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Re: Gap Dwell Times (formerly: Beating Solved)
Tesla List wrote:
>
> > Subject: Re: Gap Dwell Times (formerly: Beating Solved)
>
> >From sgreiner-at-mail.wwnet-dot-comSun Oct 13 22:22:44 1996
> Date: Sun, 13 Oct 1996 11:01:29 -0700
> From: Skip Greiner <sgreiner-at-mail.wwnet-dot-com>
> To: tesla-at-pupman-dot-com
> Subject: Re: Gap Dwell Times (formerly: Beating Solved)
>
<SNIP>
> Bert,
> Thank you for a very definitive answer. I stll have mixed feeling about
> dwell times and energy transfer. As you and numerous others have
> commented in the past there are so many unanswered questions about what
> we do, it sometimes seems that every new answer brings on 5 new
> questions.
>
> > Skip,
<SNIP>
Yeah... its the "pealing the onion" thing! And you've tended to ask some
real posers! Most of the discussion below refers to 2-coil systems,
unless otherwise stated.
<SNIP>
> >From my radar days we had to drive the pulse forming lines from the
> matched driver impedances to get maximum energy transfer. We took a
> block of energy and dumped it all at once into the line and took it out
> of the other end all at one time. In the case of the TC, I have always
> assumed that when we match up the frequencies we are essentially
> matching up the impedances of the primary and secondary. The pulse
> former in our case is the primary cap and the combination of the gap and
> cap make up our delay line. Our problem is to get complete energy
> transfer from the cap to the secondary without reflecting any back.
There's simply no way to directly compare a direct-driven transmission
line and a loosely coupled pair of tuned circuits. It's fundamentally
impossible to transfer _all_ the energy in the primary into the
secondary in one shot since we're constrained by the coupling
coefficient. For typical 2-coil TC's, 80-90% of the primary's magnetic
flux lines cannot transfer energy into the secondary. Only the 10-20%
of flux lines which are common to the primary and secondary do the work.
The majority merely recycle energy back into the tank cap for the next
half-cycle and energy "push". The above energy transfer argument holds
irrespective of the particular model we choose to use for the secondary.
[BTW, I now believe that modeling the secondary as a transmission line
unnecessarily complicates 2-coil analysis, and provides no predictive
benefit for capacitively-loaded 1/4 wave coils. Duane Bylund's
supplement to "Modern Tesla Coil Theory" presents a strong case for
using a lumped-parameter model for this condition. The effectiveness of
heavy capacitive top-loading is amply supported by experimental results
for 2 and 3-coil systems by many experienced coilers on this list. The
"deeper" explanation for why this works so well probably lies within
Greg Leyh's earlier comments on tapered transmission lines. The
"simplist" approach is not to argue with success!]
<SNIP>>
> Putting aside for the moment the problem of arcover, etc., could we very
> closely couple the primary/secondary and with one of Richard Hull's very
> fast quenching gaps apply a huge pulse to the primary, immediately
> quench the gap, and let the secondary ring, except that hopefully the
> pulse running up the secondary will create a very large spark and start
> generation of the ion cloud getting ready for the next energy pulse.
Yes, not in one huge pulse, but in two large ones. Suppose we had a k of
0.60. For this case all the primary's energy can be transferred to the
secondary/toroid in 2 primary half-cycles, at which time we would quench
the gap. (If we tried to quench earlier than this, we couldn't transfer
all the primary's energy to the secondary.) The practical rub lies in
your statement "putting aside for the moment the problem of arc-over".
Higher coupling means closer primary:secondary proximity. Worse yet,
higher coupling increases "frequency splitting" during energy transfers.
Since the pre-breakout Q of the secondary is typically much higher than
the primary Q (with gap), the primary "driving" frequency will be higher
than the secondary's natural frequency while we're "pumping" it.
If Fcenter is the uncoupled natural frequency of the primary and
secondary/toroid circuits, then Fupper and Flower for k=0.6 can be
estimated:
Fupper = Fcenter/(sqrt(1-k)) = 1.58*Fcenter (the primary "driving"
frequency)
Flower = Fcenter/(sqrt(1+k)) = 0.79*Fcenter
Note that Flower tends to be depressed in the primary circuit when
Qsecondary >> Qprimary per Terman)
This implies that, while being excited by the primary, the secondary
voltage "peak" in a 2-coil system will appear somewhere between 1/2 and
1/3 of the way down the coil! This typically exceeds the coil's
breakdown
strength unless heroic insulation measures are used. In practice,
achieving breakdown-free coupling of more than 0.25 in air-insulated
2-coil systems becomes quite difficult. In oil, who knows?!
<SNIP>
> Are you saying that the energy transfer continues after the first 1/2
> cycle of the first beat if the gap is still conducting?
Yes (but _only_ if the gap is still conducting).
> If so do you think that the energy is somehow being stored in the secondary, perhaps
> in the toroid and Cself? If this were true, how is the energy
> transferred to the secondary during the first beat, prevented from
> transferring back to the primary during subsequent beats (assuming the
> gap continues in conduction). How can there be an accumulation of energy
> in the secondary for the making of the big discharge?
<SNIP>
Energy is transferred and being stored in the series LC circuit formed
by the secondary's inductance combined with Ctoroid and Cself. The RF
ground from the secondary base is an active part of this circuit. The
_key_ to primary:secondary energy transfer lies in the phasing of each
energy "push" from the primary to the secondary. During the first beat,
each half-cycle "push" _adds_ to a growing store of energy stored in the
oscillating secondary tank circuit. Remember that, until we get breakout
from the toroid, secondary Q is normally quite high. We lose relatively
little energy in the secondary between successive pushes (assuming a
good RF ground...), so secondary energy builds during each push.
Each "pump" of energy to the secondary removes a similar amount from the
primary tank circuit. Since the primary's energy per "bang" is finite,
the pumping process stops once the primary energy has dropped to zero
(i.e,, at the end of the first beat). At this point, ALL the energy
originally resident in the primary cap has been transferred and now
resides in the secondary tank circuit (less all losses). If the primary
gap is still ionized (but not firing), it rapidly re-ignites once the
secondary (now acting like an energy-source) tries to pump its stored
energy back into the primary at the start of the next beat. Quenching at
this point prevents the energy backflow. If the gap isn't quenched,
subsequent secondary-to-primary energy transfers begin to _subtract_
from the secondary's peak energy, reducing output.
Ideally, the top terminal will begin to "break-out" at this point, and
we will have quenched the primary. Secondary energy then goes ONLY where
we want it - to the streamers!. Having the toroid breakout voltage
adjusted properly is nearly as important as quenching at the right time,
and is certainly a significant part of generating a "synergistically"
tuned system.
> Shouldn't we strive to get a single pulse of energy to the primary
> secondary system and thereby reduce gap losses and oscillatory losses?
Not for a 2-coil system. We should strive for maximizing the coupling
coefficient consistent with the breakdown limits of the system, and we
should quench once the first primary-to-secondary energy transfer is
complete . Generally, this requires _at least_ 4-5 primary half-cycles
(for k = 0.22-0.28).
I've have not seen or done a similar analysis for 3-coil systems.
Any volunteers?
<SNIP>
> But don't we eventually achieve the same amount of total amount of
> energy transferred to the secondary and therefore the same maximum
> stresses just a few beats later?
Ignoring other losses, the same amount of energy _will_ be transferred a
few primary half-cycles later for lower coupling coefficients. However,
maximum inter-turn voltage stress is determined by _how fast_ we try to
"pump" the secondary, not by the peak voltage reached once we get there.
Its sort of like comparing stresses in a dragster accellerating from 0
to 100 in 2 seconds versus 3. Although the velocity (and kinetic energy)
are the same in either case, the stresses are _much_ greater in the 2
second case.
<BIGGG Snip>
> Thanks again for a great discussion
>
> Skip
>
My pleasure, Skip.
You've continue to ask LOTS of good, thought-provoking questions. As
usual, flames and boulders are welcomed... :^)
Safe (and very inquisitive) coilin' to ya!
-- Bert --