[Prev][Next][Index][Thread]
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.
>
>
>