# Re: Fw: Fw: Space winding

```Tesla list wrote:
>
> Original poster: "Kennan C Herrick" <kcha1-at-juno-dot-com>

> I have no experience with conventional L-C-spark gap Tesla coils (mine is
> solid-state) so I hope you will excuse any misunderstanding.

Ok. Your analysis is certainly valid for a coil driven by an
continuous-wave oscillator.

> Do you have
> a reference for the derivation of the equation you quote?

Energy conservation:
The input energy at each operation cycle is what is stored in the
primary capacitor when the gap starts to conduct: 0.5*C1*Vin^2
Ideally, this same energy is transferred to the secondary
capacitance, after some oscillations:
0.5*C2*Vout^2
This results in Vout/Vin=sqrt(C1/C2)

> In my view, a
> Tesla coil secondary (or that of any transformer, resonant or not) "sees"
> only magnetic flux; it is immaterial what primary apparatus produces that
> flux.  But in the conventional T.c., that flux starts out high and then
> exponentially diminishes because of the discharging of the primary
> capacitor through the spark gap.  Thus, the flux applied to the secondary
> correspondingly diminishes over time.  But during that time, the
> secondary remains a resonant entity--until a spark occurs, that is.
> There ensues a race, so to speak, between the tendency of the secondary's
> voltage to rise due to its resonance and the action of the primary's
> voltage (and thus, its flux) in exponentially diminishing.  If the
> primary flux did not so diminish, then the secondary voltage would rise
> faster and to a greater amplitude.  Perhaps that relationship is what

Before there is significant exponential decay in the oscillations in the
primary circuit, the oscillations there transfer energy to the
secondary,
much as happen in a CW coil, initially.
But as there is no additional supply of energy in the primary, the
amplitude of the primary oscillations decay with an approximately
cosinusoidal envelope, while the amplitude of the oscillations in the
secondary grow with an approximately sinusoidal envelope. Both
oscillaltions decay exponentially due to energy losses in the gap,
secondary streamers and resistive losses, but the energy usually flows
back and forth between the primary and the secondary resonators several
times before vanishing, producing characteristic beat waveforms.
The secondary Q can at most reduce the losses. It can't result in a
voltage gain greater than what is limited by energy conservation.

> In my T.c., the primary excitation is constant during each pulse-burst
> and thus, while the fundamental behavior of the secondary is exactly the
> same, an equation such as you cite is inapplicable.  (And it clearly is,
> on the face of it:  I have no primary "C".)  Because, as I think, the
> secondary's fundamental action is always the same, I would think that my
> analysis, if correct for my case, is correct for all.

In a CW coil, the primary energy is replenished at each RF cycle,
and so the seconday can accumulate energy to an amount only limited