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total inductance of bucking coils

Discussion in 'General Electronics' started by Brett Holden, Jan 31, 2009.

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  1. Brett Holden

    Brett Holden Guest

    I need to be able to calculate the total inductance of two coupled coils
    when one coil is wound in reverse. I have a Boylestad's Introductory Circuit
    Analysis (old - 6th edition) that has a section covering this but I have run
    into a problem because there seems to be some circular reasoning in defining
    the equation (#1). (I have used brackets in place of subscripts.)

    Inductance of two coupled, bucking coils:
    1) L[T-] = L[1] + L[2] - 2M[1,2]

    2) M = .25( L[t+] - L[t-] )

    3) L[t+] = L1 + L2 + 2M[1,2]

    4) L[t-] = L1 + L2 - 2M[1,2]

    I can't use subscripts here, so formula 1 is supposed to read:
    "total inductance of two reverse wound (coupled) coils equals
    inductance L1 plus inductance L2, minus (two times their mutual

    OK, if we can define the mutual inductance "M", then all is well.

    To define M, formula 2 seems simple enough but introduces two more
    variables, L[t+] and L[t-].

    In formulas 3 and 4, variables L[t+] and L[t-] are defined, but M is used as
    a variable, so I am grasping thin air. Can somebody please help me out?

    Also, formula 1 seems to ignore the influence of coeffecient of coupling
    between the coils but maybe that is accounted for in equations 3 and 4?

    Thanks for your help!
  2. Shaun

    Shaun Guest

    What's your application, what do you want to know that for.

    You not one of those free energy nuts are you?
  3. Brett Holden

    Brett Holden Guest

    No free energy. Want to build Induction Balance metal detector. Coplanar
    coils often use a bucking coil arrangement. Transmit coil has one segment
    wound in reverse. The receive coil is positioned so as to have a null in the
    absence of target. Target detection occurs when target upsets the balance.
  4. Brett Holden

    Brett Holden Guest

    What are you, the Usenet police? I thought maybe you'd have an answer.
    Thanks for NOTHING.

  5. Brett Holden

    Brett Holden Guest

    I have found the problem. Not only did I manage to mangle the equations, I
    was trying to read something into the problem that isn't there.

    M will be an unknown between 0 and 1, depending on permeability of the
    medium and physical proximity of coil sections. Equation 1 can stand alone.

    Equations 2,3,and 4, relate M to the total inductances of two series coils
    by taking measurments with coils in series wound and bucking configurations.
    There is where the circular logic jumps up which I will happily ignore.
  6. Brett Holden said the following on 2009-02-05 17:05:
    No he is not, that would be me.

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