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RE: Math Doodling

>Original Poster: David Sharpe <sccr4us-at-erols-dot-com> 
>
>I've been doing some doodling, and off-line discussion with
>Terry, Barry Benson, and John Freau.  Here is an interesting
>math derivation to try over a cup of coffee...
>--------------------------------------
>
>Here is a simple math analysis situation that blew Richard Hull
>and Alex Tajnsek away.  Based on equations in the Heise paper and
>assuming lossless transfer of power:
>
>Vo = Vin * sqrt ( Ls/Lp )  Where        Vo = max Vout from resonator
>                                        Vin = Vin applied to tank circ.
>                                        Ls = Inductance of resonator
>                                        Lp = Inductance of tank pri.
>
>If the following equation is assumed to be correct in the time domain:
>
>Vin = Iin * sqrt ( Lp/Cp ) Where        Vin = Vin applied to tank circ.
>                                        Iin = peak tank current
>                                        Lp = Inductance of tank pri.
>                                        Cp = Capacitance of tank C
>
>AUTHORS NOTE:  This is RMS tank current times Surge Impedance equals
>               applied voltage to tank circuit.
>
>Then substituting equation 2 into 1 and simplifying results in:
>
>Vo = Iin * sqrt ( Ls/Cp )  Variables as listed above
>
>This suggests that Cp should be made a small as possible, and
>to maximize Vo, as high a Vin as possible should be employed.  This
>makes sense because Iin will go up with higher Vin, and bang energy is
>.5*C*V^2.
>
>Also, if C is made smaller, dielectric losses maybe REDUCED, with a
>given capacitor (since dielectric area and volume are reduced).
>This is the first time that in doodling with the equations, a
>possible mathematical validation of what has been touted by the TCBOR
>all along is derived, make tank capacitors small, and leverage energy
>by the use of very high voltages.
>
>FYI and discussion. Am I full of it or does this make sense???
>
>Regards
>
>DAVE SHARPE, TCBOR
>Chesterfield, VA. USA.


The above analysis assumes that the goal is to maximize Vout.  While on
the surface, this seems to be a good thing, but does that necessarilly
translate into what matters - the longest sparks?  If highest Vo really
were the goal, wouldn't it be desirable to minimize Csec and Ctop?  I
think it's clear that big Ctop's translate to big sparks.

I think what's missing is what it takes to efficiently transfer the
secondary energy into the arc.  Having a high Vo alone is not enough.

Regards, Gary Lau
Waltham, MA USA