Inductance of a coplanar waveguide

[f95toli]

Does anyone know how to calculate the inductance per unit length of a coplanar waveguide(CPW)?

There is a lof of information available about how to calculate the impedance but I can't find anything about the other parameters.

I know that I probably need to use numerical methods if I want an accurate estimate but right now I am only interested in a ballpark figure (+- 50% is fine).

The geometry is: 2 micrometer inner conductor and 3 micrometer gap. 100 nm film thickness (very good conductor) on a silicon substrate.

Basically I want to understand how the inductance changes as I modify the width of the inner conductor and the gap (essentially I want to find a geometry which minimizes the inductance, I don't really care about the capacitance or the impedance).

Can Sonnet lite (which is free, but I haven't tried it) be used to calculate stuff like this?

 

[Born2bwire]

Without any software to do it specifically, I would probably write up a simple FEM code to do it.

But if you have access to ADS Momentum, they have a lot of tools that make engineering waveguides and RF circuits a snap. They have a tool that will take in the geometry, permittivity, and permeability of a large variety of waveguide configurations (CPW included) and it will spit out the RF characteristics like phase shift, RLC, etc. You can also input a desired RLC or electrical length and have it solve for the unknown design characteristic. I don't have access to ADS at the moment. Reminds me I really need to talk to the antenna lads upstairs to get server access to the program.

Then again, given the popularity of the CPW, it would not surpise me if you can't find some heuristical expressions to estimate your electrical characteristics.

 

[PowerEngineer]

Takes me back to my college days when we had to calculate impedances for various transmission line configurations...

If you have information on how to calculate the impedance then at least this should get you close. Impedance is R + jX where X is wL - 1/wC. If you can calculate the impedance at two different frequencies, the you can find out what L should be.

 

[djhuber82]

For something free, check out AppCAD (made by Agilent, the same company that makes the MUCH more powerful ADS). It's great for calculating Zo of various transmission line structures. Once you have Zo you can back calculate inductance using Zo = sqrt(L/C) and c=1/sqrt(LC), where L and C are per unit length and c is the speed of light in the medium. I think this will work ok as long as Zo is relatively independent of frequency. I'm working from memory here so you should check these eqns before you depend on them. But if all you want to do is minimize the inductance (i.e. minimize Zo) then just use wide lines and small spacing.