Winding your own air-core inductor

[pinchy911]

I am trying to duplicate an already existing inductor by buying the components and winding it myself. I have found several different sources that give me different equations for determining inductance. My questions are as follow:

- What is the governing equation for determining the inductance of a cylinder with wire wound around it.
- What affect does layering the wire have. ie wind it once, go back and re-wind over it a second time to increase the field
- How do you incorporate the 'parasitic resistance' of the wire that varies by wire gauge/composition etc.

Lastly, this is a very small inductor (~.5 inches long) are there any tips for creating a winding apparatus...preferably with a turn counter.

 

[vk6kro]

The classic formula for winding coils is Wheeler's Formula.
There are lots of references to this if you'd like to feed it into Google.

L = (d^2*n^2) / (l + 0.45d)

where d is the coil diameter in meters, n the number of turns and l the coil length in meters.

If your existing coil has a magnetic core in it, the inductance will vary with frequency, so you need to measure the inductance at the frequency it is going to be used at.
See if a magnet attracts it. If so, you may have difficulty duplicating it unless you use the same grade of ferrite or powdered iron.

Also, the capacitance between turns can cause a coil to become resonant and behave differently to the way it would if it just had inductance. Layering the windings increases the inductance but also increases the stray capacitance and lowers the resonant frequency of the coil.

Also, the resistance of the coil measured with a multimeter may be increased by skin effect if the coil is used at high frequency.

I have seen coil winding machines with counters, but they were made by the users for their own use.

 

[Bob S]

The solenoid inductance calculator used by NASA is available for download at:
http://www.openchannelsoftware.com/projects/Solenoid_Inductance_Calculator/

The analytic equation for a single layer solenoid (thin solenoidal current sheet) is derived by Smythe "Static and Dynamic Electricity" 3rd Ed., page 340

L = pi u₀ a²n²[(z²+ a²)^1/2 - a]

where z= length, a = radius, and n = # of turns.

There are seeral on-line calculators. One used by ham radio operators is:

http://hamwaves.com/antennas/inductance.html