Re: DRSSTC driver tests- Dual resonance disaster

["Tesla list" <tesla@xxxxxxxxxx>]

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.

Ok.

> 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
rises.

>  >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?

Yes.

> 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