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total inductance, bucking coils

Discussion in 'Electronic Basics' started by BC Holden, Jan 28, 2009.

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  1. BC Holden

    BC Holden Guest

    I have a Boylestad's Introductory Circuit Analysis (old - 6th edition) that
    I was hoping would illuminate me regarding total inductance for two mutually
    coupled reverse-wound coils. 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.)

    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]


    Formula 1 reads: "total inductance (two reverse wound coils) equals
    inductance L1 plus inductance L2, minus (two times their mutual
    inductance)". 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'm left with a big hole in the process. Can somebody please
    help me out? Formula 1 seems to ignore the possible influence of coeffecient
    of coupling between the coils. Is that an issue of concern?

    Big thanks in advance!
     
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