Re: That secondary harmonic voltage distribution stuff...
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
>> Fo frequency, as I measured last night, follows the equation:
>> V(dist) = Vmax x dist ^ e
>> 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
>> Still pondering all this....
>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
>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
>if, indeed, the distribution becomes more linear as top loading is
>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 --
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...