Re: More ISSTC theory stuff (l o n g)

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

Original poster: "Antonio Carlos M. de Queiroz" <acmdq-at-uol-dot-com.br> 

Tesla list wrote:
 >
 > Original poster: "Steve Conner" <steve.conner-at-optosci-dot-com>
 >
 > Hi Antonio, thanks very much for your input.
 >
 >  >The big problem is to guarantee good matching for any load, what seems
 >  >impossible.
 >
 > At first sight it does, but I think it's not really that bad. If the
 > streamer load is not heavy enough, the output voltage (and primary current)
 > will just ring up, lengthening and heating the streamers until they present
 > the right load. (as streamers get longer/hotter their impedance decreases,
 > but this impedance is inverted by the "matching network" so the impedance
 > seen by the inverter INCREASES)

Yes, I was also thinking that the system would "auto tune" to the right
load,
the one considered in the design, but see below...

 > So, if you design to a streamer length that is appropriate to the power/bang
 > energy you are running, I think the ringup will level off at your target
 > current and it will all work out.

See below.

 > You might argue that the system could get "trapped" in a state where the
 > current rings up but the streamers for some reason don't grow to limit it.
 > But I think this will only happen if you try to produce a streamer longer
 > than your inverter can handle- your IGBTs will explode before the streamer
 > reaches target length.

I was verifying what happens with my design when the output load
changes.
The result is curious, and maybe very significant:
If only the load resistance changes, the input impedance -remains
resistive-,
and changes to match the load. This happens because of the doubly tuned
transformer, that operates independently of the load.
I verified then what happens if the capacitive loading changes, due to
streamer growth. The result is not very good: The input current
-increases-
and becomes reactive, out of phase with the voltage, for changes in both
directions of the capacitive loading.

 > Anyway this sounds like serious non-linear math, so time for me to throw
 > away the calculator and get soldering ;)

Some experiments with measurements would be interesting to see how real
this
linear modeling is. I imagine that it is realistic. I have the materials
to make an experiment, but this will have to wait some time.

 > excellent! I think I understand, in your equation, the voltage gain (n) is
 > the term we use to get the desired impedance match? And you just chose the
 > bandwidth arbitrarily? If you choose a much wider or much narrower
 > bandwidth, what does this do to the resulting component values? I suppose it
 > would affect the coupling and the tunings of both "matching networks".

Yes, the transformer gain, n, is what makes the impedance conversion.
The reactances are just to compensate each other and reduce the circuit
to an ideal transformer. The controllable bandwidth (at design time) is
an additional feature over a basic design as a cascade of L-matches.
Its main effect appears to be in the coupling between the coils.

 >  >Not very different from the usual for a capacitor discharge coil.
 > Spooky :)))) In fact I have such a coil (the Tesla-2) with similar
 > parameters to the ones you posted- but roughly twice the primary inductance
 > and half the tank capacitance.

All indicates that a conventional coil assembled as a solid-state coil
will work well.

 > However I run my stuff on 377V DC here (240v AC mains) so if I understood
 > you right, the extra voltage would compensate for the higher primary
 > impedance, and the peak primary current would still be 100A.

Yes.

 > (100/sqrt(2))A * (4/pi)*(377/2)V= 16.9kW flowing for 200uS= 3.3 Joules bang
 > energy, which is more than it had as a spark-gap coil 8-o

I get:
Rms current = 100/sqrt(2) = 70.7 A
Rms voltage = 377/2*4/pi/sqrt(2) = 169.7 V
Average power = 70.7 x 169.7 = 12 kW
In 200 us: 2.4 J

 > I'll try to run this coil as an ISSTC and get some measurements. Thanks to
 > your equation, I can easily calculate what the streamer load impedance
 > actually is, by measuring the primary current.

It will be interesting to see what happens.
I have implemented the design equations in a little program. I will see
if I add
a simulator on it too.

Antonio Carlos M. de Queiroz