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Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Hi All,

Antonio wrote:
> This story of "coherence" is very strange,

Yes, the Corums sometimes referred to the 'coherence time',
which I would normally take to be the time taken for a signal
to travel through a resonator, bounce off the far end, and
return to the start, ie the round trip time.  During that period,
the source sees only the characteristic impedance.  Once that
period has elapsed, the standing wave is fully formed.

> ...unless it means the coherence of the two (or more)
> oscillatory modes of the system, when the energy transfer
> from the primary is complete.

That seemed to be the meaning that the Corums where using it for
because they used it to label the energy transfer time, I think,
rather than the signal round trip time.  The trouble was, whatever
sense their papers contained was heavily camouflaged by lots of
extraneous and silly stuff.  But then, all that took place during
the years of the heavy pseudoscience sponsored by the ITS, so by
comparison, it must have seemed pretty impressive.  The occasional
snippet of sense appearing now and then would have been lost in
the sea of inane nonsense that passed for Tesla 'science' back

I agree with Bob's comments in which he describes the limitations
of a single LC lumped model in terms of poles and zeros.  You
can always extend the LC model with more LC pairs, thus bringing
in more poles and zeros.  Antonio's work on multiple resonance
networks provides an algebraic procedure for this.  It can also be
done numerically, the distributed model can be made to spit out
the relevant LC values to make a lumped network behave like the
real coil over some desired range of resonant modes.  We can now
generate a spice circuit file for a coil, so that spice produces
the same output as the distributed model for at least several

The single LC model can be made to match Fres, as well as the ratio
Vtop/Ibase at Fres, by choosing the correct equivalent values for
the L and C.  The errors are small from DC to Fres, but get
quickly worse above.  The LC values which give the correct Fres
and Vtop/Ibase don't give the correct energy storage at Fres,
however, because the single LC model doesn't contain a storage
element to represent energy stored in the coil's internal
capacitance (meaning - E flux lines from one point of the coil to
another).  The error is only small - a few percent.  Another way
to treat this in a lumped model is to use three capacitors, one to
ground from each end, plus a capacitance in parallel with the coil.

As Bob says, polynomials of infinite order would in principle be
needed to fully represent the distributed situation.  Another
way of expressing the same stuff is through integral operators in
which the reactances become continuous functions of position.
In practice though, there is a cut-off frequency occuring due to
coil losses.  Above some frequency there is so much loss that a
signal can never make the round trip - it decays to nothing within
the 'coherence' time.  Also, in practice, the amount of energy
in a given mode during operation becomes small enough to neglect
beyond some not very high overtone.  So really we don't need to
use huge models - unless you want to make nice animations :)

Thanks for the feedback on the introduction of Medhurst C to the
Tesla world.  I had a feeling Malcolm had something to do with it.
I wonder, how were people calculating coil resonances just prior
to that?   The inductance is not to hard to deal with, but how was
capacitance estimated?  People couldn't have still been using the
wire length thing at that late stage because their coils worked!
And some of them were quite large, so there must have been another
fairly reliable method in vogue.

There were certainly folk around who knew how to apply the laws
of physics to Tesla coils.   Digging into the list archives only
takes us back a little way, but does reveal the odd gem.  Some of
my favourite ones are by Ed Harris, for example in this one,


Ed Harris points out the error of the light-speed wire-length myth
and gives a corrected formula which is pretty close to what we
know today.  He uses 1.2 * (h/d)^0.2 for the velocity factor
coefficient.  I'll bet similar statements were made by the more
knowledgeable in every decade, too.   Another little gem of a post


which shows something of the uphill struggle that sound theory
was having against the popular contempt.  Ed obviously knew what
he was talking about.  He comments on the Corum's work:-

> ...if you are right in assserting that the Corum's are at the
> forfront of tesla coil theory, then it is no wonder that our
> predictive power is so poor.

which I rather like :)  I know exactly what he means.

Terry wrote:
> It was TWFreq originally, then went to the many iterations
> of E-Tesla...

That was it, Terry's TWFreq was the first real start on the
'capacitance problem' of the resonator.  At the same time,
Mark Rzeszotarski was computing DC inductances, and Bob Jones
seemed to be the leading advocate of the network modelling of
resonators.  All three were amongst the founder members of TSSP
which was a team effort assembled in 2000 to crack the problem of
modelling a secondary resonator.  All the pieces were in place, it
just needed a bit of software and a great deal of measurement!
Much was achieved but none of it could have been done by any
single person - there was just too much work and too many fields
of expertise which had to come together to solve the problem.

Ed Phillips wrote:
> I started to play with fitting points to the curve you sent but
> realized that I don't know you definition for "velocity factor"
> or how you compute it; I'm sure its related to wire length over
> resonant wavelength or something similar, but just don't
> remember.

Ed Phillips independently discovered those nice velocity factor
curves which you get when you plot apparent wire velocity factor
against h/d, as previously mentioned in 1996 by Ed Harris.
(Ed Phillips has been coiling for over 60 years and is still
discovering new things!  He was computing Neumann integrals to
calculate inductances and coupling coefficients way back in 1978,
when "I" was still learning to program!)  Ed's first post on the
subject of coil resonance and wire length was


and I made some comments on it in


(Ed, the formula you want is at the bottom of msg00545.)

Ed is a strong advocate of Ldc/Medhurst calculations because
they work and are simple.  Arguably, the two Eds have presented
an even simpler method via those curves.  Just look up the
velocity factor for your h/d, and calculate

 Fres = velocity_factor * 75e6/wire_length

Terry wrote:
> Cool!!  This post is almost as large as Harvey's ;-)))

Nobody can say we don't have stamina when it comes to list
posts!  Let's have more long posts - interesting things to
read during a tea break at work :)

I for one would welcome hearing more about the 'early days' from
the old timers.  Why not put a few priceless recollections into
the archives for preservation?    I'd like to know more about the
history of this hobby, its technical developments, and the people.
Who were the movers and shakers back in the 50's, 60's, and 70's?
When did people start building big coils for public performances
and special effects, and how did they design them to work without
too much trial and error?

And where is Ed Harris now?
Paul Nicholson
Manchester, UK.