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Mutual Inductance

Discussion in 'Electronic Design' started by Tim Williams, Mar 6, 2007.

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  1. Tim Williams

    Tim Williams Guest

    So, I was wondering, what is the electrical model of mutual inductance?

    It's explained in my physics textbook, with no electrical significance as
    far as I can tell.

    Leakage inductance is far simpler to deal with, but I noticed that my
    textbook doesn't mention it and internet sites deal with cored examples.
    Air core transformers have leakage inductance too!!

    Purpose: wondering what the LL of coupled, concentric solenoids with
    different diameters is.

    Presumably, k (coupling konstant) is roughly the ratio of areas, but I can't
    find where to get LL from that.

  2. Rich Grise

    Rich Grise Guest

    OK, don't quote me on this, as "officially" I'm "only" a Tech, but to
    me it just seems intuitive that the mutual inductance is how much coupling
    you have left after you subtract out the leakage inductance.

    What that means in numbers, I have no idea. I have heard that they're
    all relatively simple to measure - it has something to do with shorted
    and open windings and schtuff like that.

    Maybe google for "mutual inductance" or "coupling coefficient" or so.

    Good Luck!
  3. Guest

    The transformer equations are

    V1 = L1. d I1/ dt + M . d I2/dt

    V2 = M. d I1/dt + L2. d I2/dt

    where M is less than the geometric mean of L1 and L2, in proportion to
    the extent that the flux from the two coils is imperfectly coupled.
    For non-cored solenoids it would have to be close to the area ratio,
    but then again, the aspect ratio of the solenoids is going to have to
    come into it.

  4. Hello Tim,

    We had a discussion in the LTspice group about coupling factors sometimes

    Maybe in appendix-A of this paper is the answer.

    Mr. Lloyd H. Dixon gives an example about the difference of
    K12, K21 and "K". See Appendix A in this paper.

    Best regards,
  5. Robert Baer

    Robert Baer Guest

    I did not even get to appendix A; note on page 4, second column
    "Thus. the "leakage" flux links the outer winding but not the inner
    *Very* loud smack in the face that leakage inductance one way is
    different than the other way.
    So those "nice" symmetrical looking equations are all lies!
  6. The Phantom

    The Phantom Guest

    You understand self-inductance, yes? Ignoring winding resistances, given
    a two winding transformer, if you apply a current to one winding (or to a
    single winding inductor), the voltage across the inductor is L di/dt. In
    the case of a sinusoidal AC current i of frequency f in the inductor, the
    voltage e across the inductor is
    e = L*2*pi*f*i, or L = e/(2*pi*f*i). L is the ratio of the voltage across
    the winding to the rate of change of the current in the winding.

    Roughly, it's a relationship between the voltage across a winding and the
    current producing it.

    In the case of mutual inductance, it's the ratio of the voltage across a
    winding to the rate of change of current in *another* winding.
    Frederick Grover's book on inductance calculations
    will tell you how to calculate the self-inductance of the solenoids and
    also their mutual inductance. From this you can calculate the leakage
    inductance. However, I will tell you that it will probably be easier to
    build them and measure.
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