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Need help with Inductor equations

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

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  1. localbroadcast


    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. davenn

    davenn Moderator

    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

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