> From:         David VanHorn[SMTP:dvanhorn@CEDAR.NET]
> Sent:         Thursday, July 15, 2004 2:36 AM
> To:   PICLIST@MITVMA.MIT.EDU
> Subject:      Re: [EE:] Inductance and capacitance

>>
>>Check this out - not much but may help
>>
>>http://www.dse.co.nz/cgi-bin/dse.filereader?40f62581020b1e28273fc0a87f9906aa+EN/catalogs/DTS0000020

      > It's the same thing, I need to know the length of the coil in order to calculate
      > the # of turns. I'm looking for the close wound case, where the number of
      > turns determines the length.

      In the original formula, substitute N*diam for L. This will give you an N inside
      of the formula and another N on the left side of the equation. Rearrange terms
      so that all terms containing N are on one side of the equation, factor that side
      into N times something, and divide both sides of the equation by "something".
      For example, if

      N = a + b*len, then N = a+b*(N*diam) and N(1 - b*diam) = a. Therefore

      N = a / (1 - b*diam)

      The problems begin when the resulting equation cannot be solved. This
      would mean an equation of third order or higher. The actual equation
      will be quadratic, as you can see by using this equation for a single layer
      coil:

      L = [ N * N * A * A ] / [ 9 * A + 10 * B ]

      L is the inductance in microhenries, N is the number of turns, A is the
      mean radius of the coil (to the center of the wire) in inches, and B is
      the length of the coil in inches. Let B = N * D where D is the wire
      diameter. Then

      L = [ N * N * A * A ] / [ 9 * A + 10 * N * D ]

      Clear the fraction by multiplying both sides by [ 9 * A + 10 * N * D ]

      L * [ 9 * A + 10 * N * D] = N * N * A * A

     This gives  (A ^ 2) * (N ^ 2) - ( 10 * L * D ) * N - 9 * A * L = 0

     This quadratic equation can be solved for N. There will be two
     solutions; use the positive real root if there is one. If not, there
     is no solution.

     John Power

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