TC as pulse transformer

From:  Bert Hickman [SMTP:bert.hickman-at-aquila-dot-com]
Sent:  Thursday, June 04, 1998 6:21 PM
To:  Tesla List
Subject:  Re: TC as pulse transformer

Jim and all,

The most recent posts by Dave, Terry, Malcolm, and you have been
extremely interesting! I concur with most of the conclusions, and again
congratulate Terry for excellent experimental and technical analysis! I
did want to comment on this post since some of the conclusions may not
be consistent with known/new Tesla Coil theory. My comments are
interspersed below.

Tesla List wrote:
> ----------
> From:  Jim Lux [SMTP:jimlux-at-earthlink-dot-net]
> Sent:  Wednesday, June 03, 1998 2:36 PM
> To:  tesla-at-pupman-dot-com
> Subject:  TC as pulse transformer
> here are some ideas that have occurred to me while reading over Terry's
> most recent post.
> At some point, particularly as the Ctop gets big, can't the TC be
> considered as a air core pulse transformer.

A closer model seems to be a dual-resonant air-core transformer because
of the way energy actually transfers from the primary to the secondary
over a number of half-cycles of Fo. The good news is that Lumped
parameter analysis seems to hold for this model.

> You charge up Cpri, then discharge it into the primary of a transformer
> (which happens to have inductance Lpri). The flux of the primary is
> linked to that of the secondary, so the current in Lpri induces a
> current in Lsec. That current charges Csec (=Cself + Ctop), which then
> breaks down the air dissipating the energy.

Yes, but primary-to-secondary energy transfer is not nearly complete in
one quarter of a cycle due to the relatively low coupling coefficient in
a 2-coil system. Even if we stopped the proces at 1/2 cycle (at the
first point of zero primary current), only a relatively small portion of
initially available primary energy will have been transferred to the
>  Assume for a moment that your spark gap can act as an ideal switch. You
> close the switch, and at the perfect moment (i.e. when the capacitor
> voltage is zero, and the inductor current is maximized) you open the
> switch. All that energy has to go somewhere, and the somewhere is the
> secondary. Isec = Ipri * sqrt(Lpri/Lsec). (It is, of course, quite a
> trick to open a sparkgap switch when the current is at a maximum).

It's not clear that this would be the perfect moment, since only a small
portion of the primary circuit's energy will have been transferred to
the secondary at this instant. If we were somehow able to open the
switch, we'd develop a huge primary voltage spike from the Ldi/dt from
the rapidly collapsing primary field. Unfortunately only a relatively
small (10-25%) portion of these flux lines engage the secondary - the
remaining flux lines collapse _only_ back onto the primary, resulting in
most of the original energy being dissipated as heat, light, EMC, and
"stranded" capacitor charge in the primary circuit. Practically
speaking, [barring a single-shot explosive-type opening switch] it's not
possible to open the primary circuit at a current maximum with any
switching devices typically available to coilers, including
semiconductor or gas tube devices.
> Now that the energy is in the secondary, where does it go? The current
> in Lsec starts to charge the Ctop (and Cself), causing its voltage to
> rise. If nothing else happens, Lsec and Csec ring, and the power is
> dissipated in Rsec (mostly the winding resistance, because the
> dielectric loss of air is quite low). Another loss source is the
> effective resistance from the top elecrode to ground created by corona.

I agree, but only for the small portion of the original primary energy
transferred during the first quarter-cycle after the gap fired, plus
another relatively small portion transferred when the gap suddenly
opened at Ipmax. While this would couple an "impulse" of additional
energy to the secondary - like hitting a bell with a hammer - it will
only transfer a relatively small portion of the primary circuit's energy
to the secondary.

> And, finally, the energy in the secondary could be dissipated in
> creating a spark, which we would consider desirable.  The trick, then,
> is to set up the secondary LCR circuit such that it and the spark
> together are critically damped, because this will provide the maximum
> energy transfer into the the loss (i.e. the spark).
> For a real spark gap switch, it is impossible to turn off the switch
> while the primary current is still flowing (although a rotary gap can
> approximate this). So, what you do is put some sort of load on the
> secondary of the transformer that can take the energy out of the primary
> and do useful work before the energy has a chance to flow back through
> the switch and into the capacitor.  That load is a spark.

I agree with most of this. If we let nature take it's course, we will
transfer maximum energy to the secondary over a number of half cycles
until the primary energy becomes zero and all remaining system energy
resides in the secondary/toroid. Ideally, the air surrounding the toroid
will have broken down at some point prior to reaching the theoretical
Vmax of the secondary. By using a large Ctop versus Cself, we can
maximize the portion of total energy residing in Ctop versus Cself. This
improves the odds of quickly dumping most of the secondary:toroid
system's energy into generating and propagating streamer(s), while
minimizing the voltage collapse at the top terminal as we begin loading
it down through charge transfer to the streamers. The more energy we can
dump quickly into streamers, the less that remains to reignite the main
gap when the energy flow wants to reverse and go back into the primary
circuit. However, it's not clear that this scenario corresponds to the
critical damping case...   

> Or, if the resonant frequency of the secondary is different from that of
> the primary, you can get a lower frequency "beat" as the energy goes
> back and forth between primary and secondary (while the switch is
> closed), and hopefully, while the energy is in the secondary, and the
> current is low in the primary, you can "quench" the spark, opening the
> switch.

I think this corresponds more closely to the real-world case of most
2-coil systems. It also seems to be consistent with "best-case"
operation in high-performing coils.

> Returning to making big sparks. We know from laboratory research that
> making a big spark requires a slow rise time voltage pulse (many, many
> microseconds, if not milliseconds). We also know that we want to get
> energy from our storage reservoir (the primary cap) into the
> transformer, and then open the switch. This is starting to look like the
> desired switch is something that is unidirectional, reasonably fast and
> low loss. Perhaps a thyratron or an SCR?
> We want a slow rise time (necessary for developing a big spark), which
> means low resonant frequency in the secondary, and high inductances for
> both the primary and secondary.
> This is what Terry and Dave have arrived at, although by another route.
> They advocate high inductances, small C, and high primary voltages (to
> get the energy up).

I disagree with the part about a unidirectional switch. With a loosely
couple system, the main switch needs to be _bidirectional_ so that
energy can transfer to completion over several half-cycles, and the
switch must then be capable of being turned off once all the energy has
been transferred to the secondary system. This will "force" a perfect
quench, independent of variations in spark-loading. Heavy toploading, a
lower Fo, and relatively high (>=400 BPS) rep-rates will make big
sparks. However, this would seem to be more in the fashion of generating
repetitively arrested streamers, each one following part of a weakenned
trail blazed by its predessor, with far ends "blindly" searching for
ground.  I do agree with most of the conclusions reached by Terry and
Dave. Again, excellent thoughts, and excellent work!!

Safe coilin' to you!

-- Bert --