coplanar waveguide with thick metal

[dmcmahill]

The currently implemented equations are from relatively old circuit board technologies where the metal is thin compared to the spacing and metal width. That may not be true in a more aggressive technology and especially in IC technologies. It would be good to do a literature review and see if we can find some updated models.

[dmcmahill]

See https://sourceforge.net/p/wcalc/bugs/12/ where a with ground line in wcalc is reported as 50 Ohms but is reported as 45 in a high dollar commercial tool.

I used Wcalc for CPW grounded, 50 ohms, RO4350, and calculations give a number that is about 10% lower than the ones given by www.polarinstruments.com Si8000m ~$6k program. These guys also close the loop, by making the hardware tools that does physical measurements, using TDR. Wcalc gives the same results as many other programs, like AWR Txline, Rogers calc, and PCB Toolkit, so I assume the underlying assumptions are the same. 45 Ohms instead of 50 may be a big deal.

[dmcmahill]

This paper presents some filter designs and mentions that thick metal decreases impedance. A cursory look didn't show them using any closed form solution. I think they relied on commercial heavy weight field solvers. Section II and figure 3 in particular mention field solvers and they show some impedance curves for different metal thicknesses. They have some photos of a downright beautiful looking CPW!

https://ieeexplore.ieee.org/document/5280354

It would be a fun task if I had access to a field solver to see about generating a lot of data and then doing some curve fitting with carefully constructed fitting functions that have nice properties like monotonic in directions that should be monotonic and approach limiting cases (very thin lines, very thick lines).

[dmcmahill]

https://ieeexplore.ieee.org/document/596657 mentions using FDTD and then developing a compact model but the paper is short and missing many details needed to replicate the work.

[dmcmahill]

Regarding https://sourceforge.net/p/wcalc/bugs/14/, I ran the test case with the FreeFem setup that is now in the wcalc repo and what I'm seeing is that FreeFem gives 53.8 Ohms with Tmet = 0.01 mil and 48.8 Ohms with Tmet=2.2 mil. Current wcalc from today is giving 53.98 Ohms (the slight drop from the value in the bug report is due to starting to interpolate towards microstrip). This just reiterates that with today's geometries I need to add a thickness correction term. I'm open to suggestions if anyone has good references they can cite.

[dmcmahill]

From https://sourceforge.net/p/wcalc/bugs/14/

[LemonBoy]

The "Thickness Corrections for Capacitive Obstacles and Strip Conductors" paper by Cohn (IEEE link) may be helpful here.

There's also another method described in Gupta's "Microstrip lines and slotlines" book. I've implemented that and tried feeding the values in the example above, the resulting impedance is ~50Ohm, much better than the 55Ohm given by wcalc.