Coplanar Strip lines length

Hello,

I want to design simple coplanar striplines (two parallel copper strips) sitting on the substrate of relative perm=2.2 without any ground plane behind the substrate.

I want to have the Z0 of the coplanar striplines to be 130 ohm.
For this I used the mathematical formula given in the book " Coplanar waveguide circuits, components and system" by Rainee N. Simons (check amazon.com, its a good book on this topic).

The mathematical formula gives Zo as a function of the gap between the striplines, width of the strips and height of the substrate. Since I want Zo to be 130 ohm, the formula gives the gap=0.5mm, width=2.8mm, keeping substrate at 1.575mm (since this is the possible fabrication of substrate height).

Now when I design this simple design in HFSS I am not getting the results what the formula yielded. It is way far off.

One factor which is to be considered is the length of the striplines. However, Zo of the striplines does not depend on the length of the striplines.

So, I did a parametric simulation of striplines length from 10mm through 50 mm. The results were more weird.

Simulation Specifics:
I used two wave ports on either sides of the strips, each renormalized to 130 ohm for best matching of S parameters. Thickness of the strips is 0.017 mm(possible fabrication specs).

I have attached the HFSS file I used for the simulation. Any help will be appreciated. It is quite urgent and very important.

Thanks.

I don't know what calculations you have done to get 130 ohms but using Appcad with those dimensions & er=2.2 I get 57 ohms. Have you transposed the gap & width? Or are the definitions of gap & width different to what you might expect?

Keith.

Hello Keith,

Many thanks for your reply. I didn't know about this great tool Appcad. I have downloaded and using it for other purposes, not related to the question I posted.

I didn't see coplanar striplines in the "Passive circuits" section or any other section of Appcad. Please let me know how you used it for coplanar striplines.

Going back to the question, 130 ohm impedance was desired, not evaluated. So basing on this, elliptical integrals were used to derive dimensions of the coplanar striplines. I double checked it, I am sure I didn't transpose width and gap.

I have attached a pdf file for the definitions and formulas used for the CPS.
"S" is the gap between the two strips. w1 and w2 are widths of the two strips. In this case, w1=w2. I am taking S = 0.5mm and w1=w2=2.8mm

Also, I am using Appcad version 3.0.2. I will appreciate if you guide me through this.

Having seen your diagram I realise what you are doing is different to what I was looking at (coplanar waveguide) - my mistake, sorry.

Appcad 3.02 doesn't do coplanar striplines but I think that is why I keep a copy of the old DOS version 1.02. I don't think it assumes one strip is grounded (but the documentation is virtually non-existent) and comes out with 65 ohms with your values. I can email you the DOS Appcad if you like.

Keith.

Do I understand right that your geometry is meant as a differential CPS without any embedding ground? That's rather unusual, because the E-field has effectively no bounds, so you get an open, leaky transmission line structure.

I get a differential impedance of about 122 ohm with a different tool, however.

I misunderstand the colanar strip line, thanks FvM remind me.

Your above analysis is of a common single ended CPS geometry. The original poster is describing a different one: P.S.: I think the lack of clarity is with the original post.