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Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

"rb" wrote:
> Im glad Terry didnt kill the thread it was/is a great overview
> of developments.

Yes, I enjoyed Bob's concise summary of the history of
developments since 2000.  He has a fine grasp of all the
theoretical issues, as do a handful of others on the list.

Amongst most list members though, the majority who just enjoy
coiling and are not actively studying the theory, it seems there's
still a lot of confusion.  Some of it's down to terminology, and
I guess we should work harder to explain things better.  It's no
good referring people to a paper full of math, and for this reason
I try to do expository posts if I see something that seems to be
wrong or misunderstood.  You can't just say "Hey that's wrong"
without giving a thorough explanation of why.  Even if the advice
is rejected by the intended recipient, at least others may find
some of it an interesting read (I hope!).

It's difficult for those like me who are relatively new to coiling
to appreciate how coil operation was understood in previous decades.
A browse through older material shows a lot of really wacky stuff,
but underneath that there's a steady trend of rational development
of both theory and practice.

Prior to the last ten years, theoretical development does seem
rather weak, leading to a state of affairs in which the popular
opinion became contemptuous of theory - probably because none of it
seemed to work.  Coil development was almost entirely practical,
working to a process of evolution in which good designs were
reproduced while bad ones were left to fester at the back of the
shed.  This breeding program was successful too, because now that
theory has caught up somewhat, we find the evolved designs are not
to be improved on in any significant way by anything that theory
has to say at the moment.

A good metric for the state of theory development is the ability
to predict the coil's resonant frequency.  This was at one time
apparently done by assuming that signals travelled along the wires
at light speed, so that the frequency of resonance would be given by
c/(4*wire_length).  The extraordinary thing is that this idea
persisted for so long amongst coilers.  For one thing, it is obvious
from basic EM theory that the assumption is invalid, and for another,
a simple frequency measurement of the coil would reveal the large
error.  Interestingly, the long thin coils popular in the earliest
days would have shown the greatest error - a factor of two.  This
could not have gone unnoticed, could it?  How could anyone get a
primary into tune except by a lot of trial and error?   This must
have been a very black art, considering the type of primary caps
in use.

As time moved on, it must have become blatantly obvious that the
wire-length light-speed method was wrong and an improvement came
along in the form of a lumped model using Medhurst capacitance.
This would immediately have reduced prediction errors from 50-100%
down to 5-10%, and even better on loaded coils.  Such a major
step forward must have led most coilers to stop thinking of the
resonator as a distributed structure and instead treat the lumped
model as the real thing.    This however represented a step too
far, because for example, it failed to predict the existence of a
coil's mode spectrum.   Obviously a distributed model would be
needed in order to reveal the coil's operation in more detail.

I think the Corum's were the most prominent advocates of applying
transmission line theory to the coil, and I think any electrical
engineer would agree with them on that.  The transmission line
behaviour of wires, coils, pipes, and other extended structures
is well known, although not easy to calculate in many cases.

I don't know much about what attempts were made to apply stock
transmission line theory to solenoids during those years. Likely,
attempts would involve the standard telegraphist's equation, with
suitable estimates of the distributed reactances.  I've explained
before how this would be a little in error (worse for short fat
coils than long thin ones) because it fails to include terms for
mutual coupling.   Also, it was not easy to calculate the
distributed reactances (particularly the capacitance) which are
essential inputs to the transmission line model.   For these
reasons, and some misunderstandings which have been mentioned in
previous posts, the transmission line model fell into disrepute
(fortunately only temporarily).

The theoretical impasse was broken by Terry when he made a program
to calculate the distributed capacitance of a secondary coil and
topload.  This was, as far as I know, the first realistic attempt
to go beyond the Medhurst C lumped approximation.  The program
(E-Tesla - but it had an earlier name I think?) worked by solving
the equations for the Coulomb field using the laborious but effective
method called 'relaxation'.   Terry's program only pursued the
calculation far enough to compute a better equivalent lumped C than
Medhurst and didn't make any other use of the distributed capacitance
calculated as an intermediate step, but it did point the way ahead
and start the ball rolling.

Others at that point jumped on the bandwagon and came up with
software to compute the distributed reactances at higher accuracy.
Probably the best of these now are the programs made by Antonio.

Because these newly calculated reactance distributions also include
all the mutual reactances, we then had all the coefficients needed
to make transmission line theory correctly model a resonating
solenoid, and the resulting precision is of the order of 1% now. It
works for any shape of solenoid, thin and fat, as well as disc and
cone shaped coils.  The principles are general and the difficulty in
any particular case boils down to the accuracy with which those
reactance distributions can be calculated by field modelling.

I'm pretty sure that the access by coilers to high power computers
as well as a critical Internet forum has brought about these recent
rapid developments.

On the matter of terminology, when we say '1/4 wave theory' is dead,
we mean (I hope) that the idea that coil resonates at the free space
frequency of its wire is dead.  Instead of the effective velocity
factor being unity at all h/d ratios, it is given by the nice curve

It doesn't matter now whether you make this graph by measuring lots
of coils and plotting points, or by calculation from first principles,
you arrive at the same curve, which is nice to see.

And as for 'transmission line theory', it does work and forms the
basis of all our modern calculations, and is very accurate for all
the coil shapes for which accurate field modelling can be done.
What doesn't work is the stock telegraphist's equation employing
only rough estimates of the reactances and no account of mutual

The residual error of 5-10% in the Medhurst based lumped approximation
can be removed by using slightly different lumped reactances,
calculated from the distributed model.  These not only give the
correct frequencies when used in the lumped LC model, but also
the correct ratios between top voltage and base current, which could
be up to 20% or more out in the Medhurst version.  Bart Anderson made
available a browser based distributed model, JavaTC, which calculates
the proper equivalent reactances. This allows coilers to continue to
use traditional lumped calculations while retaining most of the
accuracy of the transmission line model.

It should be made clear that no new physics or math techniques were
required along the way, at any stage.  This development was simply
one of coiler's learning how to apply well known physics, electrical
engineering, and computational methods to coil resonance.  If you
showed our modern calculations to a physicist from 1900, he would
be quite happy with the principles employed.

A questions for the old timers...Who first introduced the use of
Medhurst C into Tesla coil calculations, and when?

Perhaps there are items in the TCBA archives that reveal how coils
were explained and calculated during those two decades?  It would be
nice to review some of them.
Paul Nicholson
Manchester, UK.