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Funny little problem - can you answer?
T3sl4co1l:
--- Quote from: Benta on May 05, 2022, 06:19:26 pm ---Why would you read 50 ohms? It's a DC measurement. You're talking AC.
--- End quote ---
If measuring one end, core to shield, shield grounded, far end flopping in the breeze: hmm probably over that distance, induction still wouldn't quite cancel out and many volts would be measured (but perhaps not destructively so). If we say the cable is well constructed and doesn't accumulate induced voltage in this way, then we're left with the cable itself, and a cable of that length will measure 50 ohms the first time, then increasing amounts once the measurement pulse has had time to propagate the full length. Because the cable is lossy, the pulses won't actually reach the far end, just smearing out, diffusing along its length instead, and so the resistance increases gradually, say some ohms per second.
Tim
magic:
Ignoring all the magnetic fields, solar wind, aether wind and other drama - just the cable - we have the following:
Say that 1V is appiled to the cable, the cable charges to 1V at a speed of 20cm/ns or so.
Say it has 100pF per meter, so 20pF/ns are flowing into it for the continuous charging.
That happens to be 20mA for 1V applied to the input - 50Ω resistance.
Checks out :phew:
edit
Which is to say, a transmission line really works at all frequencies, down to DC, regardless of its length.
Weird things only happen if it isn't terminated in its characteristic impedance and you wait long enough to discover this.
Well, OK, I suppose you will also discover at some point that a real world cable is lossy, as T3sl4co1l says.
Benta:
--- Quote from: magic on May 05, 2022, 08:40:46 pm ---Ignoring all the magnetic fields, solar wind, aether wind and other drama - just the cable - we have the following:
Say that 1V is appiled to the cable, the cable charges to 1V at a speed of 20cm/ns or so.
Say it has 100pF per meter, so 20pF/ns are flowing into it for the continuous charging.
That happens to be 20mA for 1V applied to the input - 50Ω resistance.
Checks out :phew:
--- End quote ---
You're still assuming that shield is grounded and core is connected, which is not given in the original question. Try to make your calculation with a simple conductor instead. (and PLEASE: without Van Allen belts, Earth magnetism, Aliens and other irrelevant voodoo).
T3sl4co1l:
The orbital mechanics seem relevant as, why provide such a detail otherwise; but perhaps it's merely in the collective consciousness because of certain recent videos.
If we say it's a spool of wire instead, then it all gets much simpler, indeed. :D
For which, testing impedance across far ends of the cable (it doesn't much matter whether either end is connected to the core or shield: the core simply adds Zo to the shield impedance at each end), is just some manner of, somewhere between a wire over ground plane (for whatever length of the wire is laid out on the ground*), to a spooled inductor (all the wire wound up in a more compact package).
The smaller it is, of course -- and for that matter, if it's doubled back on itself, in a "noninductive" manner for example -- the less sensitive it will be to ambient fields. So, depending on if you have this laid out maximally, like, literally looping around the Earth multiple times -- you'll have quite a lot of gain to ambient fields, particularly at very low frequencies (mains, submarine communcations, Schumann resonance, even daily ionospheric cycles I suppose), so, still some things to account for in addition to its own self-impedance; or, if in a small package and cancelled out to ambient fields, maybe not much of anything besides what's applied to it.
*Not that ground is very well defined, for short lengths; a wire in free space may be a better approximation. Which amounts to a higher Zo for that segment. Of which, a relatively large fraction of that impedance might be due to radiative loss rather than self-impedance. Depends on how good the ground is (soil? metal building?), what all is inbetween (wood or concrete floors?), etc.
In any case, that much wire, spooled up, will certainly have quite some inductance. A meter might not notice much impedance at all between the ends, at least until it charges up -- the time constant could be, fairly unsurprisingly: many seconds!
Tim
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