In search of a general transmission line simulator



Currently I'm in search of a good formula for a transmission line with almost arbitrary shape. One project is a directional coupler, another the simulation of a Log-Periodic antenna. When trying to model a two-band Log-Periodic antenna [1] originally pioneered by Günter Lindemann, DL9HCG [2] (sk), the model did not fit reality too well: The VSWR was higher than reported by people having built this antenna. The original antenna has two square booms but since NEC2 only supports round wires, the antenna was modelled with round wires.

Now for re-modelling the antenna with transmission lines (NEC2 supports those), I was searching for the impedance of the two square booms acting as a transmission line. I (re-) discovered the transmission line calculator by Hartwig Harm, DH2MIC [3] via his article in the german magazine Funkamateur [4]. But his model does not (yet?) include the parameters for two square wires. Harm uses atlc2 for estimating the parameters of his model. The software atlc2 is a reimplementation of Dave Kirkby's arbitrary transmission line calculator (which is available as source code and shipped with some Linux distributions) [5] but at least for round conductors I'm getting errors of several percent when trying to model the case of one round conductor against a wall, also reported by Harm [3]. Since atlc does not support conductors in free space we need to simulate walls in a great distance when modelling conductors.

So in search of a formula for this I discovered Owen Duffy's work [6] (via a re-implementation of his calculator by Serge Y. Stroobandt, ON4AA [7] who acknowledges Duffy). He also uses atlc [5] to compute the parameters of a model. When fitting the values of Duffy's calculator to Harm's model, I'm getting a K-factor of 1.65 but the first 2 values don't agree (the first value for d = 10 and D = 15, i.e., D/d = 1.5 is off by 6.4%, for D = 20 it's still 1.5%). Since Duffy states that "figures below about 100 Ω are likely to be underestimates" [6] I'm trusting Harm's model better for those low values but I haven't measured this and I'm not understanding Duffy's argument about the proximity effenct since the model of atlc is size-independent (it just uses D/d expressed via a pixel-drawing of the model). But since we can't fully trust the model of atlc, I'm fine with the accuracy.

I've not yet plugged the estimated impedance of the two square booms into an antenna model – but it seems the impedance is much higher than the 50 Ω of the real antenna.

[1] Michael Zwingl. Dualband Log.Periodic Antenne für 2m/70cm im Selbstbau. Technikecke, ADL 303 Ortsgruppe Mödling des ÖVSV, July 2009. Accessed 2020-02-27, in german.
[2] Günter Lindemann. Duoband LPDAs. LPDA Documentation, April 2014. Accessed 2020-02-27, in german.
[3] (1, 2) Hartwig Harm. A new approach to modeling short conductor wires in highfrequency circuits. Technical report, DH2MIC, June 2018. Accessed 2020-02-27.
[4] Hartwig Harm. Berechnung der Induktivität kurzer Leiterstücke. Funkamateur, 67:731–733, August 2018. In german.
[5] (1, 2) Dave Kirkby. Finding the characteristics of arbitrary transmission lines. QEX, pages 3–10, December 1996.
[6] (1, 2) Owen Duffy. Characteristic impedance of transmission line of two square conductors in air. Web software, July 2009. Accessed 2020-02-27.
[7] Serge Y. Stroobandt. Parallel square conductor transmission line calculator. Web software, 2018. Accessed 2020-02-27.