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Finding a graphical method
Winding a small inductor can be frustrating and usually involves several trials. Here's a simple graphical method that will produce accurate inductance values on the very first try.
Standard size coil forms up to 1/2 inch (12.5mm) diameter are used for winding the coils.
Literature methods:
The usual method for winding coils is to use Wheeler's approximate formula
Inches:
L (uH) = ( r ²n ² ) / ( 9r+10l )
where
r = radius of the coil in inches
l = length of the coil in inches
Millimeters:
L (uH) = ( 0.0394r ²n ² ) / ( 9r+10l )
where
r = radius of the coil in millimeters
l = length of the coil in millimeters
These formulas are accurate with one percent for l > 0.8r (i.e., i f the coil is not too short).
The procedure for winding a coil is described in The Radio Amateur's Handbook and several other publications. It usually involves the solution of Wheeler's formula for n, searching a wire table for a suitable wire size, then spacing the wire along the coil form to get the required number of turns in the calculated coil length.
Accurate small coils can be made if the windings are close-wound.
Then the wire size determines the coil length (number of turns x wire diameter = coil length).
For close-wound coils, Wheeler's formula can be written:
Inches:
L (uH) = (d ²n ²) / ( 18d + ( 40n / T))
where
L = inductance (uH)
d = coil diameter (inches)
n = number of turns close-wound on coil
T=number turns per inch of the particular wire size used for the coil
Millimeters:
L (uH) = (0.0394d ²n ²) / ( 18d + ( 40n / T))
where
L = inductance (uH)
d = coil diameter (mm)
n = number of turns close-wound on coil
T=number turns per mm of the particular wire size used for the coil
In this form the formula can be plotted in terms of inductance vs turns for a given wire size and coil diameter. With the resulting graphs and a fair assortment of enameled copper wire, accurate inductors up to approximately 100 uH can be wound.
If the accuracy of the inductor is important, then use as many turns as possible. The greater the number of turns, the more accurate the formula.
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