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Re: Capacitance distribution along the secondary inductor



At 08:28 PM 04/28/2000 +0200, you wrote:
>
>> Original Poster: Terry Fritz <twftesla-at-uswest-dot-net>
>>
>> Hi all,
>>
>> The question has come up as to how the capacitance along the secondary
>> really IS distributed.  I reprogrammed E-Tesla5 to cut the coil into 10
>> sections and compute the capacitance of each section.  This was done by
>> setting the voltage one a given section to what it normally is and setting
>> the rest of the coil to zero volts.
>>
>> Section Capacitance
>> 1 0.0234
>> 2 0.0550
>> 3 0.1216
>> 4 0.1595
>> 5 0.3433
>> 6 0.5482
>> 7 0.5922
>> 8 1.1191
>> 9 1.6853
>> 10 3.6935
>>
>
>Hi Terry,
>
>Most interesting. I hope you will be able to make a graph, because it looks
>to me there is something wrong with the values of section 7 and maybe 6. I
>don't think it is possible to come up with a formula that explains this
>ditribution. Sorry to bring the bad news.
>
>Ruud
>

Hi Ruud,

	No one ever said this stuff was easy! ;-)))

With more time this afternoon, I (Excel) made the graph at:

http://users.better-dot-org/tfritz/site/misc/Ruud01.gif

It is not the beautiful, flowing, and easy-to-curve-fit type of graph we
like, but it is what the program gives...  Right, wrong, or... that is what
the program gives and the summation check did clear very well...  

I guess the next question in this long ongoing quest is...  Is the Tesla
coil secondary voltage distribution a "nasty" curve or is the program
skewing the numbers a bit??

The only real thing E-Tesla5 "guesses" at is the secondary voltage
distribution profile.  E-Tesla 5 is based off curve fitting from real data
from the graph at:

http://users.better-dot-org/tfritz/VoltDistBare.jpg

This curve was then equation matched to:

http://users.better-dot-org/tfritz/DistGraph.jpg

The actual equation has a discontinuity at the area around "7" as the
profile goes from a Vm x L^e distribution to a 1/4 sine distribution.  The
section "voltage along secondary" of E-Tesla5 roughly reproduces this.  If
I had taken the distribution in 100 steps instead of 10 this would have
been a much smoother graph and the discontinuity would have been more
apparent.  So the graph is a bit rough due to the less than perfect
equation matching to real data and the long time the program takes to run.
However, in the "big picture" it appears that most of the effective
capacitance is at the top of the coil which may explain why Tesla coils act
so "lumped".  It is not surprising that the capacitance at the very top of
the coil is high since the last top turn has to charge to whole space at
the top of the coil to very high voltage.  What is interesting, is that
below the top turn, the high voltage is storing most of the energy near the
very top of the coil.  I think this explains the Tesla coil's very lumped
nature but still allows for a little distributed transmission line type of
resonance to go on too.

Of course, if Malcolm's thought that the inductance along the coil is not
constant since the current diminishes along the coil's length, this may
turn into a real mess very fast.  E-Tesla5 does not care how the voltage
gets there, it only cares about it's distribution.  T-lines, lumped things,
distributed inductance, etc do not matter to E-Tesla5.  That may be why it
works ;-)))

BTW - E-Tesla5.1 is a QBASIC program I wrote (with much help from Jim
Monte) that runs on any PC (eventually ;-)).  It calculates the Fo
frequency of a Tesla coil given a bunch of physical dimensions.  It can
easily get within 5% at max accuracy.  It is free and at:

http://users.better-dot-org/tfritz/site/programs/E-TESLA5.ZIP

You can open the E-TESLA5.BAS file in any word processor to print out the
program.  You can also list, change, and play with the program as you please.

If your are a purest, the "guessed" factor 6.611 in the Et calculation is
really 2/3 pi^2 (6.57972515207...) as discussed in yesterday's post.  But
in only makes a 1/2% difference...

Cheers,

	Terry



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