Air core inductors, calculations

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http://home.earthlink.net/~jimlux/hv/wheeler.htm

I am not sure where the lalena formula came from, although it appears to be a modified version of wheelers single layer formula. With the test coils I have made, the wheeler formulas are satisfactory.

Shape does not appear to be a really sensitive factor for coils. I minimized the wheeler equation for lowest DCR and found one minima at 6*a = 9*b = 10*c , if I am recalling things correctly. Rather large deviations from this shape (that had the same inductance) did not appear to change DCR much...

Some other equations specify that the inner radius of the windings should be equal to the length of the coil, ("b" in the equations below)

The equations below are copied from the page in the link above, but they can also be found in the ARRL handbook and many other places..
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L (uH) = 0.8 * a^2 * n^2 / (6*a + 9*b + 10*c )

where
a = average radius of windings
b = length of the coil
c = difference between the outer and inner radii of the coil.
all dimensions in inches.

It states that it is accurate to 1% when the terms in the denominator are
about equal. This is also an equation by Wheeler. It applies as long as the
coil has a rectangular cross section.
 
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