Designing Air Core Inductor
An air core coil is an inductor formed by winding several turns of enameled wire around a none
ferromagnetic cylinder. It is possible to remove the cylinder after the wire is wound around the core.
The advantages of an air core coil are:

The inductance is independent of the electrical current, because there is no ferromagnetic core
to be saturated as the current increases.

There is no iron losses which affect ferromagnetic cores, then you can get better Q
Factor and lower distortion as frequency increases.

They can be used to operate well up to frequencies about 1 Ghz.
To calculate a single layer air core coil, see the above picture and use the following
formula:
where,
 L = Inductance in uH
 a = Average diameter of the coil in Inches
 b = Length of the coil in Inches
 c = Radial depth of the winding in Inches
 n = Total turns of wire
It is important to note that the formula is valid if the value of
b is greater than 0.4a .
A practical example:
Let's calculate the inductance of the coil in the above picture. The mechanical measurements are as
follows:
 a = 0.2480 Inches
 b = 0.6062 Inches
 c = 0.0866 Inches
 n = 7
Now substitution into the formula:
$L=\frac{0.2\times 0.2480^2 \times 7^2}{3\times 0.2480 + 9 \times 0.6062 + 10 \times 0.0866}=85.3 \mbox{nH}$
