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*To*: tesla@xxxxxxxxxx*Subject*: Re: DRSSTC driver tests- Dual resonance disaster*From*: "Tesla list" <tesla@xxxxxxxxxx>*Date*: Fri, 28 Jan 2005 14:54:10 -0700*Delivered-to*: testla@pupman.com*Delivered-to*: tesla@pupman.com*Old-return-path*: <teslalist@twfpowerelectronics.com>*Resent-date*: Fri, 28 Jan 2005 14:54:31 -0700 (MST)*Resent-from*: tesla@xxxxxxxxxx*Resent-message-id*: <S0ZcNC.A.ZJG.WSr-BB@poodle>*Resent-sender*: tesla-request@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

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