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# Re: Capacitance of a coil

```Hi All,

At 08:37 AM 1/14/99 -0800, you wrote:
>
>>
>> Original Poster: Reinier Heeres <rwh-at-worldonline.nl>
>>
>> OK coilers,
>>
>> please help me on this: I'm writing a Tesla coil calc program (well,
>> just for me to understand it better and get familiair with the calcs),
>> but I don't know how to calculate the capacitance of a coil. I could of
>> course use Medhurst's formula (is there a table for H/D ratio > 5?), but
>> I wanted to know if there's another way to calc it too.
>
>You can calculate it considering it as a tapered transmission line, or as a
>series of parallel capacitors consisting of two annular rings with the size
>of the outer ring gradually increasing. Either way, you get a nasty
>integral (blows up at the bottom) that is best integrated numerically. If
>you are going to go to the trouble of numerically integrating, you might as
>well use an empirical approximation (which is what Medhurst is) that gets
>you within a few percent, particularly for a TC, where there are lots of
>other design unknowns as well.
>
>If you come up with a good analytical expression for the integration, I'd
>like to see it. I suspect that there is some standard formulation that will
>work fairly well (possibly a series expansion), but I checked all the
>standard tables (Grashteyn and Ryzhik (sp?), and the CRC math tables) and
>couldn't find something useful.
>
>

My E-Tesla program does this by a large finite element analysis.  However,
it has a lot of trouble on bare coils.  I am working on a better program
that I think will be much more accurate on the bare coil case.  I strongly
suspect that the voltage along the secondary has a sine distribution.  You
can then solve for the fields and such around the coil and then do the math
to find the capacitance.  I do think there is a closed form equation for
such a thing but it has not yet been found.  The program, in a way, will
prove or disprove this.  I need to refine my calculations to be better than
they are now.  Real bare coil capacitance is hard to measure let along
trying to figure it out with a computer....

The Medhurst equation is very good and it is a standard any other method
can be measured against.  However, a good program could be used to generate
massive amounts of data that could be helpful in finding a closed solution.

Does anyone know the claimed accuracy or limits for the Medhurst equation.
It would be interesting to know were the regions are that it starts to
loose accuracy?

Terry

```