Medhust and 1/4-wave resonance of coils.

• To: tesla-at-pupman-dot-com
• Subject: Medhust and 1/4-wave resonance of coils.
• From: "Gavin Dingley" <gavin.dingley-at-astra.ukf-dot-net> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)
• Date: Fri, 19 May 2000 17:57:49 -0600
• Approved: twftesla-at-uswest-dot-net
• Delivered-To: fixup-tesla-at-pupman-dot-com-at-fixme

Hi Malcolm, Rob and all,
I have been following the recent posts on adjustment of the medhurst
formula and it's use in calculating the 1/4-wave resonance of secondary
coils in TCs. Now I am just going to summarize what has been said so as
to be corrected on any point I may have misunderstood.

Modeling the coil as a transmission line is difficult because the
inductance per unit length is effected by mutual inductance between
turns. Also the capacity per unit length is effected by the inter-turn
capacity between turns. This results in the secondary coil seeming to be
more of a lumped LC circuit, rather than a transmission line.

Using the formula:

fr = 1/(2 pi sqr(L C))

where L is the inductance and C the self capacity of the coil. The self
capacity can be calculated with the medhurst formula. This results in a
reasonably close frequency of resonance.

However, Rob Jones states that the medhurst value for self capacity is
based upon only the geometry of a hollow cylinder and so does not
incorporate inter-capacity between coil turns. He stated that for short
coils Cself = 3 * Cmed, while for long coils
Cself = 2 * Cmed.

Using transmission line theory, a value of Cself = 2.46 * Cmed results
as a general rule. Now because 2.46 is about ((2 * pi) / 4)^2, the
formula:

fr = 1/(2 pi sqr(L * Cmed * 2.46))

becomes

1 / (4 * srq(L * Cmed)) *

Are there any limits to this formula regarding coil length, to frequency
wave length (i.e. a point where a coil starts to act as a transmission
line)?

Is there yet a similar formula for bi-polar coils?


MEDHURST FORMULA
I have come across the following for the Medhurst formula:-

Cmed = (0.256479 * H) + (0.78646 * D) pF

H is coil height in inches and D is coil diameter, also in inches.

Is this correct, and if so, does it have any H/D ratio limits?

I know this post is more a bunch of statements rather than questions,
but I want to clarify that I have got it right.

Thanks in advance,

Regards,

Gavin, U.K.

>>* I think Cmed should be Ctrue or Cself in this equation or the actual
capacitance of the cylinder in free space. - Terry <<

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