# Re: Secondary capacitance

```Original poster: "Terry Fritz" <twftesla-at-qwest-dot-net>

Hi Steve,

At 02:57 PM 5/23/2002 -0500, you wrote:
>Dear Terry:
>
>            In regards to your post of (Vs) secondary output voltage, do you
>believe that the secondary capacitance (Cs) should be calculated by adding
>the self capacitance of the secondary along with the toroid terminal
>capacitance?
>In other words should Cs= Secondary self capacitance + Toroid capacitance or
>should the capacitance of the toroid be ignored.

The secondary coil's capacitance and the top terminals's capacitances are
"combined" together in a complex way.  the electrostatic fields around each
"meld" together to make a composite capacitance.  Here are some diagram's
showing the electric fields around a Tesla coil:

http://hot-streamer-dot-com/andrewb/models/models.htm

There is no easy way to calculate this by hand but this computer program
will crunch through like a billion calculations to tell you the combined
capacitance.  It uses finite element analysis and gausses law:

http://hot-streamer-dot-com/TeslaCoils/Programs/E-Tesla6.zip

Here is an excerpt from the original program that sort of explains it
=============================================
tesla-at-pupman-dot-com
Terry Fritz <twf-at-verinet-dot-com>
New Fo, Cself, Ctotal Program
1/3/99  01:17pM

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:
..........
=========================================

Today's E-Tesla6 (The latest highly polished and tested incarnation of the
original TWFreq) will give you the resonant frequency and top capacitance
with a few percent.

>    Secondly, If I'm using a 4 inch diameter coil similar to yours posted on
>your website in which my NST is 15kv/60mA along with a SRSG with a break
>rate of 120 BPS, can I assume that my capacitors (15 nF from Geekgroup)  are
>charging fully to 15000 volts.  Does Vp indeed equal 15,000 volts ?

15000 volts is an "RMS" voltage.  The peak voltage is:

15000 x SQRT(2) = 21213 volts

so use 21213 for Vp.

Cheers,

Terry

>
>Sincerely,
> Steve Lawson
>

```