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*To*: tesla@xxxxxxxxxx*Subject*: Re: LC III*From*: "Tesla list" <tesla@xxxxxxxxxx>*Date*: Wed, 30 Mar 2005 16:51:03 -0700*Delivered-to*: testla@pupman.com*Delivered-to*: tesla@pupman.com*Old-return-path*: <teslalist@twfpowerelectronics.com>*Resent-date*: Wed, 30 Mar 2005 17:05:59 -0700 (MST)*Resent-from*: tesla@xxxxxxxxxx*Resent-message-id*: <LHjgeC.A.nUF.l7zSCB@poodle>*Resent-sender*: tesla-request@xxxxxxxxxx

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 then.

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 modes.

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,

http://www.pupman.com/listarchives/1996/january/msg00096.html

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 is

http://www.pupman.com/listarchives/1995/august/msg00020.html

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

http://www.pupman.com/listarchives/2004/July/msg00406.html

and I made some comments on it in

http://www.pupman.com/listarchives/2004/July/msg00545.html http://www.pupman.com/listarchives/2004/July/msg00683.html

(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. --

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