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Re: Math Doodling

Hi David and list

Your doodling may answer Finn's query about the low primary inductance in
bigger coils.

If V_in = I_in * sqrt(Lp/Cp) 

a low Lp will result in a higher I_in for a fixed V_in and Cp.

If V_out = I_in * sqrt(Ls/Cp)

then V_out will be larger as a result of that higher I_in. Also, a larger
coil has a 'relatively' larger Ls which would again increase V_out.


Safe coiling,

Gavin Hubbard

P.S. If spark length really does depend on V_in, then perhaps I will
someday have a use for my 150kV X-ray power supply unit *grin*.


At 09:53 PM 6/9/99 -0600, you wrote:
>Original Poster: David Sharpe <sccr4us-at-erols-dot-com> 
>
>Terry, ALL
>
>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.
>
>
>