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Re: DRSSTC driver tests- Dual resonance disaster

Original poster: "Antonio Carlos M. de Queiroz" <acmdq@xxxxxxxxxx>

Tesla list wrote:

Original poster: "Steve Conner" <steve.conner@xxxxxxxxxxx>
 >These values, 200 Ohms and 52 nF, look quite strange for streamer load.
Well the reason is that I am using a fake "secondary" with the same number
of turns as the primary, and resonated with the same size of capacitor as
the tank capacitor. It's safer and more convenient than a real Tesla
resonator for prototyping. If it were a real resonator this would correspond
to about 220k in series with 15pF.


As long as breakout always happens before the first "notch" and loads the
coil heavily enough to stop reversal, primary current feedback should be
safe. Or, I think the reversal could be got rid of by deliberately mistuning
one of the resonators or skewing the drive frequency to one side of centre.

At least you guarantee that the switching is soft. But if the system tries to revert and the feedback reverts the driver, the input current

 >Look at these simulated waveforms (mode 17:19:21...
Does this mean that the lower and upper split frequencies of the resonators
are 17:21 and the drive frequency is 19?


Also can your software simulate
self-resonant tunings (which I guess would be represented by say 17:17:21 or
17:21:21 in your example)

It can simulate what happens if you drive the system at any frequency,
including the resonances, but so far can't design a system that behaves optimally (what criterion?) if driven at one of the resonances.
There are classes of optimal designs where the driving frequency is
shifted to a side, as mode 17:19:25 (for sinusoidal input, the difference between the numbers shall be two times an odd integer), but
the required element values may result impractical.

On a similar note, I have been trying to derive an equation for the steady
state transimpedance (ie Iin=f(Vin, Vout, L1, L2, C1, C2, k, omega) where
Iin, Vin, Vout are complex quantities) I want to know this because it would
let you predict the worst case primary current in a self resonant coil,
knowing the breakout voltage and the coil constants, and adding the boundary
condition that Iin and Vin are in phase.
I know that several of the transfer functions are ill defined at the poles
for a system with no loss resistance (for instance vout/vin tends to
infinity, Iin/Vin tends to infinity) but I believe Vout/Iin should tend to a
constant at the poles. My reasoning is that Vout and Iin both tend to
infinity, and infinity divided by infinity could perhaps be a finite number

Vout/Iin takes out the primary capacitor from the circuit, and results in a second-order transfer function, with just one resonance. It goes to
infinity too if the excitation is at the resonance.
Of more interest would be formulas giving the voltages and currents after a number of cycles. I have some derived for my designs, giving
the maximum voltage gain and the maximum input current. The sstcd
program uses them to predict these values.

If you (or anyone else) have the transfer function for the dual resonator in
pole-zero form I'd be very interested to see it. I tried deriving it myself
but it's a long time since I've been in a maths class :-(

This is not difficult to derive. An algebraic math program helps with
the boring details if you want quick results. But the resulting expression is quite big (specially if losses are included) and not very useful.

Antonio Carlos M. de Queiroz