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At the moment, I study something about audio-frequency track circuits for railway applications and to understand its operation, an accurate model of such a circuit is required.

The circuit of audio-frequency track circuits uses the actual railway track as a conductor to let the current flow through. Also, since the normal length of track circuits can be in a range of 400 m to 2 km, these tracks may be treated as transmission lines.

Normally, transmission lines can be modeled as lumped or distributed parameters, which contain series impedance (i.e. resistance and inductance) and shunt admittance (i.e. conductance and capacitance).

I would like to know whether this range of frequency (i.e. 1kHz - 20kHz) will have any effects on these parameters? As I know it will definitely affect the resistance due to the "skin effect", but I do not know about the others.

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  • \$\begingroup\$ Explain how the transmission line is made i.e. do you apply a signal across two rails and treat the two rails as a balanced t-line or, is it something different? What happens when solid conducting railway wheels on a solid metal axle short out things? What are you trying to achieve that gives motivation to anyone making an answer? Demonstrate that this isn't some pie in the sky waste of time idea about nothing important please. \$\endgroup\$
    – Andy aka
    Apr 15 '20 at 12:22
  • \$\begingroup\$ Also consider conductance G of the dielectric between the conductors, since it is open to weather conditions (snow, rain) and contamination (particularly leaves). I'd expect that there are research papers on this in specialist locations eg IRSE.org or within Rail Interest group at TheIET.org. \$\endgroup\$
    – Martin
    Apr 15 '20 at 12:37
  • \$\begingroup\$ Dear Andy, I found some literature that railway tracks had been represented with the pi-model and some with t-model, so I don't this arrangement is significant to the question. When there is a solid-conducting wheelsets across the track within the track circuit, the signalling system will be able to detect the presence of train. Therefore, in this regard, you can ignore the presence of train. If this is properly answered, it will unlock the potential of improving the audio-frequency track circuit in many aspects, e.g. reduce overall costs, having better maintenance planning, etc. \$\endgroup\$ Apr 15 '20 at 13:53
  • \$\begingroup\$ Wavelength of 20 kHz is about 15 KM. \$\endgroup\$
    – stark
    Apr 15 '20 at 13:55
  • \$\begingroup\$ Dear Martin, normally there are ballast (i.e. sharp-edged rocks), fixings, bolts and nuts laying between two tracks, these things together with the climate at the site (e.g. temperature, rainfall and humidity) will definitely affect the conductance of the railway tracks model. However, these effects have not been thoroughly studied as it is so interrelated to many factors, therefore, it is still a subject to be studied. That said, this is the reason why I only focus on the frequency effect of these parameters, instead of the climate. \$\endgroup\$ Apr 15 '20 at 13:58
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Skin effect is not a consideration at these frequencies, they barely start becoming an issue in the low MHz range

Capacitance will increase how much load the audio amplifier will have to drive as things get longer, while they are generally built to compensate more of an inductive load. so some resistive loading on the amplifier may help if it is struggling, or a smaller resistance e.g. 1 ohm in series with the output could improve things,

If the signal is across both tracks then you end up with similar to a bifilar winding, meaning a lot of the inductance is cancelled out,

Various parts may act as antennas, but at the frequencies involved the energy that could couple in would be extremely weak

Main concern would just be the amount of capacitance the amplifier has to drive, and the amount of resistance, 1KM of even copper track assuming model railway would likely be tens of ohms if not nearing 3 digits.

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  • \$\begingroup\$ Dear Reroute, thank you for the information that the skin effect. Also, the nominal series impedance of the railway track is about 1 mΩ/m and 1 μH/m. To be honest, I do not quite get your 2nd to 4th paragraph, this might be because I have power electrical background, electronics. In this matter, in one end of the track circuit will be a transmitting end that transmit a voltage signal of 1700 Hz. This signal will travel along the railway track to the recieving end, which will operate a simple relay in order to indicate whether the section is clear or occupied. \$\endgroup\$ Apr 15 '20 at 14:04
  • \$\begingroup\$ Skin effect can very much be an issue at lower frequencies. For instance in powerlines: at 50 Hz, the skin depth is only a few centimeters, greatly decreasing the current carrying capabilities of thick solid conductors. \$\endgroup\$
    – polwel
    Jul 15 at 7:17

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