Re: I've lost my k. Can someone help me find it?

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Bert Hickman by way of Terry Fritz <twftesla-at-qwest-dot-net>" <bert.hickman-at-aquila-dot-net>

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-dot-com

Tesla list wrote:
> 
> Original poster: "Lau, Gary by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<Gary.Lau-at-hp-dot-com>
> 
> THANK YOU (please pardon my shouting) for performing and reporting on such
> a detailed experiment.  The alleged coupling "sweet spots" have long been
> suggested to theoretically be significant, but it's also been my
> observation that performance simply increases with increasing k until
> racing arcs occur.  Time to retire this to the "coiling myths" graveyard.
> Hey, there's an idea for a useful web page!
> 
> Regards, Gary Lau
> MA, USA
> 
> >Original poster: "Daniel Barrett by way of Terry Fritz
> <twftesla-at-qwest-dot-net>" <dbarrett1-at-austin.rr-dot-com>
> >
> >    Hi List-
> >
> >    Thanks to everyone who helped me find my K. I spent about 3 hours with
> >my single-MOT coil  today constructing an arrangement to vary my secondary
> >height. I carefully measured K12 at each 1/8" interval beginning with the
> >bottom turn of secondary 1/2 inch below the primary plane, all the way up to
> >4" above. Armed with this spiffy spreadsheet we went out to the backyard to
> >play. After trying all the variations I came to the following conclusion:
> >
> >    "It just doesn't freekin' matter."
> >
> >    I don't see any sweet spots, nulls or anything exciting at all. Arc
> >length appears to be proportional to K until it gets so high that racing
> >arcs occur and corrona starts coming out of all the bits it isn't supposed
> >to.
> >
> >    I get arcs about 60 inches (at 1.4kW) with k at about .19 and racing
> >sparks above about .21.  My observations suggest that K is not something
> >worth tweaking, at least not as important as detuning to compensate for
> >streamer loading, spark gap, etc.
> >
> >Is this consistant with what others are seeing?
> >
> >Does it become more critical at higher power levels or other conditions?
> >
> >db