Re: Self capacitance and Medhurst

            Re: Self capacitance and Medhurst
            Thu, 27 Mar 1997 15:12:52 +1200
            "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
            Wellington Polytechnic, NZ

Hi John,
            You write in reply...
<big snip>
>  Actually the Medhurst equation follows closely with my empirical
> equation
> based on wire length. That is for coil self capacities of a typical
> Tesla
> coil and H/D ratios over one. With ratios under one the two equations
> diverge. I note that the lookup table doesn't go below H/D = one. 

The short precis of the table that was listed didn't but Medhurst's 
original certainly did. I sent you the computer program I wrote based 
on it didn't I?  As Micheal Cranford pointed out, I got one data 
point in error (finger trouble). Medhurst tested over 40 coils before 
publishing that. I am merely following in his footsteps. The 
existence of the formula was unknown to me when I first started 
experimenting and I respect his experimental work most highly now.

> The differences are only with the ratios under one which are not
> typical Tesla coils.
> Did your testing include coils with H/D ratios less than one to
> verify the Medhurst equation?

Most certainly. I take pains to test ideas experimentally to see which 
are valid in the strict sense of the word. The last thing I wanted 
was to publish bad data although I did have to publish corrections to 
some bits of the article that I unwisely included.

    FYI, I first became worried about a number of wirelength formulae
when I tried designing coils based on them only to have them resonate 
at some other frequency. I then set up a spreadsheet to find out why 
using wirelength was a problem. I found that I couldn't make a 1/4 
wavelength of open wire at some F converge with the same length 
rolled up as a coil. At that point, I realised there was something 
wrong with the ideas being used. I then started looking at using 
Cself and Lself to predict frequency and from there it was a short 
step to find Cself formulae which were applicable to grounded coils.
The last step was finding one that covered the possible range that 
could be used in Tesla service.
    Then I started to wonder why this was so. I came to the 
conclusion that coiling up a length of wire was in essence modifying
its C and L to the point where wirelength no longer meant anything. In 
doing this, we have reduced the physical length of the wire to the 
physical length of the resonator. Doing this does several things:

- increase Lself enormously through mutual inductance between all 
lengths of the wire
- decreases Cself enormously though reducing the length of the 
resonator (long wire) to that of the height of the coil
- Cself is reduced so much that the increase in L cannot compensate
and any coil you wind will always resonate at a higher frequency than 
the length of the wire would suggest without the addition of a top 
- the physical length of the resonator is now so short relative to its
frequency of operation that its radiation efficiency drops to near 
zero and Q roars upwards as a result (greatly boosted shunt Z).

     I think I posted my analyses to you at some stage?  For the 
benefit of those that don't have them, you can arrange for the wire 
to be 1/4 wavelength long *in the coil* by the following procedure 
(and you can do it entirely on paper before you purchase a thing - 
personally guaranteed :)

- Choose a former you want to use (height, diameter)
- Choose an arbitrary number of turns (300, 1000, whatever)
- Calculate the inductance (using, say Wheeler's single-layer formula)
- Calculate the length of wire, multiply it by 4, then divide the 
  speed of light by this value (using the same units of course). This 
  gives a resonant frequency such that the wire is 1/4 wavelength 
- Using the inductance calculated above, calculate the capacity 
  required to resonate that inductance such that you hit the 1/4 wave 
  frequency according to the wirelength.
- Now calculate the coil's Cself using *Medhurst* or something that 
  is in good agreement with it.
- Finally, subtract Cself from the required capacitance to resonate 
  the coil.
  *This is the amount of capacitance you must add in the form of a 
terminal to make the wire resonate at the 1/4 wave frequency when it
is wound on the coil.*

    Guess what? A further analysis showed that it doesn't matter what
coil you wind *on that particular former*, it always requires the 
same terminal capacitance to perform this trick!! Why? Because 
Cself is largely invariant for a particular former. I repeat, it has 
*nothing* to do with the wire itself!

>  Did you test a coil that would be about 12" radius and 6" long 
> with a 39 pf self capacity?

Not that particular size but certainly that H/D. I think Dr 
Rzeszotarski has done a fairly large low one though. Important to 
remember that Medhurst based his results on careful experiment. The 
realisation that the capacitance was isotropic was one I came to
after discovering what worked and what didn't. I'm not particularly 
keen on building a coil I'll never use, and I don't think it would 
prove of any use to you to have me say that I found the values in 
agreement. More convincing for you to do it for yourself I think. I 
would most certainly build one if you found it differed from the 
result that formula gives.

> Although this size coil would probably never be used, it would be
> interesting to build and test it. However, Tesla's Colorado Springs
> coil was 50 feet diameter and 8 feet high with a .16 H/D ratio.

No problem. The full data tables given by Medhurst covers that one 
(given that it is worked against ground and not connected to 
anything else at the top).
> Somewhere I read that the coil self capacity is almost eliminated
> when the wire separation is 31 mils or more!! Have you ever noticed
> this coil self capacity characteristic with your tests?

No! Because the coil is not isolated but connected to a voltage source
(nee ground). We are *not* dealing with inter-turn capacitance. We 
are dealing with a particular case. One end is tied to an impedance 
near zero. Ironically, the Corum's own diagrams of the progression 
from cavity resonator to open resonator show exactly the nature of 
Cself. I only first saw those last year.

> As the coil self capacity is undesireable it would seem that wire
> spacing or thick insulation would be an advantage.

It doesn't work that way for a grounded resonator - period. Tesla 
couldn't make it work either. If anything, thick insulation should 
increase the capacitance if it did work that way (c.f. a air-
dielectric cap with a plastic dielectric cap) 

> I note in Skip Greiner's post "Final test on new TC"  that his
> secondary wire insulation is about 33 mils thick. With this wire
> separation the coil self capacity would be almost eliminated.

Work the equations on it. I did, and I calculated his Fr almost spot-
on. I could not possibly have done good analyses of H/D ratios on 
paper without first knowing that the equations I was using were good 

> Could this be one of the reasons he is getting such extra long spark
> lengths for the wattage input he is using?

His Cself is not all that low as you will see if you calculate it. His 
primary reactance is quite high at Fr and that would certainly count. 
I'll know for sure when I have the coil charted. I'll take the 
opportunity to repeat this: numerous experiments I've done show that 
system performance is dictated by primary losses - secondary losses 
are far lower. The Zo of the secondary is one factor I'm looking at 
through the charting exercise (nowhere near complete yet sorry :(

> > I am always glad to compare notes with you Malcolm because you
> apparently have tested more coils than any other coiler and have
> accumulated the most data. Keep up the good work.
>  John Couture

Thanks for your comment.