Di =inner diameter in inches.
s =distance between windings in inches.
w =wire diameter in inches.
N = number of turns.
Do =outer diameter.
1 inch = 0,0254m=2,54cm = 25,4mm.
This formula applies at 'low' frequencies (<30MHz)
) using enameled copper wire. Some people call it "magnet
More about flat spiral air core
A flat spiral coil is a type of an air core inductor
usually incorporated in the primary of a tesla generator,
RFID tag, and proximity detectors. In the same category
as the flat spiral coils we have planar spiral coils,
planar square spiral coils, planar rectangular spiral
coils, planar hexagonal spiral coils and octagonal spiral
coil. Planar coils are mostly used in high frequency
applications and designed as tracks on a circuit board.
Take a look at our planar coil calculator here.
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, platsic, 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
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
dur 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.