These formulas, developed by Wheeler at the (then) NBS, give approximate inductances for various coil configurations. They are primarily based on empirical measurements, and are accurate to a few percent.
Single layer air core solenoid
L (uH) = r^2 * n^2 / (9 * r + 10 * l)
where
r = coil radius in inches
l = coil length in inches
n = number of turns
Multi layer air core solenoid
L {uH} = 31.6 * N^2 * r1^2 / (6*r1 + 9*L + 10*(r2-r1))
L{uH} = Inductance in microHenries
N^2 = Total Number of turns on coil Squared
r1 = Radius of the inside of the coil {meters}
r2 = Radius of the outside of the coil {meters}
L = Length of the coil {meters}
Note the similarity to the formula for the single layer
air core coil. Hope this helps everyone.
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.
Flat "pancake" coil
L (uH) = r^2 * n^2 / (8 * r + 11 * w)
where
r = radius to center of windings in inches
w = width of windings (in inches)
n = number of turns
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