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?