Re: Self capacitance and Medhurst

To: tesla-at-poodle.pupman-dot-com
Subject: Re: Self capacitance and Medhurst
From: Tesla List <tesla-at-stic-dot-net>
Date: Mon, 24 Mar 1997 21:00:48 -0600
Approved: tesla-at-stic-dot-net
Subject: 
            Re: Self capacitance and Medhurst
       Date: 
            Tue, 25 Mar 1997 07:59:53 +1200
       From: 
            "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
Organization: 
            Wellington Polytechnic, NZ
         To: 
            tesla-at-pupman-dot-com


John,
         I spent months testing Cself formulae while researching an 
article before I found Medhurst. You wrote....

>  Capacitance is mostly dependent on the dielectric and area. For a coil self
> capacitance this would relate to the wire insulation and wire length. The
> Medhurst equation uses only radius and coil lengh for the coil self
> capacity. As Steve points out this can lead to some wild results.

This is not correct IMHO. In fact it turns out that Cself is 
isotropic in nature and not inter-turn. It appears from what I've 
read in the CSN that Tesla didn't get this one either. If your 
scenario is correct, his various attempts to reduce Cself by using 
series capacitors etc. in the windings should have worked. They 
clearly didn't and he was forced to concede that Cself was here to 
stay. If you look up the windings, each turn is shielded from all but 
its immediate neighbour so you end up with a sum of tiny capacitances 
in series. I challenge you to present a coil (no terminal) whose 
Cself is other than that given by Medhurst's formula (to within 5%).

> For a coil 1.5" radius and 15" long with .032 total dia wire (15/.032 = 468
> turns). Medhurst would give about 5.8 pf for the coil capacity.
> 
> For a coil 12" radius and 6" long with 0.1" total dia wire (6/.1 = 60
> turns). Medhurst would give about 39 pf coil self capacity.
> 
> Note that both of these coils use about 370 feet of wire. This  would
> indicate the coil self capacities would be about the same. The ratio of
> 39/5.8 = 6.7 to one is to great for use with Tesla coils. This would
> indicate Medhurst should be modified for use with Tesla coils or some other
> equation should be used. If  the look up table is used it would need more
> fixing. I do not believe grounding is a factor.

Indees it is and was stated as a condition of the formula's 
applicability. Once again, I would find a counter-example convincing 
(for a grounded winding). Things change dramatically when the 
winding is not grounded of course but that hardly applies to a 
resonator worked against ground. I'd suggest formulae for ungrounded 
coils more correctly applies to a suspended half-wave system. 

> There have been many coilers who have tried to come up with an equation that
> works including N. Tesla (CSNotes), Corum's, and others. I researched this
> problem several years ago when I was working on the JHCTES computer program.
> I finally used an equation based on empirical data. 
> 
> This is another example of where radio equations must be used with caution
> for Tesla coils. This is also why you will not find Tesla coil design info
> in the standard radio books but have to go to the Tesla List or the few
> books that have been written on Tesla coil design. These books, like mine,
> are based on empirical data from real-world coils plus radio theory. These
> books are still in the development stage. Much more building, testing, and
> book writing by coilers is needed for Tesla coils.
> 
>   John Couture

Well I spent 3 - 4 months hunting and testing before deciding to 
publish that one. There are minor variations on it that also come 
close but their range of coils is somewhat restricted. *None* of the 
wirelength formula worked in most cases and many didn't even work 
for one case. I have run this formula on over 50 coils so far. A 
counter-example is called for I think. Prove me wrong.

Malcolm