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*To*: tesla@xxxxxxxxxx*Subject*: Re: LC III*From*: "Tesla list" <tesla@xxxxxxxxxx>*Date*: Sun, 27 Mar 2005 22:06:39 -0700*Delivered-to*: testla@pupman.com*Delivered-to*: tesla@pupman.com*In-reply-to*: <200503271831.j2RIVpO02223@abelian.demon.co.uk>*Old-return-path*: <teslalist@twfpowerelectronics.com>*References*: <200503271831.j2RIVpO02223@abelian.demon.co.uk>*Resent-date*: Sun, 27 Mar 2005 22:06:49 -0700 (MST)*Resent-from*: tesla@xxxxxxxxxx*Resent-message-id*: <n9RUx.A.DGF.oD5RCB@poodle>*Resent-sender*: tesla-request@xxxxxxxxxx

Original poster: Terry Fritz <teslalist@xxxxxxxxxxxxxxxxxxxxxxx>

Hi Paul,

Hi Terry, All,

> Transmission line theory was popular in the 80's especially > with the Corums.

And they got that bit right!

Yes indeed!! They broke through the haze and made a great theoretical leap!! But they took the "first version" too seriously and would not accept the modifications that were required... The grand idea was right, but the application was not allow to mature to the point where it really "worked"... They would not address the obvious flaws... The fact that they could not predict Fo was a giant one... They did not have the tools to fix it... Once the Medhurst capacitance correction was used in lumped theory, they were toast... I hope others will not condemn me for saying they were a "little arrogant" ;-)) But if they would have been able to work out the bugs, things would have progressed a decade sooner...

We do in fact use transmission line theory, implemented as finite element models. The basic telegraphist's equation doesn't work because it ignores all the mutual coupling, and the modified differential equations for the current and voltage are given in pn2511, equations 4.16 and 4.17. This is just the telegraphist's equation with a couple of extra integral terms to provide the capacitive and inductive mutual coupling.

Those couple of extra terms are the difference between "it works" and "it does not work" for the average fellow. Anyone with a calculator got the lumped stuff to work... Now we have 3GHz computers so the heavy duty transmission stuff (with all the details) works too!!!

The solenoid exhibits all the same properties as the familiar transmission line of a coax cable. The mode spectrum, propagation and phase delay, SWR, characteristic impedance, reflection coefficients at the ends, and impedance inversion along a quarter- wave. End effects and mutual coupling provide lots of non- uniformity, so things are quantitatively different. For example the modes are not harmonically related, and the characteristic impedance is complex and frequency dependent. Dispersion is a major feature of the behaviour.

Fortunately, for coiling, we don't need any of that detailed knowledge.

No, but it is VERY comforting to see that it is there and working well :-)))) Having 1000% of what is really needed, is not a problem :-)))

We can just use the distributed models to calculate 'equivalent' reactances which we can then use in a lumped equivalent model of the system. This represents an improvement on earlier methods which relied on the product of low frequency inductance and Medhurst C in lumped models.

There was at one time a silly debate over whether a Tesla coil was a lumped or transmission line resonator. There was a general failure to realise that these are just two models of the system, the latter a distributed version of the former. It is a matter of free choice which model you apply, it does not involve a change in the mode of operation of the coil.

But one "worked" and one "did not", that was a giant difference. But that is fixed now!!! We have YOU to thank for that!!!

By correct choice of equivalent reactances, the lumped model can be aligned with the distributed model at chosen spot frequencies.

Terry attempted to settle the matter experimentally, http://hot-streamer.com/TeslaCoils/MyPapers/topsync/topsync.html

but the experiment was based on a false proposition. Both the lumped and transmission line models give the same phase relation- ships between the terminal currents and voltages.

Yes, but that was NOT what "they" were saying.... They saw the "whole coil" as a simple 1/4 wave whip antenna where the current and voltage at the "top" would be 90 degrees from the "bottom". Seems silly to you and Robert, but that "was" the "common belief". I still get "stunned" remarks about that... Even though the conclusion was obvious to those that really understood such things, there were a ton of folks that looked at that paper and realized that their "beliefs" were in big trouble... There were a large number of coilers out there that looked at that paper and realized the "1/4 wave theory" (as they understood it) was in big trouble... They had heard many "hints" of trouble, but that paper was sort of the "shot heard round the world"...

The constant phase is implicit in the standing wave - that's what makes it stand - and both models predict it. No experiment will reveal a difference because the difference is just a choice of models, not a different type of coil resonance.

But actually, is the Tesla coil really a "standing wave" thing ?? The ring up, firing, streamer load... It is very dynamic. Are we fooling our selves by implying it is a standing wave?? Perhaps the "standing" components or greater than the "dynamic" ones?? It is my feeling that there really are no "standing waves" (except CW coils!).

Terry later made up for this by measuring the current distribution of a coil at three resonant modes,

http://www.abelian.demon.co.uk/tssp/tfcp260302/

which should leave no one in any doubt that we are dealing with distributed resonances, and that they are correctly predicted when the mutual coupling and other non-uniformities are taken careful account of in the telegraphist's equation.

That was a really hard experiment!! Glad it worked out so well!!!

I always like this one too ;-)))

http://hot-streamer.com/TeslaCoils/MyPapers/NSVPI/NVSPI.htm

Shows what you can do with 10 cents in parts ;-))

Cheers,

Terry

-- Paul Nicholson Manchester, UK. --

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