01:17 PM 1/3/99 -0700
To: tesla@pupman.com
From: Terry Fritz
Subject: New Fo, Cself, Ctotal Program
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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.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@verinet.com