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