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Re: Corum's new paper, a "naive swindle"?

Tesla List wrote:
> 
> Original Poster: gbyrd-at-aros-dot-net
> 
> Hi all,
> 
> My name is Duane Bylund, and I am new to this list (as of 4-10-2000). I
> recently ran across a paper by the Corum brothers titled "Class notes:
> Tesla Coils and the Failure of Lumped-Element Circuit Theory". Many of you
> have probably read this, and it has brobably been hashed out on this list.
> I do not know the way people feel about this paper, but, as I "stand on the
> other side of the fence", I would like to put my 2 cents worth in.
<SNIP>

> Duane A Bylund


Duane, Terry, Malcolm, and all,

A very warm welcome to the List, Duane! Although you may be new to this
list, your pioneering Tesla Coiling efforts are certainly recognized and
acknowledged by many here. Congratulations on authoring a very
well-written practical Tesla Coiling book (MODERN TESLA COIL DESIGN
THEORY, 1991) - it has admirably withstood the test of time! 

I've stayed out of most of the Helical Resonator/Lumped Parameter
discussions, except for some earlier off-line discussions on coherence
theory and energy conservation with Terry and Malcolm. The issues are
quite complex, and like many others on this List, I've spent
considerable time pondering them. The Corums present a very well
researched, and superbly referenced argument that Tesla Coil resonators
are in fact distributed-parameter structures. Terry, Duane, Malcolm, and
MANY others on this list have presented compelling experimental evidence
that the secondary and toroid can indeed be successfully characterized
by lumped-parameter behavior _when operated in 1/4 wave resonant mode_. 

SO WHO's RIGHT??

Well, this question might be compared to some of the heated arguments
between early physicists about whether light consisted of particles or
waves. While some experiments clearly demonstrated particle-like
behavior, other equally valid experiments demonstrated wave-like
behavior. It's now known that light exhibits both properties, and it's
meaningless to describe light's behavior as being ONLY one OR the other.
Physicists and optical engineers today simply select whichever
mathematical treatment is _simplest_ for the problem at hand. I suspect
a similar situation applies as to how we treat the behavior of Tesla
Coil resonators from a scientific versus a practical/engineering
standpoint.

While one can argue about the style of their writing, I have little
doubt that the Corums are indeed correct - a scientifically complete
description of the behavior of a base-driven resonator can only be done
through the use of distributed parameter transmission-line theory. Swept
frequency measurements clearly show the formation of multiple nodes, and
while the addition of topload C may change their position, it does not
eliminate these nodes. This certainly confirms underlying behavior
that's more complex than can be described by a simple lumped-parameter
model. HOWEVER, there's also compelling evidence that a lumped parameter
model can successfully describe resonator behavior _when operated in the
1/4 wave regime_. 

There are some very troubling aspects within the Corum paper, and some
of their other papers as well, particularly when they attempt to extend
helical resonator and self-coherence theories to real-world 1/4 wave
disruptive coils... 

First, the Corums' use of Q or VSWR multiplication to estimate Vmax
implicitly assumes that the resonator is driven from a sinusoidal CW
source, and that energy can build up within the resonator, unabated,
over many cycles until total system losses balance input power. While
this argument might arguably apply to a vacuum-tube or solid-state CW
coil prior to breakout, it will lead to overstated Vmax predictions for
disruptive systems where resonator energy (and therefore output voltage)
will be limited by the initial primary capacitor's energy/bang. Their
contention that, as VSWR goes to infinity, so does Vmax ignores the
energy budget realities of capacitor-discharge coils. Any theory,
however elegant, must ultimately comply with Conservation of Energy -
there are aspects of helical resonator theory (and especially the
application of resonator coherence theory) which appear to violate this
Law. 

Second, the Corums are correct - in order to _completely_ describe the
overall behavior of circuits and circuit elements "from DC to light",
one must resort to using distributed parameters and Maxwell's equations.
All RF and microwave engineers are fully aware of this, and contend with
this reality every day! However, under limited conditions, the
mind-boggling complexity of the real world can often be simplified and
_approximated_ quite accurately through the use of lumped parameter
models and classical circuit theory. The fact that a lumped-parameter
model REALLY applies only under a set of limited conditions is
oftentimes quite acceptable from a _practical_ standpoint. More
importantly, the lumped parameter model yields acceptably accurate
results _with significantly less intellectual and mathematical pain_
than more rigorous models. 

This has been amply demonstrated for practical high-Q Tesla Coil
resonators by many of us on this List. The 1/4 wave resonant frequency
can be quite accurately estimated by using Medhurst's approximation for
self-C and Wheeler's formulas for L. And, the impact of adding a topload
capacitance can also be estimated as long as the shielding effects of
the resonator have been properly accounted for. In their attempt to
demonstrate the failure of the lumped model, the Corums choose to ignore
resonator self-capacitance, leading to gross errors in their predicted
resonator 1/4 wave frequency for the Lumped Model. Their lumped
parameter analysis is thus VERY misleading. It certainly does NOT
represent a "failure" of the lumped parameter model as much as it does a
misapplication. As Terry and others have shown, analyses incorporating
Medhurst's capacitance result in predicted Fo that are every bit as
close as helical resonator theory. And as Terry's real-world voltage and
current measurements indicate, actual 1/4 wave voltage and current
relationships seem to indicate more "lump-like" behavior than distribued
behavior for top-loaded coils.

To contend that the Lumped Model is "wrong" and a "failure" is
hyperbole. To term it a "naive swindle" of marginal utility is gross
overstatement. and is condescending to those who actually DO understand
these issues. The Lumped Model is a _workable_ simplification for
admittedly very complex phenomena. BUT, it can be demonstrated to fairly
accurately "model" 1/4 wave systems, and is particularly useful in their
practical design. It can easily be incorporated into design aids, such
as WinTesla, or private spreadsheets with a high degree of accuracy.
It's interesting to note that the professional literature of Pulsed
Power systems is FULL of examples of lumped-parameter air-core
transformer models and designs - simply because the approach works! 

So who's right?? Well, from a practical perspective, I put my money on
Lumped Parameter analysis for future coil designs, while mentally
accepting that it is, in fact, a simplified view of a more complex
"distributed" picture. However, as the Corum (mis)example shows, you DO
need to apply the approach correctly... :^)
 
Safe coilin' to you all!

-- Bert --
-- 
Bert Hickman
Stoneridge Engineering
http://www.teslamania-dot-com