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Single layer air core inductor calculator

The calculation is based on the classic Wheeler's formula for single-layer inductance (air core, tightly wound), which dates back to the radio days of the 1920s:

L = 0.001N2D/((228D/2) + 254l)

Where:
L is the inductance in henry's.
D is the coil diameter in meters.
l is the coil length in meters (>0.8radius)
N is the number of turns.
The diameter is measured from center of wire trough center of the coil and to center of the wire on the opposite side.

This formula applies at 'low' frequencies (<3MHz) )using enameled copper wire (magnet wire) tightly wound.

Small reductions in the inductance obtained can be achieved by pulling the turns apart slightly. This will also reduce self-resonance. Other combinations of wire and coil diameter may be tried but best results are usually obtained when the length of the coil is the same as its diameter.

If you need good induction stability in the presence of vibration then wind the coil on a support made from a suitable non magnetic plastic or ceramic former and lock the windings using epoxy glue or other suitable adhesive.

Sylindrical air coil
Required Inductance (L):
Coil Diameter (D):
Wire Diameter (d):
Coil Length (l):
Number of Turns (N):
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More about air core inductors
What is an air core inductor?
An "air core inductor" is an inductor that does not depend upon a ferromagnetic material to achieve its specified inductance. Some inductors are wound without a bobbin and just air as the core. Some others are wound on a bobbin made of bakelite, plastic, ceramic etc.

Advantages of an air core coil:
Its inductance is unaffected by the current it carries.
This contrasts with the situation with coils using ferromagnetic cores whose inductance tends to reach a peak at moderate field strengths before dropping towards zero as saturation approaches. Sometimes non-linearity in the magnetization curve can be tolerated; for example in switching power supplies and in some switching topologies this is an advantage.
In circuits such as audio cross over filters in hi-fi speaker systems you must avoid distortion; then an air coil is a good choice. Most radio transmitters rely on air coils to prevent the production of harmonics.
Air coils are also free of the "iron losses" which a problem with ferromagnetic cores. As frequency is increased this advantage becomes progressively more important. You obtain better Q-factor, greater efficiency, greater power handling, and less distortion.
Lastly, air coils can be designed to perform at frequencies as high as 1 Ghz. Most ferromagnetic cores tend to be rather lossy above 100 MHz.

And the "downside":
Without a high permeability core you must have more and/or larger turns to achieve a given inductance value. More turns means larger coils, lower self-resonance due to higher interwinding capacitance and higher copper loss. At higher frequencies you generally don't need high inductance, so this is then less of a problem.
Greater stray field radiation and pickup:
With the closed magnetic paths used in cored inductors radiation is much less serious. As the diameter increases towards a wavelength (lambda = c / f), loss due to electromagnetic radiation will become significant. You may be able to reduce this problem by enclosing the coil in a screen, or by mounting it at right angles to other coils it may be coupling with.
You may be using an air cored coil not because you require a circuit element with a specific inductance per se but because your coil is used as a proximity sensor, loop antenna, induction heater, Tesla coil, electromagnet, magnetometer head or deflection yoke etc. Then an external radiated field may be what you want.

A more luxiry calculator could be found here.
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