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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:
- Math Doodling
- From: David Sharpe <sccr4us-at-erols-dot-com> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)