# Comments on t.c.'s as transmission lines

The Corums in their recently-posted paper on Tesla coils characterize
them as transmission lines.  Altho I learned my College rf upwards of 50
years ago & haven't used it all that much in the interim, my recollection
of a transmission line is that it is a mechanism for transferring rf from
one place to another, and it fundamentally incorporates a means for
minimizing its radiation to space.  A Tesla coil, on the other hand,
incorporates no such means.

I would think that a t.c. would more accurately be characterized as
partially a transformer and partially a highly-loaded 1/4 wave antenna.
The lowest part, nearest the primary, is of course the transformer, with
the upper (major) part acting as an antenna.

By "loaded" I mean that the antenna incorporates a lot of inductance
along its length, viz. the coil itself, making it physically a whole lot
shorter than 1/4 wave of its resonant frequency.

As the voltage rises on the t.c./antenna, the coil starts to radiate
energy to space just like an ordinary antenna.  That radiation energy
loss, plus smaller losses within the coil, is what keeps the voltage at
the top from rising to infinity given finite input energy.

If there is no spark (no corona and the top electrode having a
sufficiently large minimum radius facing space), then, after the primary
excitation is removed, the voltage exponentially decays--with a rate, I
suppose, dependent primarily on the intrinsic Q of the coil.

When there is a spark, then what happens is merely this:  The energy that
would otherwise have radiated away into space subsequent to that time,
exponentially decaying in amplitude should the excitation have been stopped at
that time, just gets "radiated" very quickly, i.e. via the spark.  But
all the time during which the voltage is building up, our t.c. "antennas"
are doing their thing, pumping energy into space, and that's where a lot
of the energy from the primary goes.  We'd like it, instead, to go into
the ZAP but first principals would seem to deny us that.

Observing the secondary-voltage waveform of my FET-driven coil, it
appears that the "area under the curve" of the building-up portion of the
wave is more or less the same as that of the decay portion subsequent to
removal of the (pulse-burst) excitation, absent a spark.  That tells me
that, if I cut off the excitation just at the time of the spark (which I
do utilizing a crafty little circuit I designed for the task), then the
amount of energy I've "wasted" in radiation is the same as that that I've
dumped into the spark.  50% efficiency at best!  So sad.

I'd be happy to be corrected on any of this.  And lastly, I don't
understand a lot of the terms the Corums use in their paper.  "Velocity
inhibited", "slow-wave", "partially coherent", "frequency dispersive
resonator", "guide phase constant", "inhibited velocity factor",
"equation of continuity", "line splitting passband broadening", "degree
of coherence of the up and back resonator waves"?  Those terms are new to
me and I would value either precise definitions or citations as to where
those could be found.

Ken Herrick
kcha1-at-juno-dot-com

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