# Re: That secondary harmonic voltage distribution stuff...

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At 07:25 AM 08/27/1999 -0500, you wrote:
>Tesla List wrote:
>>
>> Original Poster: Terry Fritz <twftesla-at-uswest-dot-net>
>>
>> Hi All,
>>
>>         I have noticed that the secondary voltage distribution graph for
>my coil's
>> Fo frequency, as I measured last night, follows the equation:
>>
>>         V(dist) = Vmax x dist ^ e
>>
>> where;
>>
>> V(dist) = The voltage along the secondary with the base being zero.
>>
>> Vmax = The maximum voltage (the top voltage in this case).
>>
>> dist = the distance along the coil were the base is 0, the middle is 0.5,
>> and the top is 1.
>>
>> e = the natural log (2.7818...)
>>
>> I don't know if this means anything profound or not, but the match is darn
>> close...
>>
>> Still pondering all this....
>>
>> Cheers,
>>
>>         Terry
>
>Terry,
>
>This is an extremely interesting result, since it shows an unexpectedly
>different voltage distribution that the mostly-sinusoidal one would
>expect from a 1/4 wave theory open resonator! In fact, if your
>measurements and approximation formula are close to being correct, fully
>25% of the total output voltage would be confined to the uppermost 10%
>of the winding(!). Previous wisdom/theory assumed that most of the point
>of maximum voltage stress for an unloaded resonator would be confined to
>the bottom portion of the resonator, with a maximum of only about 15% of
>the total voltage stress appearing across the bottom-most 10% of the
>winding.
>
>It would be interesting the see if a similar distribution applies to the
>case where the resonator is "pumped" from a primary EM field at Fo, and
>added. It may also be that the base-driven CW case may exhibit a
>different voltage distribution than the disruptive case during energy
>transfer to the resonator during ring-up...
>
>Very interesting results indeed!
>
>-- Bert --
>

Hi Bert,

E-Tesla3 makes graphs of voltage distribution.  I have always thought that
the sine distribution looks a little "wrong".  I based that sine
distribution on my work with transmission line models of long ago.
Apparently, that distribution is indeed WRONG!!  Them darn transmission
line models!! ;-)))  My very old work with non-linear coil winding was to
try and relieve the high voltage stress in the lower secondary area that a
sine distribution would cause and prevent arcing on the lower part of the
coil as you mention.  Funny how that is never a problem.... *:-O   (Duh!)

E-Tesla3 has a constant in it that uses many nasty integrals to figure out.
After a while, I just fudged that constant and used the number that worked
without going through the integrals and confirming every last detail in
that calculation.  If I had, I may have spotted that something was not
correct (I probably would have gotten lost in the math first).  I suspect
that the sine and l^e distributions are proportional, so the program worked
even with a sine distribution on the secondary.  I have been sort of busy
so I haven't gotten back to the program but there is a logical explanation
of what was going on with that.  The solution is to simply change the
distribution and re-fudge the nasty integral calculation ;-)  E-Tesla4 can
map and calculate the harmonics but the capacitance calculation for each
section and how to determine where those sections begin and end would be a
mess.  Probably beyond the program's "real" use to simply find Fo...  This
all does explain why E-Tesla3 has trouble doing the bare coil case with
high accuracy...  Interestingly, after looking at all this, I would not be
surprised if the Cself calculation has a reasonable closed form.  The
physics is not that intractable....

Antonio posted an old experiment that was probably done with a disruptive
system that you suggest but it was wire driven and not a coupled system
apparently,  The results are shockingly similar!  Since the effects are a
resonant effect, I don't think it makes much difference how the voltages
are induced.  As to what effects the dynamics of a pulse discharge system
have on all this,  I think the principles will still hold true, but we have
been surprised before...

Cheers,

Terry

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