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Re: Tesla simulations vs. scope traces
From: Antonio Carlos M. de Queiroz[SMTP:acmq-at-compuland-dot-com.br]
Sent: Friday, December 26, 1997 1:58 PM
To: Tesla List
Subject: Re: Tesla simulations vs. scope traces
Rscopper wrote:
> The reason the first C and the last L don't follow the exact formula, is that
> I made sure the total was equal to my measured values without having to have
> more sections.
You could rescale the other values. But the different values don't change much
the simulation results.
> I think the model is a good start, however a few things are missing. If the
> system is modeled by a mass on a spring that is thinner at one end and gets
> thicker as the windings progress, It would react to higher frequency
> vibrations at the thinner end, and then propagate to the other end as I
> believe the current in a TC does.
I didn't yet build a tesla coil to test what would really be an adequate model,
but all the papers that I have seen published in "serious" journals say that
two series RLC tanks with the inductors coupled is an adequate modeling.
The reason is simple: The wavelength of a 100 kHz electromagnetic wave is
~3 Km. A transformer would have to measure at least some 30 m to show measurable
distributed effects (in physical size of the coils, not length of wire, because
the magnetic coupling is what matters). The terminal has a distributed capacitance
that can cause some complication, but consider that the coil capacitance is frequently
much greater that the terminal capacitance.
> If you then model the mass sitting in a
> bucket of jello (toroid-C) it would take a few oscillations before it could
> break-out of the liquid (sparks).
The mechanical analog for the toroid would be just more mass. Think about a spring
with mass (inductance with parasitic capacitance) connected to a mass (the toroid
terminal). The spring alone has a resonant frequency, that decreases when the
mass is connected to it, exactly as happens in the secondary of a Tesla coil.
Sparks would act as brakes applied suddenly to the system when the speed of the
mass exceeds a certain value.
> I not sure of the analogy for the R-windings
Resistance is equivalent to friction proportional to the speed of the mass. As
air resistance.
> and for the C made of the cylinder of the windings to ground (not
> self-C), with humidity added in for kicks.
Capacitances to ground and to the terminal. I am also not sure about what would
be an adequate analog for this.
> But I don't think the system is as simple as a RLC model.
A decision about this requires a comparison of simulated (or calculated) and
precisely measured waveforms. A Tesla coil secondary can approximate an helical
antenna if the resonance frequency is high enough and the coils big enough.
A lumped model of this can be built by splitting the coil in sections, as you did,
but I don't see reason to use unequal sections. All the inter-winding capacitances
and mutual inductances must be present in the model.
Antonio Carlos M. de Queiroz
mailto:acmq-at-compuland-dot-com.br
http://www.coe.ufrj.br/~acmq