impedance shift in VLF transmission line - RF Cafe Forums

 Post subject: impedance shift in VLF transmission line

Posted: Mon Apr 12, 2010 9:56 pm 

I understand that in an electrically "short" transmission line, the impedance of the cable can be ignored. But what if I have an impedance shift due to cable damage on an electrically "long" transmission line, but it is close to the transmitter? Should I expect reflected power issues? In this example, I'm talking about damage 1000ft from the transmitter on a system operating at around 10 kHz with a cable several miles long.

 Post subject: Re: impedance shift in VLF transmission line

Posted: Fri Apr 16, 2010 12:08 pm 

Greetings dbickham:

That's a really good - and intriguing - question. What is the nature of your 10 kHz system? Is it a coaxial line or more like power line communications?

The wavelength 10 kHz in air is 98357 feet, while in coax cable with a relative dielectric constant of 2.07 (solid PTFE) the wavelength is 68363 feet, so in either case, your impedance shift at 1000 feet is at most only 1/68th of a wavelength away - virtually right at the transmitter output. If you are using digital modulation and want the edges to be clean at the receiver, you need to be concerned about the higher frequency content; e.g., 7th harmonic at 70 kHz has a wavelength of 9766 feet in the example coax, so you are beginning to approach the 1/10th-wavelength rule of thumb for where transmission line length starts to matter.

So, if your highest frequency content is really 10 kHz, that is in the low analog range where transmission line RF impedance is not really very important over a small fraction of the wavelength. As long as the damage does not severely affect the DC resistance or compromise the dielectric breakdown voltage necessary to operate your system, then you should be OK.

Looking from the receiver end - say 2 miles away - the impedance shift is possibly within 1/10 of a wavelength 10560/68363 = 0.154, so the receiver could see a noticeable mismatch, but that should not be a significant problem.

This is more of a rationalization than a rigorous analysis, but I think it works in this case. Anyone disagree?

BTW, here is a link to my frequency-to-wavelength converter if you need it:

http://www.rfcafe.com/references/calculators/wavelength-frequency-calculator.htm

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- Kirt Blattenberger
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 Post subject: Re: impedance shift in VLF transmission line

Posted: Fri Apr 16, 2010 12:54 pm 

Derr, ummm, well...
If you have a high power eg audio amplifier at 10kHz with a nominal 8 ohm output impedance and a short circuit occurs in eg a loudspeaker line, the final stages will fry unless you do something quickly, like pull the "big switch", at least I think so.
The case cited seems very similar, to me.

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At bottom, life is all about
Sucking in and blowing out.

 Post subject: Re: impedance shift in VLF transmission line

Posted: Fri Apr 16, 2010 7:54 pm 

I'd say it depends on the level of damage, like Kirt wrote. It seems the original poster has determined that the damage is not bad enough to consider replacing or repairing the cable unless absolutely needed because of any bad affect it might have on the Tx. From a VSWR standpoint it would be interesting for someone to actually do the simulation. If I had the software I'd do it. Seems to me its so close to DC that only the resistance and voltage breakdown is important here. But hey I'm not an engineer with all the fancy schooling.

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... Jose' Arrina

 Post subject: Re: impedance shift in VLF transmission line

Posted: Mon Apr 19, 2010 8:57 am 

Hi Jose'
You and Kirt are right, of course it does depend on the nature of the fault. Usually with cables though a fault is pretty catastrophic like say 1 or 2 ohms cross-connection "short".
As for simulating the effect of low resistance/low capacitance faults, I have had in the past (when my brain cells were firing on all cylinders) some success with Mathcad, which I find very user friendly for EM simulation as a) it handles complex algebra and b) it presents your execute text file as you write it and then re-edit it when it fails to run.
I have some time on my hands right now due to Icelandic volcano ash grounding flights, so I will play around with it.

_________________
At bottom, life is all about
Sucking in and blowing out.