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[SOLVED] Modeling Parallel Wire Transmission Line

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Junior Member level 1
Sep 18, 2010
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I am modeling a two wire transmission line in Q3D. I want to determine the impedance of the line with arbitrary sized conductors and distance between them. I've gotten results that I am having trouble reconciling with the standard equation for two wire transmission lines L.

In the model results I have self inductance for each wire L1 and L2, capacitance for each wire C1 and C2, and mutual inductance for the two wires Lm.

So, my question is how do I derive an impedance figure for the line using the model results, in particular how does the mutual induction result figure in to that?


I am now obtaining results that agree significantly closer to actual test measurements than to the standard formula for parallel wire transmission lines. That's satisfying, although I have run two simulations to do it, one with the wires open to get the capacitance, and one with the wires shorted to get the inductance. This will work for me, however there must be a better way.

One possible method is to use a symmetry plane (magnetic or electric wall) and model just one conductor. For common mode you need the electric wall in symmetry plane, for differential mode you need the magnetic wall.

I used symmetry planes with other simulators. As I understand it, they're used to speed up the sim by eliminating redundant areas of the model. In Q3D these models only take about one minute or so to run in full 3D.

The problem, rather than time of run, is that I have to run two simulations, one for the common mode to get the capicatance figure and one in differential mode to determine the inductance figure as you say.

The model is slightly different in each case. The common mode one has two nets one for each wire and each with it's own source and sink. For the differential mode the two wires are shorted at one end and the whole thing uses a single source and sink at the other end.

In this way, I obtain capicatance and inductance figures that yield a reasonable characteristic impedance figure for the line that is close to the figure for actually built and measured transmission lines.

I originally had trouble getting reasonable results from running just one sim in the common mode just described. The self inductance and mutual inductance results from that sim put the impedance of the line significantly higher than the actually built and tested value for the line modeled.

With the two sim method, I am getting within about 10% of the actually built and tested value. That's close enough for me because the variances from hand fabricating these line will probable run about that anyway.

So, the problem at this point is really just the awkwardness of having to adjust the same parameters on two slightly different models and run two simulations instead of just running one to get the desired results. I expect with symmetry planes the case would be the same.

I didn't talk about speed but simulation methodology. In our RF courses on coupled line analysis, we took advantage of symmetry planes to calculate even and odd mode impedance (equation math, not simulation).

Your solution with two separate models for L and C will work as well, if your line segments are short enough (lambda/20 or less).

I don't know Q3D, but in RF field solvers you can create a 2 port model and then convert the S-parameters to Z-parameters and Y-parameters. Z11 is the input impedance with port 2 open (to extract shunt C) and 1/Y11 is the input impedance with port 2 shorted (to extract series L).
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I had read Q3D needs lambda/10 or smaller because it uses quasi-static analysis, so I was using 0.095*lambda. In any case, Q3D also does 2D extraction. So I built a 2D model and that gives me all I need in one go even faster than the 3D model. It always helps to use the proper tool for the job.

I appreciate your help and consider this thread solved.

Fred B

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