Topband: "return" current - what is it?

[Robert Carroll]

Knowing both Tom and Yuri to be two of the best and brightest, I am sure
this is going to be an interesting discussion, and only the devil is making
me stir the pot a little in an impractical way. Kirchoff's Law is a
derivative of Faraday's law, and if you are in a situation where Mr.
Faraday's law is applicable, so is Kirchoff's law.  A very gory exposition
is provided by our electro-physicist buddies:

http://www.ing.uc.edu.ve/~azozaya/docs/tem2/zozaya_ajp_75_565_07.pdf


   
Mr. Kirchoff was a very productive fellow, having deduced, often from
thought experiments, similar laws named after him that apply to blackbody
radiation and photons.  His law that EE's love was motivated by thought
experiments at DC.  He also thought about the following situation.  A very,
very long wire in the free space of the cosmos is fed by a current source at
its center.  To keep the thoughts simple, toss in that the wire has no
resistive loss and that the current source is injecting 1 Ampere and
operating at 2MHz.  Just to cover your backside you might toss in that you
were in a nice part of space with no significant curvature weirdness.  How
much current would be measured in the wire at say 1 light year away from the
injection point?  You can rack your brain as to whether a numerical analysis
method of moments program running on the latest NASA parallel processing
behemoth would give an accurate answer, but there is no need.  That wire
would have emitted radiated power in each small segment along the way with
the total power emitted exactly equal to the power supplied by the source as
captive electrons within the wire oscillated their little hearts out.  With
finite current in, finite power would be radiated, and for all practical
purposes most of it would have been radiated segment by segment along the
wire long before Mr. Kirchoff could have been teleported a light year away
to make a confirming measurement.  When he did arrive at the chosen
measurement point he would find nearly but never all of the injected current
had disappeared.  This would not have been a surprise to him but maybe to
the rest of us. How could this have happened?  The wire was lossless after
all.  And if Mr. Kirchoff had brought along the proper sensor he might have
been able to detect a small but finite current travelling farther out on the
wire but nothing returning from reflections off the end of the wire,
especially since it has no end in the limit of his thought experiment.  In
fact there would be no standing waves anywhere on this wire in any practical
sense because it was for all practical purposes a travelling wave antenna
with no reflections coming back from the almost infinitely distant end.  The
electrons at his point of measurement would barely be oscillating at 2 MHz
and unless he had the very latest Agilent equipment he would not be able to
detect a standing wave there either despite the very distant end of the wire
being unterminated. 

What does this have to do with the current discussion?  Nothing in a
practical sense.  But it does point out one thing.  Kirchoff's law as we EEs
usually apply it is in reality a DC law.  It DOES usually apply to the RF
situations we encounter in hamdom--if we apply it carefully, as Yuri's
reference points out.  You won't find many successful designers applying it
in the same manner at 50 gigahertz. 

And hello to Yuri, whom I have not seen eyeball to eyeball in many years. In
case you don't know Yuri he is a true medical miracle.  How is the Tesla
Club, Yuri?  Plum Island has been up for sale if there is interest.  I'm
staying clear of it, though.

73
Bob W2WG 

P.S.  Don't fool around with a very long wire in space.  You might find
potentials (be careful how you define potential) on it produced in other
ways than by your little 2 MHz current injection if the wire is long enough.

-----Original Message-----
From: topband-bounces at contesting.com [mailto:topband-bounces at contesting.com]
On Behalf Of Yuri Blanarovich
Sent: Sunday, August 05, 2012 9:51 AM
To: topband at contesting.com topband at contesting.com
Subject: Re: Topband: "return" current - what is it?

Here we go again, speaking of misinformation, peer review, spreading false
"guru" stuff.
You can not apply Kirchoff law from DC circuits to the current behavior
along the STANDING WAVE RF radiator.