Voltage/Length (fwd)

From:  Bert Hickman [SMTP:bert.hickman-at-aquila-dot-com]
Sent:  Tuesday, January 27, 1998 9:12 AM
To:  Tesla List
Subject:  Re: Voltage/Length (fwd)

Tesla List wrote:
> ----------
> From:  John H. Couture [SMTP:couturejh-at-worldnet.att-dot-net]
> Sent:  Monday, January 26, 1998 6:19 PM
> To:  Tesla List
> Subject:  Re: Voltage/Length (fwd)
>   Antonio -
>   How do you do the calcs for finding the secondary voltage per Greg Leyh's
> problem with 3 MV and 100 pf? Do you use this equation?
>     Joules = .5 C Vs^2
>   Many coilers use this equation but do not explain the fact that the
> voltage is a transient.
>   Or do you use this equation?
>     Vs = Vp sqrt(Cp/Cs)
>   Note that when the Vp and the Cp/Cs ratio is held constant the Vs voltage
> can be changed only by increasing the input wattage and size of the coil.
>   Do you have any comments on my post regarding power magnification to Jim
> Monte per "Magnifying power (was voltage/length)?
>    John Couture
> At 04:42 AM 1/25/98 +0000, you wrote:
> >

John and all,

Both of the above equations can be used only to describe the peak
voltage that the secondary can attain with a given bang size. In
particular, if both primary and secondary are tuned to the same resonant
frequency, then the peak secondary voltage (constrained by conservation
of energy) can be shown to be:

  Vs(max) = Vgap*sqrt(Cp/Cs) = Vgap*sqrt(Ls/Lp)

In a disruptive coil, each gap firing is an independent event. There's
no "residual" energy left over from the previous bang that contributes
to the following one. Each "bang" has a maximum of 0.5*Vgap*Cp^2 Joules
of initial energy. A substantial fraction of this initial energy will
make it to the secondary during the first transfer - in a well running
coil perhaps over 85% based upon measurements of successive energy
transfer peaks with unquenched gaps. 

Now, because of gap, skin effect, and groundpath losses, a more
appropriate equation for Vs would thus be:

  Vs(max) = F*Vgap*sqrt(Cp/Cs)  where 0.5 < F < 0.9 typically

Now, if I have 1 bang/second or 400 bangs/second, the above equation
does not change! Vs does not increase with increasing input power levels
(although sparklength may for other reasons). Cs may increase a bit in
the latter case because of additonal ion-cloud loading. Also, the above
equation is only appropriate if I don't have loading from secondary

By measuring successive beat amplitudes, it's relatively easy to
demonstrate that "F" in the above equation is usually >0.5 for a
reasonably constructed coil, and typically is in the 0.8 to 0.85 range
for well constructed, well coupled systems. Energy transfer between the
primary and secondary tuned circuits is actually quite efficient, all
things considered. The primary and secondary tank circuits smoothly
exchange an ever-decreasing level of power back and forth for as long as
the gap fires for each bang. 

However, the overall portion of power transfered either way is
considerably higher than the 12% level you quoted for a coil the size of
Greg's (or probably any coil made by an active Tesla List member for
that matter), especially during the first couple of transfers when the
gap current is highest. John, something appears to be amiss somewhere in
the model you're using, or in the set of assumptions used for your

Safe coilin' to you!

-- Bert --