# Math Doodling

```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...
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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.

```