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Re: Secondary Theory (Was Bipolar Coil)-Heretical view

Hi Jim,

	It is very true that using the three lumped parameters (Lsec., Cself, and
Ctop) will predict Fo, voltages, and currents well.  However, the secondary
system is not just three simple components.

	First I'll mention the problems with the old 1/4 wave and wire length
theory.  It was assumed that for electricity to travel the length of the
secondary, that the electrons would travel through the whole length of the
wire.  Thus, the electrons would flow from the base, to the terminal, and
back.  This is very similar to a 1/4 wave antenna.  The resonant frequency
is simply determined by the time it takes for light to travel the length of
the wire.  This seemed like a reasonable way to determine Fo and explain
why a bare coil resonates at such a low frequency.

	However, there were problems.  Medhurst found that an inductor's Fo
frequency was related to the inductance and dimensions of the coil instead
of the wire length.  Given a coil of a fixed height and diameter, it could
be shown that a single capacitance could be used to determine Fo along with
the coils inductance regardless of the length of the wire.  The wire
lengths did not have any correlation and, indeed, it was simple to wind
coils that violated a simple wire length model.

	The next problem was the extreme sensitivity of Fo to external influences.
 If just the wire length were controlling Fo, then simply placing ones hand
near the coil should not alter the frequency to the extreme degree it does.
 It was obvious that the external fields around the coil were having a very
profound influence on the resonating system.  Medhurst put these two
together into the Cself of the coil.  The coil was now an inductor that had
a "self capacitance".  If you know the inductance and the self capacitance,
you know Fo.  Medhurst did his excellent work and found an empirical
equation to find Cself based only on coil dimensions.  It is well known
that this equation (the Medhurst equation) can predict the coils Fo
frequency with remarkable accuracy.

	However, there was still a belief that the 1/4 wave model was valid.  No
one really had any reason not to think that the secondary still acted like
a 1/4 wave antenna instead of a simple inductor in parallel with a
capacitor.  Indeed, the distributed capacitance along the coil fit an
antenna model better than a lumped model.  Problem was, no one could find
the parameters that would govern this system.  The Corums changed that.
Their "Slow Wave Helical Resonator Theory" adapted transmission line theory
to the Tesla coil.  They used standard transmission line parameters and
equations to form a model that had distributed components of inductance,
capacitance, and losses.  This model also allowed for 1/4 wave phenomena to
still exist.  However, there was a problem.  No one could ever find the
parameters needed to use the equations.  Every coil seemed to have it's own
parameters.  The Corums often sighted the formulas by Kandoian and Sichak
for finding the transmission line parameters but, in practice, those
parameters never worked well.  A small error would give vastly different
results.  It could also be argued that the use of this empirical formula
was not appropriate.  However, this theory gave a whole new set of
equations and even introduced the smith chart to Tesla coiling.  Sounded
good, had all the "stuff", based on true electrical engineering theory...
Just didn't work.  They wrote their work up and it was widely distributed.
Few people really understood both Tesla coils and transmission line theory
well so the problems were not easy to discover.  Most people just read the
papers, looked at the equations, fearlessly tried to calculate something
with them, and concluded that it looks great and must be true despite the
fact that they personally did not have the skills to use the darn thing.

	So, you assumed that the Corum's model was correct but used Medhurst to
find Fo because all that Smith chart stuff was impossible to understand.
However, many people realized that "something was wrong"...

	I am an electrical engineer and I do understand Tesla coils and
transmission lines.  So "no problem"!  I'll just click up MathCad, punch in
the Corum's equations, and I'll be set...  Two weeks later, nothing was
working.  The equations gave all kinds of results depending on all kinds of
things.  I started to listen to the "other guys".  Malcolm was the first
person I remember that seemed to have a problem with the 1/4 wave theories.
 It was the coherence theory of the Corum's.  Sounded good on paper, but
was never demonstrated and violated the conservation of energy.  Once I saw
that the Corums could be wrong(!), I started going back and checking
everything I could.  Basically, the 1/4 wave theories didn't work and the
lumped models did...

	The fiber optic probes were coming together about this time (they were
originally made to study this problem), so I hooked them up to the coil and
made a bunch of measurements.  They were easily able to resolve and measure
the phase shift from the top to the bottom of the secondary which would
once and for all determine how much phase shift was going on.  The results
were that there was practically no phase shift!  Exactly what the lumped
models predict!  I wrote up the "top and bottom" paper and started the
"thrash the 1/4 wave theory" thread on this list.  For me, the 1/4 wave
theory fell apart like a house of cards.  I was finally able to find the
"true" transmission line parameters for a coil and it looked like an
extremely short antenna "stub" with lots of L and C.  Resonant yes, 1/4
wave, not at all...  It was like using a 1/4 inch wire in place of a true
108 inch CB antenna.  It was simply far far shorter than needed to support
1/4 wave effects.  It was far closer to a lumped inductor and capacitor
than a 1/4 wave antenna.

	Soooooo...  Where are we now...

	I now believe that the secondary "can" be modeled as an antenna.  A very
very short one.  My coil has a wavelength of a few thousand feet and it
looks like an antenna 2.5 feet long.  It does not transmit well at all.
There is hardly any phase shift from top to bottom.  The reason the wire
length theory is not valid is because, unlike in a straight wire antenna,
the windings are all magnetically linked to each other.  Current at the
base of the coil does not need to travel a few thousand feet to reach the
top.  It only has to travel 2.5 feet and magnetically couple to the top.  A
far shorter path and I would submit the "coffin nail" for the 1/4 wave
theory.  The Tesla coil is not a straight wire in free space.  It is a coil
in free space.  The current does not travel trough the wire but is induced
in the coil's turns by magnetic induction.  Current in the bottom turn can
induce current in the top turn in a few nanoseconds.  The effects are, for
all practical purposes, lumped.

	The secondary is an inductor, It sits is space and therefor has
capacitance due to its physical dimensions as any conductor would.  Voltage
on the coil stores charge in this capacitance in the space surrounding the
secondary.  In can do this in a fraction of a nanosecond so the time delays
are not significant.  This capacitance is linked to the coil's turns all
along the coil's length.  This capacitance is distributed in that way, but
there is practically no time delay involved.  Medhurst's equation does
accurately predict this capacitance given the dimensions of the cylinder.
When you place a top terminal on a coil, it adds capacitance to the
structure thus lowering the resonant frequency.  The voltage along the
secondary is distributed as a sine function with the base being at zero
volts and the top being at full voltage.  The current is a "delayed" cosine
wave.  Full current at the base but only maybe 30 of that current is seen
at the top of the coil.  The current divides between the self capacitance
and the top capacitance.

	Wheeler's equations can tell you the inductance of the coil as can any LCR
meter.  There are no significant exceptions there.  Medhurst's equations
can tell you the self capacitance of the inductor also, without exception.
Fields programs (like my own E-Tesla3) can determine the resonant frequency
of a coil with a top terminal using the rules in the last paragraph along
with field theory and Gausses law.  It can also generate arrays that show
the voltage distribution around a given coil.  The accuracy is within 5%
despite the fact that I wrote it :-))  Programs like MicroSim can be used
to very accurately model Tesla coil systems using lumped parameters
although it does not show the inner workings of the secondary coil as we
have discussed.  

	So, I think we really do know a lot and we are on the right track.  Of
course, that's what Tesla, the Corums, and who knows who else thought...
The difference is, our ideas seem to work in every situation for everybody.

	I do not claim to have "invented" any of this.  I may have helped to
develop some of this or demonstrate something here or there, but many
people have contributed to all this, not just me.   Indeed, I suspect that
Medhurst could have told us all this long ago....

There is still more to be discovered.....

	Terry  



At 09:01 PM 5/16/99 -0700, you wrote:
>Terry, Malcolm et all,
>
>    At the risk of sounding ill informed, I'd like to play Devil's advocate 
>on the 1/4 wave theory. While there is no dispute that lumped parameters 
>"get the job done", perhaps some subtlety has
>been overlooked. Could the discrepancy between the wire length and actual 
>resonant frequency be a function of velocity? Coil geometry
>has a great deal to do with the final outcome for many reasons, not
>the least being distributed capacitance. It sounds reasonable that the
>more "media" the electrons have to slog through, the slower the velocity. 
>Different combinations of LCR will render the pure length
>parameter meaningless, yet it still could be a 1/4 wave phenomena.
>
>   Now that I've braced myself, go ahead and blast me!
>
>Jim McVey
>
snip..........