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0.5*C*V*V vaild? (Was Output Voltages and Voltage/Length)


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From:  Antonio Carlos M. de Queiroz [SMTP:acmq-at-compuland-dot-com.br]
Sent:  Friday, February 06, 1998 2:07 PM
To:  Tesla List
Subject:  Re: 0.5*C*V*V vaild?  (Was Output Voltages and Voltage/Length)

Mark S. Rzeszotarski wrote:

> I have also built a series of tesla coils with back-to-back
> LED's placed every 2 inches along the length of the coil with various H/D
> configurations to examine the voltage rise in these rather heavily damped
> coil systems. 

LEDs connected in series with the coil would measure current, as the voltage over a
conducting LED is practically constant. LEDs connected in parallel with the coil
sections, with series resistors, would measure voltages. What connection are
you using? (The readings would be proportional, anyway.)

> 1.  The voltage distribution goes from a minimum at the base to a maximum at
> the top when tuned to the quarter wavelength of the coil system, even in a
> damped coil system.

This looks strange. I would expect more voltage at the base, where the coupling
is higher, or almost constant voltage along all the coil sections, that is what
the lumped model predicts. Is this coil a capacitor-discharge coil or a CW coil?

> 2.  Adding a toroid or sphere to the top tends to linearize the voltage rise
> somewhat, so that the turn-to-turn voltage stress is lessened especially
> near the top of the coil.

Looking at LED lights is not a very reliable method for measuring linearity,
as LEDs are very nonlinear.

> Typical oscilloscope probes have 10-30 pF of
> capacitance, which greatly affects the readings unless you have a huge coil
> system with a Csec of perhaps 10-20 times this or more.

Better to use a metal sphere connected to the oscilloscope and put near the
coil. Some calibration procedure is required.

> 4.  The Corum brothers suggest that the voltage rise in a helical resonator
> can be rather astronomical.  I disagree.  My measurements of the maximum
> possible voltage at the toroid tend to agree with the equation:
> Vsec(max) = Vpri x SQRT(Cpri/Csec), or the equivalent:
> Vsec(max) = Vpri x SQRT(Lsec/Lpri), which is essentially the lumped circuit
> model.

Can someone point where I can find a rigorous analysis of an helical resonator?
(Not the lumped model, that I know well. The distributed model, that I strongly
suspect that is not valid for any tesla coil of reasonable size...) 

>         There is an interplay of energy storage between the capacitance (1/2
> Csec V^2) and the inductance (L dIsec/dt), (as well as an interplay between
> the primary and secondary systems while the spark gap is conducting).

You can simulate this with a program that I wrote (lumped model):
ftp://ftp.coe.ufrj.br/pub/acmq/teslasim.zip

I agree with the other comments.
 
Antonio Carlos M. de Queiroz
mailto:acmq-at-compuland-dot-com.br
http://www.coe.ufrj.br/~acmq