An air core coil is an inductor formed by winding several turns of enameled wire on a none ferromagnetic cylinder that the cylinder can be removed after construction the coil.
The advantages of an air core coil are;
1st let's begin with a medium frequency range. Which means MHz range which is very useful for VHF, UHF etc frequency response designs.
And also the coil must be first wounded on a plastic former of the adequate diameter (equal to the required core diameter).
The winding must be tight and adjacent turns must be as close as possible.
After the winding is complete, slowly withdraw the core without disturbing the coil.
Now apply a thin layer of epoxy over the coil surface for mechanical support.
Remove the insulation from the coil ends.
This is the most famous equation for inductor fabrication and there is another euqation with further dimensions of the model. It says the following equation can be used for even to operate truly at frequencies high as 1 GHz.
L = Inductance in uH
a = Average diameter of the coil in Inches
And also for this equation, b > 0.4*a
When you want to make an inductor which produces a requred inductance all you need is to find the turns of the coil ( N ) by the above equations for the neccessary frequency. ;)
Sources : www.newcircuits.com, www.circuitstoday.com, www.k7mem.com, www.aliexpress.com