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Re: Gap Dwell Times (formerly: Beating Solved)



Skip,

There's no easy way to explain this! We want the primary to ring for 1/2
a BEAT [Fupper - Flower], not for 1/2 a primary cycle. Coupled LC
circuits work BEST when their uncoupled resonant frequencies are close
or the same. Loosely inductively-coupled resonant circuits exchange
energy back and forth between the primary and secondary at the "beat"
frequency. Because of the loose coupling, it takes a number of cycles
for all of the primary energy to transfer to the secondary or
vice-versa. If we had a lossless system, this exchange and re-exchange
of energy would continue indefinately at the beat frequency. Steve Roy's
earlier example using coupled-pendulums was a fairly accurate
representation using a mechanical analog. 

The greater the coupling coefficient, the fewer primary oscillations
required to complete an energy transfer "beat". Since coupling only
takes place while the gap is firing, we would like to turn off the gap
at the _first_ point where the primary has minimal energy (NOT the first
zero current rossing). In this case, most of the energy that was
originally in the primary LC pair now resides in the secondary/toroid
pair (less losses). 

With the gap quenched, the secondary will ring down at its uncoupled
resonant frequency. The rate at which the secondary's energy is
dissipated now depends on its Q, and whether energy is _also_ being lost
via a corona discharge (the case we usually want). If the gap fails to
quench, much of the secondary's energy couples back to the primary and
is subsequently dissipated in the gap. In this case, any further
increases in primary power merely heat up the gap and may result in
decreasing output from the secondary. 

You CAN increase the coupling coefficient and jam more energy into the
secondary in a shorter amount of time. The "gotcha" is that the
secondary may be stressed beyond its dielectric strength during the
primary to secondary energy-transfer. This transfer usually occurs at a
_higher_ frequency than the secondary's 1/4 wave ring-down frequency,
causing voltage peaks at points lower than the top of the secondary
winding. Increasing the coupling coefficient only worsens this effect:
2-coil systems typically "max-out" at k=0.28 or less due to secondary
winding flashovers. 

Going to an oil-immersed coil might allow you to go to higher coupling
coefficients IF you can also prevent the gap from re-igniting when the
secondary tries to dump its energy back into the primary. 3-coil systems
avoid the secondary breakdown problem (but not the quenching problem) by
base-driving the third coil/toroid _at_ its natural ring-down frequency
from a tightly coupled primary:secondary pair. Proper high speed
quenching is still somewhat of an art.


Some other backup information (ignore if you bore easily...):
============================================================
Most operators of large coils tend to set the "uncoupled" primary
frequency (i.e., with no secondary) below that of the uncoupled
secondary/toroid resonant frequency to compensate for additional
capacitance of the ion cloud which forms around the discharge terminal.
Because of gap losses, the "effective" Qprimary is typically much less
than Qsecondary (w/o discharge) - 11 vs 140 for my system. At typical
coefficients of coupling, the system exhibits two frequency peaks at
Fupper and Flower when measured at low power via a signal generator and
back-to-back pair of LED's.

During operation, Qsecondary (w/o discharge) is significantly greater
than Qprimary (with the gap), and Fprimary is initially tuned to be less
than Fsecondary. It can be demonstrated for this case that the primary
current will tend to oscillate at Fupper during primary-to-secondary
energy transfers. During this time, the secondary/toriod pair is
magnetically "driven" at a frequency _higher_ than its natural 1/4 wave
frequency. Once the gap quenches, the secondary then rings down at its
1/4 wave frequency (adjusted for ion cloud capacitance). This former
case is covered in the "Radio Engineers' Handbook", Frederick Terman,
McGraw Hill, 1943, section 3, paragraph 6. I've also verified Terman's
results experimentally via high-power "single shot" measurements with a
storage scope.

If the secondary discharge can be held off until almost all the primary
energy has been transferred (using an optimally-sized toroid), AND if
the gap is quenched at the first minimum of primary energy (1/2 Beat),
maximum power _will_ be transferred from the primary to the secondary.
If spark length is a function of the amount of energy available, this
should translate into maximum spark length. Waveforms showing the energy
transfer and interchange process can be graphically seen in the latest
series of simulations on Dave Huffman's site: ftp://d0huff.fnal.gov/ftp.

If you quench too early (say at the first zero crossing of primary
current), only a _small_ portion of primary energy will have been
transferred to the secondary. The rest of the energy gets expended in
trying to heroically extinguish the gap! This case is illustrated in the
graph in the appendix of the Corums' booklet "Vacuum Tube Tesla Coils",
page IV-10. The predicted "best case" quenchtime was calculated to be
about 10 uS based upon the upper and lower coupled resonant peaks.
When quench times were forced to be less than 10 uS, there was a
_dramatic_ falloff of output, MUCH more severe than having too long a
quench time. For example, at 5 uSec, secondary output is only about
10-15% of the optimal value. Dave could probably punch-in a slightly
different set of gap opening times on his model to simulate this effect
graphically as well (hint, hint...).

Whew!! This is _heavy_ stuff! Think I'll go play with some sparks now...

As usual, flames, semantic corrections, and insults are heartily
welcomed! :^)


-- Bert --

<The mother of all snips...>

> Richard and all
> 
> This brings up a question which has been on my mind for a long, long
> time.
> 
> If we only want the primary to ring up for 1/2 cycle .... why is it
> necessary that the primary and secondary be correctly tuned? I know this
> to be true and you know that I continue to try to build a 1/4 wave
> secondary but I still can't put it together. Why can't we just closely
> couple the primary to the secondary and jam the power in? I guess I need
> something physical to put picture what is going on. I will certainly
> appreciate any light that the group can shed on this.
> 
> Skip Greiner