The air core Inductor

The air core inductor

There are some occasions when you have an air core inductor and you don´t know its value (Henrys).

There is a way to obtain this value if you have the external inductor measurements.

L(uH)=
(0,393 a²N²)/(9a+10b)

Where:
- n: is the number of inductor spires
- a: It is the inductor radius in centimeters
- b: is the inductor length in centimeters

This formula is a good approximation of the inductor inductance for a length equal ore greater to 0.8a. See the following picture.

Example # 1:

We have an inductor with 32 spires, 13 turns per centimeter and a diameter of 25 mm. What the inductance will be?

- a = 25 mm/ 2 = 1.25 centimeters
- b = 32 / 13 = 2.46
- n = 32

Then: L = (0,393 x 1.25² x 32²) / (9 x 1.25 + 10 x 2.46) = 17.54 uHenrys

Example # 2:

We want to build a 10 uH inductor, with 2.54 centimeters in diameter and a length of 3,175 centimeters.

Then:
- a = 2.54 centimeter / 2 = 1.27 centimeters
- b = 3,175 centimeters
- L = 10 uH

We clear from the original equation the n variable.
n = [10 x (9a+10b) / (0,393 x a²)]^1/2

and by replacing the values we get the following.
n = [10 x (11.43 + 31.75) / 0,393 x 1,613]^1/2= 680 ^1/2 = 26.1 spires

Notes:
- the parentheses to 1/2 power is the same as a square root
- uHenry = microHenry

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