Superconducting microstrip line

[ghribi]

sonnet superconductor

Hi
I want to know if it is possible to simulate a superconducting microstrip line using cst or sonnet.
It is said that is possible using sonnet. However I didn't success to do it ! I work with Nb material around 90 GHz. The parameters I set in sonnet for the material are :
Type : General
Rdc =2.1638e-6 ohms/sq
Rrf=0 ohms/sq
Xdc=31250000.0 ohms/sq
Ls=4.0951e-14 ph/sq
The substrate I used is 280microns thinck silicon (eps=11.9)

In the other hand, I wonder if it is possible to do the same with CST using ohmic sheet as a material. Unfortunately, it doesn't work very well for me. May be I did something wrong.

Anyway, if someone already did it, I am interested to know how. If you have never tryed, try doing it : it is realy interesting and useful for the future of passive microwave devices and so associated softwares.

Thank you

 

[Phytech]

You need to set Rdc=0, which is ideal conductor. Superconductor has the capability of expelling magnetic field from its body besides having zero dc resistance.

I am not familiar with the recent versions of CST, but both Sonnet and IE3D can do the job well.

 

[Joe_User]

Type : General
Rdc =2.1638e-6 ohms/sq
Rrf=0 ohms/sq
Xdc=31250000.0 ohms/sq
Ls=4.0951e-14 ph/sq

Are you sure you wanted Ls to be 4e-14 pH/sq? That's 4e-26 H/sq. I'm not a superconductor expert, but that seems too small to me. Also, I am surprised to see you using both Xdc and Ls. The net surface reactance is the sum of Xdc and Omega*Ls.

 

[ghribi]

Thank you for your answer

- for Ls, I just calculated it as
Ls=w*lamda,
with w=2*pi*f,
f=90GHz and
lamda=lamda_l0/sqrt(1-T);
this is for a temperature T=4K and a london length lamda_l0=32e-9m.

- for Rdc, I just used the model given in the sonnet user guide. I don't know if I have to trust it or not (page 72 for the join file)
Xdc in the user guide is the surface reactance. If it is w*Ls, why is there both Ls and Xdc for the input properties of a general metal type in sonnet?
Thanks

 

[Joe_User]

I used your values and calculated ~4.1e-14 Henries. The equation in the manual is for Ls in Henries, but sonnet has you enter it in pH. Therefore, you should enter 4.1e-02 into Sonnet.

If it is w*Ls, why is there both Ls and Xdc for the input properties of a general metal type in sonnet?

I think the "general" metal type is not just for superconductors. It is "general", in that it can be used for many applications. So, in general, sonnet allows you to set your surface reactance to be constant with frequency (Xdc), proportional to frequency (Ls), or any combination of the two (Xdc + omega*Ls).

 

[ghribi]

I tried with your parameters and the result is nearly the same. I mean for short lengths of a microstrip line, the transmission should be nearly as PEC for Nb at 4K. If it worked for you, can you send me your file ; may be I have another problem on other settings.
Thanks

 

[Joe_User]

I have not tried it. If you post your circuit, I could look at it.

 

[ghribi]

Here is the file.
Thank you very much.

 

[Joe_User]

The file you uploaded was a *.pat file, which is related to the far-field antenna pattern. You need to upload the *.son file.

 

[ghribi]

Sorry,
Here is the file

 

[Joe_User]

OK, I took a look at your file and I think I know what is going on. The first thing I did was to sweep the frequency from 1 to 110 GHz. I noticed is that above about 50 GHz, the results are very "noisy". This is probably because of box resonances, but could also be caused by the substrate overmoding or the line overmoding. I noticed the substrate is starting to approach a quarter wavelength at 77 GHz so I would not expect your circuit to behave properly above this frequency. I like to use an 1/8 wave as a good rule of thumb for a substrate thickness.

Below about 40 GHz, the line looks like a good transmission line, so I concentrated my efforts on this band. First, I found no difference between using Ls=0.04 pH and Ls=0, just as you said. So then I multiplied Ls by 100 and saw a change in the S-parameters. This told me that Sonnet must be doing something with the Ls value.

So then I wondered that maybe the effect of the surface inductance is just too small notice. So, since this is just a simple transmission line, I asked Sonnet to show me the L and C value of the line (they call it the N-coupled Line model, but in this case N is 1). At low frequency, the L is about 1 nH. Since the surface inductance is 0.04 pH per square, and there are 10 squares, the net effect of adding the surface inductance is only about 0.4 pH. So, it makes sense to me that you wouldn't be able to notice a change in 0.4 pH when the inductance of the line is about 1 nH.

So, I think we have the answer: Sonnnet is using the surface inductance correctly, but the effect is so small, you'll never notice it.