Formula for true self capacity of a coil.

To: tesla-at-pupman-dot-com
Subject: Formula for true self capacity of a coil.
From: "Gavin Dingley" <gavin.dingley-at-astra.ukf-dot-net> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)
Date: Mon, 29 May 2000 12:27:11 -0600
Approved: twftesla-at-uswest-dot-net
Delivered-To: fixup-tesla-at-pupman-dot-com-at-fixme

Hi Bob, Terry, Malcolm,
I think I may have found a formula for true self capacity of a coil,
well this is it:-


C = (  (11.26 * H)   +   (  (16 * R) + ( 76.4 * R^(3/4) )  )    /
(sqr H)

C is the coil capacitance in pF, R is the coil radius in meters and H
the coil height in meters.

I hope that makes sense?!

It came from a TCBA article written by D. C. Cox. Pres., Resonance
Research.

Measured Values for Capacitance of Spheres and Toroids
by:  D. C. Cox. Pres., Resonance Research
Volume 17, #3 TCBA News 1998

A photocopy of the article was sent to me by Don Butler, a fellow coiler
in the U.K.
I had sent the article to Bob Jones, but there appeared to be
complications in reading it, so I tried the formula my self to see what
would happen, the result looked good.

I wrote a program that calculated coil inductance, Medhurst C and "Cox"
C, along with the lumped LC resonant frequency using Medhurst and
resonant frequency using the Jones formula with Cox's self capacity of a
coil.
I then plugged Malcolm's coil data from an earlier post into the program
and this is what came out:

Coil 1)

Hs = 21.75",     Ds= 4.75",     N approx 870t,    L = 17.87mH
1/4 wave = 394.5kHz

Cmed = 8.8pF

Ccox = 22.18pF

Lumped LC (using Cmed) fr = 401.43kHz

Jones (using Ccox) fr = 397.07kHz

-------------------------------------------------------

Coil 2)

Hs = 22.75",     Ds= 5.95",     N approx 910t,    L = 29.3mH
1/4 wave = 269kHz

Cmed = 9.9pF

Ccox = 24.64pF

Lumped LC (using Cmed) fr = 298kHz

Jones (using Ccox) fr = 296.678kHz

-------------------------------------------------------

Coil 3)

Hs = 16.2",     Ds= 9.05",     N approx 650t,    L = 42.25mH
1/4 wave = 212.7kHz

Cmed = 11.19pF

Ccox = 33.6pF

Lumped LC (using Cmed) fr = 230.41kHz

Jones (using Ccox) fr = 208.78kHz

-------------------------------------------------------

The Jones formula is;

fr = 1/ (4 * sqr(L*Ccox) )

Well it appears to work, and using Medhurst C in the Lumped formula also
seems to work two. Of course, the Jones formula is more versatile when
calculating wavelengths other than 1/4-wave.

Regards,

Gavin, U.K.