Re: DRSSTC design procedure - draft

["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>
 >
 >  >Any mistuning (including operation at the
 >  >resonances) increases it.
 >
 > Hmm. So operation at the resonances is now mistuning?

If the system is designed to operate between the resonances and
the driving frequency is changed, initially the output voltage
drops and the input current increases, but by small amounts.
After a certain displacement, a second "beat" appears after the
"normal" beat of the output voltage, that reaches higher voltage,
but the input current almost doubles. With more displacement
a third beat appears, with still higher voltage and current.
This goes on (with hard switching) until a resonance is reached,
where the output voltage and the input current grow continuously
and the switching is soft again.
My design then creates a local maximum for the voltage gain,
with an absolute minimum for the input current.

 > I'm sure when Jimmy Hynes made his original coil, he explored much the same
 > region of parameter space that Antonio is recommending now. I can't find
 > accurate data on it, but I think he had C1=0.6uF, L1=13uH and k12 roughly
 > 0.1, and used an excitation frequency at the geometric mean of the two
 > resonant frequencies.

The geometrical mean is good too, specially when a resistive load
is being driven.

 > However, the experimental results showed that it worked better when retuned
 > to operate at one of the resonances.

Probably because his driver could switch larger currents.

 > I do realise that this could have been an accident, and there may have been
 > an even more optimal design nearby in parameter space that he just missed.
 > Looking at Antonio's work, it's tempting to suggest that if Jimmy had only
 > made some slight changes to align his system with a particulat set of magic
 > mode numbers, the performance would have improved drastically.

If the system is designed with the driver operating at its maximum safe
current by my method, no other tuning will produce better results (I
think
so far). If the driver can allow more current, operation at one of the
resonances can produce greater output. But then it's a question of
redesigning the system for the greater current to obtain even greater
output.

 > But my own personal belief is that Antonio's theory gives over-optimistic
 > results because it doesn't take streamer loading into account. Anyway,
 > there's no way we can model this yet as we don't have an accurate dynamic
 > streamer loading model. So again more experimental work is called for... It
 > shouldn't be too hard to make a DRSSTC that can be assembled in "Ward Mode"
 > or "De Queiroz Mode" and a comparison done.

My previous design method, based on an impedance matching network,
produces practically the same element values of the lossless design,
so resistive loads are not a big problem. Capacitive loads would cause
mistuning, but then the idea of using a pll to adjust the input
frequency may help.

  > I would be happy to try this. Maybe Antonio could suggest a design
that
 > would turn my OLTC II resonator into an optimal DRSSTC?

Let's see:

 > Data and constraints for OLTC II:
 > Secondary inductance: 225mH
 > (Secondary + toroid) capacitance: 31pF
 > Resonant frequency: 62 kHz
 > Breakout voltage of toroid: ~600kV
 > Flashover voltage of resonator: ~770kV
 >
 > Power source: H-bridge powered by 600V DC
 > Maximum I2t of power source: 600A rms for 1 millisecond (=360 x 10^6 A^2.s)
 >
 > Tank capacitor: I have about 40 1uF 1000V caps that can be assembled in any
 > combination you like. (capacity 20J)
 >
 > Desired bang energy: As high as possible given the above constraints. The
 > design method I published results in about 21J. The secondary can only hold
 > about 6J before breaking out, but the remaining energy is fed from the
 > inverter and primary tank straight into the discharge while it is alight.
 >
 > L1=?
 > C1=?
 > k12=?

With the driver feeding the streamers, maybe better to use the impedance
matching design. The formulas are in:
http://www.coe.ufrj.br/~acmq/tesla/sstc.html

With Lb=225 mH and Cb=31 pF, the input frequency shall be 60263 Hz.
I will assume:
600 V of peak input voltage (square wave).
600 A of maximum output current at steady state.
6 J at the output capacitance, at steady state.

This results in:
Ca: 209247.3768533974 pF
La:   33.6725524037 uH
Lb: 224997.1794122552 uH
kab:    0.1003695810
Cb:   31.0000000000 pF
Optimal streamer load: Rb=844514 Ohms
Input impedance at steady state: Ra=1.2732395447 Ohms

This design reaches steady state in 0.3 ms (18 cycles), after some
"overshoot" on the specifications:
Maximum VCa (V)=     9840.90575 (  10.13212 J) at       124.41244 us
Maximum ILa (A)=     -779.23138 (  10.22301 J) at       128.46285 us
Maximum VCb (V)=   723602.44281 (   8.11581 J) at       186.61866 us
Maximum ILb (A)=        8.51576 (   8.15819 J) at       191.01910 us
This leaves some time to continue to push energy into the streamers.

The same design, but with 8 J and 41 pF at the output capacitance
(a lot of capacitive streamer loading):
Excitation at 52401 Hz

Ca: 276746.6471913645 pF
La:   33.7819780991 uH
Lb: 224997.2741393207 uH
kab:    0.1152414634
Cb:   41.0000000000 pF
Rb: 638535.0921930474 Ohms
Ra:    1.2732395447 Ohms
More primary capacitance and an adjustment in k.

Estimating the energy going to the streamers (my simulator doesn't
calculate this yet). At each cycle of 52401 Hz (19 us), at steady
state, the input energy is 0.5*1.27*600^2*19e-6= 4.34 J
In just 5 cycles you have 21.7 Joules.

I recommend running some simulations to see if I didn't make a
mistake...

Antonio Carlos M. de Queiroz