Superconducting Microwave Resonator

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I am trying to simulate superconducting microwave resonator (notch type). Need some advice on how to take into account Kinetic Inductance and better ways to take into account superconductivity than just setting electrical conductivity to a extremly high value. Need to see proper S21 behaviour at resonant frequency, open to new ideas for meshing as well.


3 Replies Last Post Jun 20, 2024, 2:13 a.m. EDT
Edgar J. Kaiser Certified Consultant

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Posted: 4 months ago Jun 18, 2024, 9:29 a.m. EDT

I do not really have solutions to your problem but I am interested in the topic. I am not an expert in superconductors. I found that kinetic induction is significant at optical frequencies, not at 6 GHz, but maybe this is different in superconductors? What other aspect in superconduction besides zero resistivity is relevant in an RF problem? I would think that PEC should be ok for the job.

What S21 behavior are you expecting in your device?

Cheers Edgar

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Edgar J. Kaiser
emPhys Physical Technology
www.emphys.com
I do not really have solutions to your problem but I am interested in the topic. I am not an expert in superconductors. I found that kinetic induction is significant at optical frequencies, not at 6 GHz, but maybe this is different in superconductors? What other aspect in superconduction besides zero resistivity is relevant in an RF problem? I would think that PEC should be ok for the job. What S21 behavior are you expecting in your device? Cheers Edgar

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Posted: 4 months ago Jun 18, 2024, 1:16 p.m. EDT

Not an expert either, although I have worked with superconductors (twice).

Right now you have specified your conductor to have a very high conductivity, although you don't actually use it in your model as you have made all the conductors perfect.

Now if you make the surfaces of the conductors have an impedance boundary condition, Comsol will calculate a surface impedance using the usual skin depth expressions and the surface impedance will have a phase angle of 45 degrees.

BUT the surface impedance of superconductors (according to one reference I saw) is pure imaginary, phase angle of 90 degrees.

Maybe a surface current density expressed as a function of tangential electric field??

If you need to mesh a thin layer a swept mesh is usually the best approach. However if you model using the surface impedance you will not need to solve for the interior of conductors.

Not an expert either, although I have worked with superconductors (twice). Right now you have specified your conductor to have a very high conductivity, although you don't actually use it in your model as you have made all the conductors perfect. Now if you make the surfaces of the conductors have an impedance boundary condition, Comsol will calculate a surface impedance using the usual skin depth expressions and the surface impedance will have a phase angle of 45 degrees. BUT the surface impedance of superconductors (according to one reference I saw) is pure imaginary, phase angle of 90 degrees. Maybe a surface current density expressed as a function of tangential electric field?? If you need to mesh a thin layer a swept mesh is usually the best approach. However if you model using the surface impedance you will not need to solve for the interior of conductors.

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Posted: 4 months ago Jun 20, 2024, 2:13 a.m. EDT
Updated: 4 months ago Jun 24, 2024, 4:54 a.m. EDT

Yes. The surface impedance is purely imaginary. I am most likely to apply a Impedance boundary condition with a user defined surface impedance or a complex conductivity from material properties. However I am not able to select the Impedance boundary condition on the work plane boundaries as it is inside the vaccum block. How do I get around this?

Yes. The surface impedance is purely imaginary. I am most likely to apply a Impedance boundary condition with a user defined surface impedance or a complex conductivity from material properties. However I am not able to select the Impedance boundary condition on the work plane boundaries as it is inside the vaccum block. How do I get around this?

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