between the ring and the PEC. This reduces the field strength and the inductance. It is equivalent to having a ring with opposite currents the other side of the boundary.

Hi Malcolm,

Thanks for your response. I tried that and got some different results but not what I was expecting. I think my setup is wrong from the port side. How would you setup your port for this kind of situation, which wave mode should I be looking at?

I don't know what your port arrangement is. These rings only have much inductance for waves travelling in the x-y plane, and polarized (E) in that plane. The capacitors you have added will only have significant effect for waves travelling in the x direction. The resonant frequency will be much higher for waves travelling in the y direction, and higher again for waves travelling in the z direction.

I've changed some things since the last time. Currently, my port arrangement is such that port 1 on the left is the only source of excitation and port 2 is there to check the S21 parameter. One of my lumped elements is a capacitor of 5 nF while the other is an inductor of 18.5 nH, these are to simulate SMD components that would be attached on top. The only resonance behaviour I see is in the GHz regime rather than the MHz as I would expect with my capacitor/inductor values. I'm haven't found any resources that say whether or not the ports and lumped element features are meant to work together like this. Do you know if that is the case?

I may have been mistaken between the x and y directions, but it shouldn't make that much difference!

However, based on this paper

https://www.hilarispublisher.com/open-access/0--magnetic-polarizer-for-15t-mri-2332-0796-1000242.pdf

the resonance should be in the region 18 to 40 MHz. (theirs is 30MHz which is about half of 1/(2pisqrt(LC)) for 37.2 nH and 0.13 nF.

Are you sure you have the right capacitor and inductor values?

I have used ports and lumped elements together in CST and they seem to work together all right.

I'm actually trying to repeat the work from the same group, I've used their values but can't get similar results :

https://link.springer.com/article/10.1007/s12596-017-0397-y?shared-article-renderer

When I'm using ports with lumped elements, do I need to do thing in particular to make it work?

Not as far as I know

Have you made it a serial or parallel circuit? Do you have 0 ohms resisitance in parallel with your inductor or capacitor?

Your tracks look thicker than I expect. This will reduce inductance. Copper on PCB isn't usually that thick. Shouldn't make all that much difference though.

It's currently an RLC serial with 0 ohms resistance for both. The track is 0.2mm which is as mentioned in the paper. They mention the electric permittivity as 0.4, which I'm not sure is accurate for a PCB.

Permittivity of 0.4 is totally wrong - unless it is the meta-material permittivity. 2 to 3 would be more realistic.

I think it is something about the lumped elements - there really is no sign of them in the S parameters, and there should be. Try changing the resistance from very low to very high and see if anything changes.

I've tried that with no luck. What port settings would you use in this situation? Like the number of modes, polarization, etc...

I expect you have the port mode you need. The boundary conditions should allow propagation of a plane wave polarized with E in the y direction, and I expect the cell is narrow enough that any wave with E in the z direction doesn't propagate.

You can plot the modes from 2D results at the bottom of the tree on the left.

Maybe something is shorting out the discrete elements. What happens if you delete them and just leave two gaps?

Thank you so much for all your help Malcolm, I've managed to get some resonant behavior finally. In one of my sims. I'm not sure why it behaves this way yet but I'll figure that out eventually.