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Coil Math Comments


        Hi Everybody,

   A few days ago a list of various formulas was posted by Richard Quick,
 these various formulas can be, and often are helpful in designing coil
 systems. However, they do as we all know have their limitations. 
   I would like in particular, to address the formulas that had to do with
 secondary resonant frequency, and secondary wire length. First off, the
 formula used to determine the length of wire for a certain 1/4 wavelength
 in feet was given as:
                
                    300000
                L=  -------  / 4 X (3/.9144)
                       F
   Where L is the 1/4 wavelength in feet, and F the frequency in KHZ.

 This formula can be simplified by writing it as follows:
                  
                     75000
                L=  -------  X 3.281
                       F
                       
   The other formula was given as a method of calculating the resonant 
 frequency of the secondary coil, and it was:


                           300000
              F=  ----------------------------
                  T x W x 3.14 x (.9144/36) x 4

  Where as:

        T= # of turns
        W= coil width (radius)
        F= freq in KHZ.

   Now for the sake of experiment, lets look at a fictious coil of the 
 following dimentions:
                      35" long winding
                      10" diameter winding
                      826 turns of # 18 wire (2161.3 feet)

   Using the given formula for calculation of the frequency of a coil we
 find that the above mentioned coil should be resonant at approximately  
 227.692 Khz.
   Here is where the goofy stuff starts, using the above calculation of
 227.692 Khz, lets go back to the first formula, according to it a 1/4
 wavelength of wire at 227.692 Khz would be about 1080.736 feet. Now it
 should be apparent that there is a difference of 50%!

   In short, the formula for reqired wire length should be completely
 thrown out, it will and I think often does, cause nothing but confusion,
 it is based on the length of wire in "freespace" which a wire wound on a
 cylinder certainly is not. 
   The formula given for secondary frequency is useful IF one remembers
 EVERTHING affects the frequency of a secondary and the formula simply puts
 you in the ballpark. TESLAC uses a little different formula for secondary
 frequency calculation that I have found to within 10-15% for aspect ratios
 between 2 and 3.5 to 1, it is:

                       /--------------- 
                   \ /  1.175 x L/D
            F=         ----------------
                           N x D

   Where    N= # of turns
            D= diameter of winding
            L=length of winding

  Using this formula the above mentioned coil figures to be resonant at about
 245.5 Khz.
  The point of all this is to be aware that all this formula stuff has its 
place, but care and practical experience also must be used. And with the
availability of various formulas like this without proper tutoring can be
misleading and confusing the newcomer in coiling.

                        Mark Graalman



... Alias, Mark the spark
___ Blue Wave/QWK v2.12


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