Coil Math Comments
Subject: Coil Math Comments
From: mark.graalman-at-mediccom.norden1-dot-com (Mark Graalman)
Date: Mon, 14 Aug 1995 05:49:00 -0500
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Resent-Date: Mon, 14 Aug 1995 06:55:42 -0400
A few days ago a list of various formulas was posted by Richard Quick,
these various formulas can be, and often are helpful in designing coil
systems. However, they do as we all know have their limitations.
I would like in particular, to address the formulas that had to do with
secondary resonant frequency, and secondary wire length. First off, the
formula used to determine the length of wire for a certain 1/4 wavelength
in feet was given as:
L= ------- / 4 X (3/.9144)
Where L is the 1/4 wavelength in feet, and F the frequency in KHZ.
This formula can be simplified by writing it as follows:
L= ------- X 3.281
The other formula was given as a method of calculating the resonant
frequency of the secondary coil, and it was:
T x W x 3.14 x (.9144/36) x 4
T= # of turns
W= coil width (radius)
F= freq in KHZ.
Now for the sake of experiment, lets look at a fictious coil of the
35" long winding
10" diameter winding
826 turns of # 18 wire (2161.3 feet)
Using the given formula for calculation of the frequency of a coil we
find that the above mentioned coil should be resonant at approximately
Here is where the goofy stuff starts, using the above calculation of
227.692 Khz, lets go back to the first formula, according to it a 1/4
wavelength of wire at 227.692 Khz would be about 1080.736 feet. Now it
should be apparent that there is a difference of 50%!
In short, the formula for reqired wire length should be completely
thrown out, it will and I think often does, cause nothing but confusion,
it is based on the length of wire in "freespace" which a wire wound on a
cylinder certainly is not.
The formula given for secondary frequency is useful IF one remembers
EVERTHING affects the frequency of a secondary and the formula simply puts
you in the ballpark. TESLAC uses a little different formula for secondary
frequency calculation that I have found to within 10-15% for aspect ratios
between 2 and 3.5 to 1, it is:
\ / 1.175 x L/D
N x D
Where N= # of turns
D= diameter of winding
L=length of winding
Using this formula the above mentioned coil figures to be resonant at about
The point of all this is to be aware that all this formula stuff has its
place, but care and practical experience also must be used. And with the
availability of various formulas like this without proper tutoring can be
misleading and confusing the newcomer in coiling.
... Alias, Mark the spark
___ Blue Wave/QWK v2.12
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