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Original poster: Terry Fritz <teslalist@xxxxxxxxxxxxxxxxxxxxxxx>

Hi Paul,

At 11:23 AM 3/28/2005, you wrote:
"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.

I think you and Robert are both from England. I get the impression they teach these things better there, or you guys are just smarter... Or, "I" just was not listening enough in class :o)) But I certainly have noticed that you and Robert seem to "really get" this stuff!!! I just want to THANK both of you for your help over the years!!!!


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.  ....

Realize too that papers, like the Corums, cost a lot of money to get hold of and took a long to arrive... I still have my old letters to odd mail order place to get hold of that secret information :o)))) It was messy heavy reading and if you didn't understand it was "you" who had the problem. After spending months working through it and finding out that is was all screwed up, one no longer looked kindly toward it >:P One thing I try to do as a result is always be very open and try to explain to all the details... If I am wrong, they will catch me more easily and we can all get over it. But usually they really help a lot!! I have since given my many hundreds of dollars of papers away to those that wanted them... It is no accident that now days everything I do is "free" :-)) But back in the 80's, it was almost like a "cult" to try and get hold of the great, hard to get, secret Tesla coil information... But the Internet put an end to all that...

For me, the bottom line was that the secondary was mostly a simple inductor with some odd capacitance added. Years latter, that all became clear. We will not mention the silly "coherence" thing :o))) But that was the easy part since it was obviously wrong due to the conservation of energy long ago. Now with DRSSTCs, maybe that has new meaning IF there was any meaning to it in the first place...

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.

They did try to model coils after transmission line theory and they were right!! However, they were not able to really get it to "work" and give meaningful examples. They just did not have the tools needed to work out the messy details... I am sure "they" tried far harder than anyone!! They "knew" they were right, but they just could not really show it... I think a lot of their "arrogance" was born of the great frustration they must have had... They knew they were right, but they could not make the numbers work... Today, we crunch billions of numbers to do it, they did not have that option... I am not sure how they would react today seeing that you have done what they were not able to do...

I don't know much about what attempts were made to apply stock
transmission line theory to solenoids during those years.

I don't like to think about the months waisted... Those that have been watching me for years easily sense my "attitude" as a result ;-)) There was also a very large "racket" just to sell "hyped up, mysterious, worthless pulp" to the Tesla coiling masses for pure profit... Never have forgiven them >:))

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.

I spent months and many hundreds of hours on that and am happy that worked!!! I still have to thank the real programmers that took my feeble BASIC program and really made it work well and fast!! I included the original post about it at the end here... It was TWFreq originally, then went to the many iterations of E-Tesla... Probably should have named it for Gauss.... But it was only a little "step" really. Mark's MandK program was a big one too!! Those two programs together filled the last "big" holes... Mark had pi/2 factor error for a long time... I was up at like 3am working on that.... I remember the painstakingly measured error... 1.57... Hmmmm..... But he finally found it!!! When it came to calculations, we could then take on anybody at that point!!! MicroSim modeling also really hit with the LTR coils!! Suddenly, computer models were making "better" coils... Those that scoffed at calculations and computers trying to figure out Tesla coils were then "on the run" ;-)) I used to take three hours to run, now it runs in a key press... It is not really "efficient" now on a 3GHz computer due to excessive hard disk file writing...

This paper demonstrated that those that "make" coils with "calculators and computers" were now a real force to be reckoned with!!


We could calculate it, we could predict it, and we could prove it ;-)))

The LTR could also "extend" the art... Those models made a "better coil". The LTR coil... A "triumph" of computer modeling!!! Computer models predicted the LTR and "later" we made them!!! The LTR coil was simply "invented by computer"... Much later, the OLTC was also invented by computer when "they" verified that a single turn primary could easily couple the needed energy via Mark's MandK program... If that simulation would have said the coupling was 0.001, the OLTC would have been gone right there... In those days, I got so excited about model results that I ended up crashing my car thinking about them ;-)))

Now days, it all seems so easy ;-)) But I remember many days when "I" was the whacko for challenging the "seat of the pants" coilers. But I knew things were right and with the list everyone was able to join together to work out the problems. Unlike the Corums, we had about 1000 folks working it ;-))) Seems every glitch or worry was solved by someone out there!!!

I guess I should point out that I never yelled or disregarded them for disagreeing with me. I simply asked what was wrong with the idea and then went working on fixing it... Problem after problem... Solution after solution... They "ran out" of problems eventually!! I remember many times worrying that everything had to agree with Richard Hull's "real world" stuff... If it didn't, it was probably wrong... I always relied on real world data and information to keep things straight. Those that disregard the real world measurements and "truth" will have a "problem" with me ;-))

We always have a problem with "new ideas" that can't be verified.... "Q = Sum E x eo" could not be verified in Gauss's time... But E-Tesla certainly proved it for us - 200 years after... Always a hard call.... I sneak around it with my "practical" thing... If someone does have a new theory of the universe, take it to Cambridge rather than us...

I may have been a "cheerleader", but "I" really did not do much... I tried to define the problem of the day and hoped someone else would figure it out ;-)) I have a lot of test capability so that was my "niche"...

For those that never cared about the theory, the MMC capacitor was probably the biggest "overnight success" story in the history of coiling!!! That certainly showed that things can change very fast and for the far better!!!! I wonder if Chip was ever able to dump is half finished rolled cap? I spread 1000 MMC caps on his kitchen counter and I don't think he worried about caps blowing his roof up anymore ;-))

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.

Yes!! Antonio was always they guy I trusted for anything "electrostatic". I worried for a long time that much his stuff did not include losses... But then he figured out the inductance of may OLTC triple parallel primary and the "exact" capacitance of toroids and stuff!!! I don't worry anymore ;-))

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 can't even keep up with all the wonderful tools out there now ;-)) But it is wonderful that so many of the giant monsters that used to dominate Tesla coil theory are dead now!! We can finally move on...

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.

I make that error all the time... I'll try to be more careful...

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

Before 1998... I want to say Malcolm? I think I remember him as being the one that brought it to us!! That was a GIANT leap forward!!!!

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.

I have all the issues... But you sort of just have to read them one by one, year to year... I never have been a big history buff...

For the future, it the DRSSTC for sure!!! Complex electronic crap thing? Yeah... So was the cell phone in the 80's ;-))) For the pioneers of the DRSSTC, save your notes and stuff, historians will be knocking at your door soon ;-)))

Cool!!  This post is almost as large as Harvey's ;-)))



Paul Nicholson
Manchester, UK.

Terry Fritz <twf@xxxxxxxxxxx>
New Fo, Cself, Ctotal Program
1/3/99  01:17pM

Hi All,

We have often wanted to know the resonant frequency, self capacitance,
and total capacitance of our secondary coils before they are built. Wheeler's
formula gives us the secondary inductance to a very good accuracy so calculating
the inductance of the secondary has never been a real problem. The Medhurst
equation supplies us with a number for the secondary self capacitance that is
fairly accurate. However, once you put a terminal on the top of the secondary,
things get bad. The terminal is placed within the self capacitance space and
has the effect of adding to the self capacitance. There are rules and ideas
about how to guess at this situation but guesses are all there are. People have
done experiments but the experimental set up never seems to match our systems
well and the results may not be very good. You won't find a good single equation
for this situation.

So.... the real problem is finding the total capacitance of our secondary
systems by calculation rather than building it and seeing how close we guessed.
If one thinks about all the variables the problem quickly seems impossible.

However, consider this. The capacitance of an object is simply the charge in
Coulombs on the object divide by the voltage. If we know the charge and the
voltage we know the capacitance (and Fo). The voltage is really easy. It can
be any arbitrary voltage ( I use 100 volts... for no real reason). Then the
problem is simply to find the charge, on the coil system, at that voltage. Sounds
hard to figure out and the mental effort behind the solution is in the realm of
genius. Fortunately, around 200 years ago Karl Friedrich Gauss (1777-1855)
figured it out for us. It doesn't mater how complex or messy the dimensions of
the charged object are. All that matters is what the field around it looks like.
Gauss came up with what is known as Guass's Relation. It is:

"The total flux passing outward through any closed surface equals (1/eo) times
the total electric charge inside the closed surface."

In other words, if you throw any shaped charged object into a bag with lots of
little electric flux sensors sewn into it.  The charge on the object will be
equal to the sum of what all the sensors measure times eo.  Or...

Q = Sum E x eo

So... That still sounds harder than just building the darn thing and seeing
what happens :-) However, we now know how a secondary coil's voltage is
distributed. It is a sine shaped distribution along the length of the coil.
The top of the coil and terminal are at the same potential while the base is
grounded. Thus we can set up a computer simulation to find the electric field
around the coil given it's dimensions. The finite element analysis technique
to do this is well known by people who worry about such things. It is really
very simple but takes a very large number of calculations. So the computer
can crunch out the field distribution. Our task (the computer's task) is to
simply place a virtual surface around the coil and add up all the flux passing
through it. The surface can simply be a sphere with the Tesla coil contained
inside it. This is the simplest surface to use for our needs. There are no
unknowns here. Just Gauss's wonderful relation, some simple math and one heck
of a lot of calculation. We have the relation, the math is straight forward,
and modern computers can easily do the calculations in some reasonable time frame.
So we have all the parts. So... would someone please write a program to do this?...

Too late! :-))   I couldn't wait.  It is still an alpha version but I
think it works well.  It is called TWFreq and is available at my site:


I'll call this the Alpha version. It is written in DOS's QBASIC (which is
included since modern OSs don't have it anymore). It will run on any PC.
It will run in a DOS window on NT and the like. If it works out, someone can
rewrite it in some nice language since it is short, simple, and straightforward.
Programming is not one of my strong points... I hear there are DOS emulators for
Macs. If so, it should work fine on those too. This is a straight text based
program with no fancy stuff. It can be converted to any computer's BASIC
programming language (it needs more than 8k of RAM :-)). Nothing fancy. Expect
it to take at least a few hours to get down to a stable number. The extra cash
you paid for the faster computer will pay off now. It writes the voltage field
data to disk periodically so you can print the field plots out if you have Excel97
or some other program that can do surface plotting. It can be modified to do
field stress too very easily. It only does one terminal but two terminals or other
configurations would be easy to add. Just a matter of putting the shape in.

Basic instructions are included and any problems found or suggestions should be
sent to me for fixing. The program works fine on my system and the parts I can
mix and match together but only a real field test will insure it "really" works.
If you know your system well, please report the accuracy to me so I can determine
if there are any weak spots and come up with a good number for claimed accuracy.
There are no "fudge" factors in it now but that could change :-))

This program has never been field tested before so the guarantees are zero.
However, it should work.  I hope it works out.  It will fill a one of the few
holes we have left in Tesla coil design for the armchair coiler...

Good luck!    We'll blame Karl if it doesn't work :-))