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Re: Re: [TCML] Top volts with losses (formula bad)



Dex Dexter wrote:
Formula is not good.Forget about it!
It is useless even for values like Q1=Q2=20 and k=0.18.
Well,I concentrated my investigations only to voltage
magnitudes near the first notch times characteristic
for loseless tesla coil.That was mistake.
Max secondary voltage in typical tesla coil with
heavier damping (and same k) usually occurs before
that time...Damn.I don't know how I could miss
something like that.
An exact formula can be derived (for the linear case, of course), but it would be very complicated. The system is of order four, and the exact solution for the output waveform has two sinusoids multiplied by decaying exponential terms. If wou want only the envelope, the solution is something as A*e^(-a*t)+B*e^(-b*t), assuming
complex natural frequencies.
The required terms come from the roots of a complete fourth-order polynomial. The program Teslasim, that I wrote some time ago, computes the exact expressions
for the waveforms.
The program is at: http://www.coe.ufrj.br/~acmq/programs.
The documentation of the program lists the exact solutions in Laplace transforms.

Antonio Carlos M. de Queiroz

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