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Re: Math Doodling

I saw all this before the list did and was thinking too that "something was
wrong" but I couldn't figure it out...

After I posted this to the list last night.  I also finally realized that
Iin was proportional to SQRT(Cp) and it would cancel out and give the old
equations.  I decided to wait and let someone else figure it out at that
point (since I had a head start) and give the list a chance to play with
this.  Bert figured it out in a day.  It took me three ;-))

Apparently Dave's equation does not hold up but I do want to thank him for
giving it a darn good try!!  It is this kind of "doodling" that can really
change things on the rare ocasions when someone makes that breakthrough
discovery.

Keep doodling Dave!!

	Terry



At 07:42 AM 6/10/99 -0500, you wrote:
>Hi Dave!
>
>I've got to admit, this post got my eyebrows too! :^)
>
>Interesting result - however, this would imply that Vo approaches
>infinity as Cp approaches 0, which clearly can't be. 
>
>The root of this quandary stems from the fact that Iin is not
>independent of Cp: 
>
>>From the second equation (below), we get:
>  Iin = Vin * sqrt(Cp/Lp)
>
>Plugging Iin into the last equation to get it into a form using only Vin
>we get:
>
>  Vo = Vin * sqrt(Cp/Lp) * sqrt(Ls/Cp) 
>
>which then simplifies to the more familiar Vo = Vin * sqrt(Ls/Lp)
>
>As Cp is changed, the impact of the sqrt(Ls/Cp) term is exactly
>cancelled by the sqrt(Cp/Lp) term, leaving the output as only a function
>of sqrt(Ls/Lp) as expected. 
>
>-- Bert --
> 
>
>
>Tesla List 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.
>
References: