# Need help with Inductor equations

Discussion in 'General Electronics Discussion' started by localbroadcast, Mar 6, 2015.

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Mar 3, 2015
Hello. I need to design an inductor with a specific inductance that operates below the saturation point of the core at a specific current. In order to design this, I've been digging up the equations needed to do so. I would just like some advice as to weather or not my equations are correct. Here's what I have so far:

β = Flux density (T), Φ = Flux (Wb), A = core cross-sectional area (m2), H = Magnetic field strength (AT/m), N = # of turns in coil, I = current (A), ℓ = axial length of coil (m), L = Inductance (H), μ = permeability (H/m)
β = Φ / A
H = [ NI ] / ℓ
L = [ N2μA ] / ℓ
μ = μoμr
μo = 4π x 10-7 (perm. of free space)
μr = relative permeability of core material
μ = β / H
β = [ μNI ] / ℓ

If I take the formula for flux density:
β = [ μNI ] / ℓ and rearrange it to ℓ = [ μNI ] / β
And then I take the inductance formula:
L = [ N2μA ] / ℓ and rearrange it to ℓ = [ N2μA ] / L
Since both equations now solve for ℓ, we can say that:
[ μNI ] / β = [ N2μA ] / L
This simplifies down to:
NA / L = I / β
Which rearranges to:
β = IL / NA
Since we have another formula solving for flux density:
β = Φ / A
We can combine the two equations making:
Φ / A = IL / NA
Which rearranges and simplifies to:
L = ΦN / I

Basically I would like to know if the equation I've come to, L = ΦN / I, can anyone tell me if this is incorrect? And if it's incorrect, can you explain what's wrong with it?

2. ### davennModerator

13,901
1,971
Sep 5, 2009
DONT start another thread on the same topic

the last one was closed for a reason .... because you wouldn't listen to what people were telling you
and I doubt that it would be any different in this thread

Regards
Dave