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Re: Magnifier system
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> From MALCOLM-at-directorate.wnp.ac.nzSun Nov 17 22:55:20 1996
> Date: Mon, 18 Nov 1996 12:54:42 +1200
> From: Malcolm Watts <MALCOLM-at-directorate.wnp.ac.nz>
> To: tesla-at-pupman-dot-com
> Subject: Re: Magnifier system
>
> As a matter of convenience I use the quantities that appear to us as
> inductance and capacitance to predict the fundamental vibrational mode
> of the coil. They work well in practice. However, as the Corum's
> have shown, these things can be shown even more convincingly by
> examining the structure as a waveguide. I have serious doubts whether
> their predicted voltages for cap discharge systems are correct though.
Hi Jeff, Malcolm -
Just to throw in my two cents worth on this particular point:
Mathematically, the analysis of lumped components will agree with a full
analysis of the transmission line structure on some level. The agreement
gets better as the number of discrete lumped elements increases --- this is
essentially what you do when you convert discrete sums to integrals. For
example: a tesla coil does behave like a transmission line (coax cable) in
the sense that it has an infinite number of resonant modes (1/4, 3/4, 5/4
... wavelengths). A lumped circuit model of the coil which has one L and
one C to represent the coil can give the lowest mode (1/4). But now break
the original L and C into pieces, and you'll get two resonant modes (1/4)
(3/4). One thousand L's and C's will give the 1000 lowest frequency
resonant modes of the transmission line, etc...
[ for anyone interested, I have a QuickBAsic program which will solve the
coupled differential equations for up to 100 L's ( with user specified
mutual coupling) C's and R's in a tesla coil-like structure - the voltage
or current at each node is plotted in time so that one can see how
discretized waves propegate on such a structure].
Also the integral formulation of the problem of tesla coil resonant modes
is difficult at best. John Kraus gives the essentials as applied to antenna
structuces in his book "Antennas". An approximate solution was given by
Pierce in his work on travelling wave tubes and I have a simplified formula
for tesla coil work if anyone wants me to dig it up ( It agrees fairly well
with the medhurst lumped L C formulas). Finally an exact formula for tesla
coil resonant frequencies in terms of ordinary functions is almost
certainly not possible but that doesn't mean you couldn't do it on a
computer.
-Ed Harris