.. title: In search of a general transmission line simulator
.. slug: 27
.. date: 2020-02-27 15:55:00
.. tags: hamradio,documentation,english,open source,howto
.. description:
.. wp-status: publish
.. |--| unicode:: U+2013 .. en dash
.. |ohm| unicode:: U+02126 .. Omega
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 |ohm| 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 |ohm| 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] 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] Dave Kirkby. `Finding the characteristics of arbitrary
transmission lines`_. QEX, pages 3–10, December 1996.
.. [6] 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.
.. _`transmission line`:
https://en.wikipedia.org/wiki/Transmission_line
.. _`directional coupler`:
https://en.wikipedia.org/wiki/Power_dividers_and_directional_couplers
.. _`Dualband Log.Periodic Antenne für 2m/70cm im Selbstbau`:
http://adl303-archiv.oevsv.at/technikecke/dlogpant/index.html
.. _`Duoband LPDAs`: https://www.dl9hcg.a36.de/download/LPDAbau.zip
.. _`A new approach to modeling short conductor wires in highfrequency
circuits`: https://www.qsl.net/dh2mic/tlc/tlc-e.pdf
.. _`Characteristic impedance of transmission line of two square
conductors in air`: https://www.owenduffy.net/calc/tstl.htm
.. _`Parallel square conductor transmission line calculator`:
https://hamwaves.com/zc.square/en/
.. _NEC2: https://www.nec2.org/
.. _`Finding the characteristics of arbitrary transmission lines`:
http://atlc.sourceforge.net/qex-december-1996/atlc.pdf
.. _`arbitrary transmission line calculator`:
http://atlc.sourceforge.net/