RE: [TCML] output voltage for Tesla transformer

["Lau, Gary" <Gary.Lau@xxxxxx>]

Theoretically speaking, there are indeed "magic" coupling values which should result in most efficient pri/sec energy transfers and peak performance.  But I have tried slowly varying the coupling on my coils and recording the maximum spark lengths, and I have not noted any particularly sweet spots.

Bert Hickman posted about this in 2002, and I've re-posted his thoughts below.  This may explain why I was unable to find a sweet spot on my coil.

Regards, Gary


Original poster: "Bert Hickman by way of Terry Fritz <twftesla@xxxxxxxxx>" <bert.hickman@xxxxxxxxxx>

Gary and all,

I agree. This is a situation where practical insulation difficulties (for air insulated systems) conspire with relatively high primary gap losses to minimize the benefits of low "magic" k values.

For the benefit of newer list members, certain coupling coefficients (called "magic" k values) permit the primary energy to be transferred to the secondary over an integral number of half cycles at coil's operating frequency (Fo). For these k values, primary voltage and current can _simultaneously_ hit 0. leaving no residual energy in the tank circuit. With non magic k values some of the initial bang energy will become "stranded" as residual voltage across the primary tank capacitor when the gap stops conducting. If some of the initial bang energy is left stranded in the primary tank cap, that leaves less that can make it to the secondary.

The number of half cycles and the corresponding "magic" k values follow:

   Half
  Cycles    Magic
  (at Fo):    k:
  ========  =====
    2       0.600
    3       0.385
    4       0.280
    5       0.220
    6       0.180
    7       0.153
    8       0.133
    9       0.117
   10       0.105

It turns out that magic "k" values actually do work in practice, at least for higher k values. For example, a k of 0.60 or 0.385 is often used in the design of efficient high-power, high voltage resonant pulse transformers for pulsed power applications. However, it becomes quite a challenge to achieve high coupling coefficients while at the same time avoiding dielectric breakdown. This requires paying close attention to E-fields and dielectric strength. It usually requires multiple layers of Mylar or Polyethylene film insulation, conical or graded HV windings, and total immersion in an insulating oil or a pressurized gas (SF6).

Because of poor gap quenching and racing sparks, even well designed classical air insulated two coil systems tend to hit a practical coupling limit of ~0.22 or so (up to ~0.25 for Richard Hull's Nemesis system). Poorer designs may even have difficulty reaching 0.133. At these coupling levels, a primary to secondary energy transfer takes from 2.5 to 4 cycles at Fo to complete. By this time there's relatively little of the initial bang energy left in the primary circuit since it has either been transferred to the secondary or has been burned up in the main gap.

This is most likely why there's seemingly little difference between using "magic" or poor value of k - at this stage there's simply very little total energy remaining in the primary tank circuit. If some, all, or none, of this remaining energy gets "stranded", there's little practical difference in the amount of energy that makes its way to the secondary. And there's correspondingly little difference (measured as streamer length) between using a "magic" k or a poor k value. Since disruptive systems have heavy gap losses, the optimum strategy appears to be increasing k until limited by the insulation strength of the secondary/P-S system or the quenching ability of the main gap.

However, suppose we're able to use a more efficient "gap" (such as a large bank of IGBT's in an OLTC). In this case, it should be possible to achieve higher coupling coefficients than previously possible with spark gaps. Maybe a k of 0.28 (or even 0.385!) assuming that racing sparks don't spoil the party - maybe oil immersion time? If these could be achieved, the benefits of using "magic" k values might become more
readily apparent.

Best regards,

-- Bert --
--
Bert Hickman
Stoneridge Engineering
"Electromagically" (TM) Shrunken Coins! http://www.teslamania.com



> -----Original Message-----
> From: tesla-bounces@xxxxxxxxxx [mailto:tesla-bounces@xxxxxxxxxx] On
> Behalf Of nnanred1@xxxxxxxxxxx
> Sent: Saturday, November 17, 2007 3:44 PM
> To: tesla@xxxxxxxxxx
> Subject: RE: [TCML] output voltage for Tesla transformer
>
> hi,
> there is a set of magic numbers for coupling coefficients and tuning ratios that force
> the two waves running in the coupled system to align at a magic time.
> when these voltage waves align, the charge "stacks" in the system to produce a
> local voltage maximum.  the word local is used in a "calculus" sense.  for u see
> there are magic numbers that produce grand maximums in voltage which are
> greater than all local voltage maximums.  these grand maximums in physics are
> most interesting.
> it is good to study these papers as they contain the governing equations for the
> electrical circuit in which u are interested.  (unless u work in a corporation or the
> goverment where studying is silly)
> by now

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