Single layer air core inductor design calculator

info Winding the wire in a single layer produces an inductor with minimal parasitic capacitance, and hence gives the highest possible self-resonant frequency (SRF). Striving to obtain a high SRF and low losses is the key to producing coils which have radio-frequency properties bearing some useful resemblance to pure inductance.

The calculation is based on Wheeler’s 1928 formula for a single-layer solenoid which is given in its original form as:
L = a² N² /(9a + 10b) ,[microHenries] , b > 0.8a
Where b is the coil length in inches, and a is the radius in inches.

To convert this formula to SI units, we will use the symbols r = radius, D = 2r = diameter, l = solenoid length.
Factoring b from the denominator gives:
L = 10-6 a² N² / [ b (10 + 9a/b)] [Henrys]

The quantity a/b is dimensionless, and so we can immediately substitute in the denominator:

L = 10^-6 a² N² / [ b (10 + 9r/l)] = 10^-6 a² N² / [ b (10 + 4.5 (D/l)))]

Factoring 10 from the denominator gives:

L = 10^-7 N² ( a² / b ) / (1 + 0.45 (D/l)) [Henrys]

where..

L is the inductance in Henry
D is the coil diameter in meters
r is the radius in meters (or D/2)
l is the lenght of the coil in meters
N is the number of turns

Please note that the accuracy of this formula is ±0.33% if the ratio of D/l>0.4. so this formula fits best for long solenoids.

noteThis formula applies at ‘low’ frequencies (<3MHz) using enameled copper wire (magnet wire) close wound.

Tip 1Small 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.

Tip 2 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.

Please note that the diameter is measured from center of wire trough center of the coil and to center of the wire on the opposite side. Dimensions
Required Inductance (L):
Coil Diameter (D):
Wire Diameter (d):

Coil Length (l):
Number of Turns (N):

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