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New Fo, Cself, Ctotal Program
Hi All,
We have often wanted to know the resonant frequency, self capacitance, and
total capacitance of our secondary coils before they are built. Wheeler's
formula gives us the secondary inductance to a very good accuracy so
calculating the inductance of the secondary has never been a real problem.
The Medhurst equation supplies us with a number for the secondary self
capacitance that is fairly accurate. However, once you put a terminal on
the top of the secondary, things get bad. The terminal is placed within
the self capacitance space and has the effect of adding to the self
capacitance. There are rules and ideas about how to guess at this
situation but guesses are all there are. People have done experiments but
the experimental set up never seems to match our systems well and the
results may not be very good. You won't find a good single equation for
this situation.
So.... the real problem is finding the total capacitance of our secondary
systems by calculation rather than building it and seeing how close we
guessed. If one thinks about all the variables the problem quickly seems
impossible.
However, consider this. The capacitance of an object is simply the charge
in Coulombs on the object divide by the voltage. If we know the charge and
the voltage we know the capacitance (and Fo). The voltage is really easy.
It can be any arbitrary voltage ( I use 100 volts... for no real reason).
Then the problem is simply to find the charge, on the coil system, at that
voltage. Sounds hard to figure out and the mental effort behind the
solution is in the realm of genius. Fortunately, around 200 years ago Karl
Friedrich Gauss (1777-1855) figured it out for us. It doesn't mater how
complex or messy the dimensions of the charged object are. All that
matters is what the field around it looks like. Gauss came up with what is
known as Guass's Relation. It is:
"The total flux passing outward through any closed surface equals (1/eo)
times the total electric charge inside the closed surface."
In other words, if you throw any shaped charged object into a bag with lots
of little electric flux sensors sewn into it. The charge on the object
will be equal to the sum of what all the sensors measure times eo. Or...
Q = Sum E x eo
So... That still sounds harder than just building the darn thing and seeing
what happens :-) However, we now know how a secondary coil's voltage is
distributed. It is a sine shaped distribution along the length of the
coil. The top of the coil and terminal are at the same potential while the
base is grounded. Thus we can set up a computer simulation to find the
electric field around the coil given it's dimensions. The finite element
analysis technique to do this is well known by people who worry about such
things. It is really very simple but takes a very large number of
calculations. So the computer can crunch out the field distribution. Our
task (the computer's task) is to simply place a virtual surface around the
coil and add up all the flux passing through it. The surface can simply be
a sphere with the Tesla coil contained inside it. This is the simplest
surface to use for our needs. There are no unknowns here. Just Gauss's
wonderful relation, some simple math and one heck of a lot of calculation.
We have the relation, the math is straight forward, and modern computers
can easily do the calculations in some reasonable time frame. So we have
all the parts. So... would someone please write a program to do this?...
Too late! :-)) I couldn't wait. It is still an alpha version but I
think it works well. It is called TWFreq and is available at my site:
www.peakpeak-dot-com/~terryf/tesla/misc/twfreq.zip
I'll call this the Alpha version. It is written in DOS's QBASIC (which is
included since modern OSs don't have it anymore). It will run on any PC.
It will run in a DOS window on NT and the like. If it works out, someone
can rewrite it in some nice language since it is short, simple, and
straightforward. Programming is not one of my strong points... I hear
there are DOS emulators for Macs. If so, it should work fine on those too.
This is a straight text based program with no fancy stuff. It can be
converted to any computer's BASIC programming language (it needs more than
8k of RAM :-)). Nothing fancy. Expect it to take at least a few hours to
get down to a stable number. The extra cash you paid for the faster
computer will pay off now. It writes the voltage field data to disk
periodically so you can print the field plots out if you have Excel97 or
some other program that can do surface plotting. It can be modified to do
field stress too very easily. It only does one terminal but two terminals
or other configurations would be easy to add. Just a matter of putting the
shape in.
Basic instructions are included and any problems found or suggestions
should be sent to me for fixing. The program works fine on my system and
the parts I can mix and match together but only a real field test will
insure it "really" works. If you know your system well, please report the
accuracy to me so I can determine if there are any weak spots and come up
with a good number for claimed accuracy. There are no "fudge" factors in
it now but that could change :-))
This program has never been field tested before so the guarantees are zero.
However, it should work. I hope it works out. It will fill a one of the
few holes we have left in Tesla coil design for the armchair coiler...
Good luck! We'll blame Karl if it doesn't work :-))
Terry
terryf-at-verinet-dot-com