Coplanar waveguide transmission line calculators (CPW, GCPW)

Hi folks

I’ve just emerged from a rabbit hole & thought I’d share what I learned regarding available impedance calculators for coplanar waveguide (CPW) and coplanar waveguide w/GND (GCPW). As always, use this information at your own risk.

The short version is this:

  1. I do not trust the Kicad calculators for CPW & GCPW
  • (FWIW, I’m using Kicad 6.0.7-f9a2dced07~116~ubuntu20.04.1)
  1. If designing GCPW, I plan to use this calculator from Chemandy:
  2. If designing CPW, I plan to use this calculator from Microwaves101

If you want the long version, here goes…

I work for a small, somewhat new company. We don’t have hundreds of thousands of dollars worth of VNAs & TDRs laying around, nor do we own E&M solvers of any sort. Translation: nothing I’m about to share is backed up with my own simulations or measurements.

I was recently needing to design an antenna feed line for a particular transceiver chip we are using. This chip called for the feed to be on the top layer, copper keepouts on the inner layers, and a bottom-layer ground. By definition this resulted in a GCPW structure.

I was planning to use the Kicad calculators, but after some sanity-checking I noticed that the results weren’t making sense. First, when I increased the dielectric thickness (H), the GCPW results didn’t converge with CPW. This would be expected since the ground plane interacts less & less with the trace as it moves farther away. Second - and perhaps more concerning - was that the CPW impedance was lower than GCPW for a large portion of the plotted range. This should not be the case. You’d expect GCPW to start out lower & gradually converge to the CPW result as the gnd plane moves away. (See plot & dimensions below)

W = 24 mils
S = 5.5 mils
T = 2.1 mils
Er = 3.75
Loss tan. = 0.018
Freq = 1 GHz

This sent me on a search to understand what was going on, and to find an impedance calculator that I could trust. I checked many (see below). Some were CPW, some were GCPW, and some were both.

Here’s a plot of CPW & GCPW results for all calculators for the geometry above. Note that I couldn’t plot Antenova’s results; their calculator operates differently & you can’t fully specify your geometry.

I realize there’s a lot of data there & it’s tough to pick out any given graph. But the main take-away is that results vary widely. I would have expected (hoped?) that all the CPW calculators would produce similar results - within reason, of course. And ditto for GCPW. But this was not the case.

One argument to be made is this: “Impedance calculators are based on equations, and those equations come with caveats. How do you know your geometry fit the caveats?”

Great question. I didn’t.

Why? Because in many cases the equations/caveats weren’t given. For example, Kicad makes no mention of what its CPW & GCPW calculators are based on, so it’s impossible to know whether or not you’re using the calculator over a valid range of geometries.

In the end, I chose to trust the Chemandy GCPW calculator. This was based on several factors:

  1. It gives a reference for its equations (“Transmission Line Design Handbook by Brian C. Wadell) - not all calculators do.
  2. They have an About Our Calculators page which gives a nice comparison of their GCPW calculator vs. Sonnet 3D. Results compared well. This page also makes the point that most of their calculators have been in use for several years and complaints about their accuracy are rare. Plus, the fact that they even HAVE an “About Our Calculators” page says that they understand people want to know this kind of stuff. That tells me they probably take more pains to get the details right.
  3. My above “All Calculators” plot shows that as dielectric thickness H increases, Chemandy’s results converge with those of certain CPW tools (Microwaves101 & PW Circuits). This fits with intuition. As the ground plane gets farther away, GCPW should behave more like CPW.
  4. I found this comparison between Chemandy results vs. Ansys field solver. For the geometry used, the results were nearly identical (26.6 vs 26.7 Ohms). This gave additional confidence.

For CPW, I would use the calculator from Microwaves101 - even though they put a caveat on it regarding it being approximate, etc. My reasoning is this:

  1. They give a reference for their equations, whereas some other sites didn’t.
  2. Their CPW results converge with GCPW results of Chemandy (& others that match Chemandy). Again, it gives a warm fuzzy that CPW & GCPW results converge as dielectric thickness increases.
  3. In general, I’ve found Microwaves101 to be a very reputable site. They seem to really know their stuff - and not just theory, but what happens in practice as well.

I understand that these subjects could be looked at deeper and with more rigor. Nevertheless, I hope that my journey into the rabbit hole helps someone.

Have a good one!