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Re: Tesla Coil Operation
Tesla List wrote:
> I agree that there are direct analogies between capacitors, inductors,
> masses , and springs. I have been able to set up the 2nd order differential
> equations for these parameters on a spreadsheet and print out the graphs for
> the single RCL circuit representing the TC primary or secondary circuits. I
> overlooked the operating spark gap. However, I have never seen a solution
> for the actual coupled TC primary and secondary circuits using the 4th order
> differential equations. I doubt that anyone has ever done this. I hope that
> coilers will not refer me to books that are hard to find and do not show the
> proper information.
The exact analytic solution for a 4th order system involves finding the
roots of a 4th-order polynomial, to find the natural frequencies. This
is perfectly possible, but the expressions are rather complicated in the
general case.
The classical approximate solution for the Tesla Coil model, assuming
low-loss, can be found in the paper (a very readable paper):
K. D. Skeldon, A.I. Grant, and S. A. Scott, "A high potential Tesla coil
impulse generator for lecture demonstrations and science exhibitions,
"American Journal of Physics, Vol. 65 (8), pp. 744-754, August 1997.
The solution appears also in the book "Static and Dynamic Electricity",
by W. R. Smythe (1939), with extensive discussion (a rather heavy
reading), and in several other places.
What is much simpler to do is to find a numerical solution. An
exact numerical solution is relatively easy to obtain.
And I can say again that it is implemented in my Teslasim program.
(that also doesn't compute the mutual inductance...)
Note that that analysis is applicable only while the primary gap is
conducting, and models it as s simple linear resistor, what little
difference makes if the losses are small.
Antonio Carlos M. de Queiroz
(For Teslasim, look at http://www.coe.ufrj.br/~acmq/links.html)