REDUCTION OF SKIN EFFECT LOSSES 505 



Also equation (III-36) can be written 





Equation (III-39) is a very good approximation for a for a stack of 

 infinitesimally thin laminae, but is inadequate for the discussion of situa- 

 tions where the finite value of W/b is important. Equation (III-40) on 

 the other hand is a good approximation to a when W/6 is appreciable, but 

 the assumptions made in deriving (III-40) do not allow us to go cor- 

 rectly to the limit W/b = 0. 



To estimate how small W must be before equation (III-40) fails, let us 



set ( — /j equal ^^ ( ~ ) ( "7 ) • We will also set €1 = e, since it is 



only then that these terms are important. In this case, 



W = - Jn - (III-41) 



(J \ Mo 



If we take e to be 5 times the dielectric constant €0 of free space, and take 

 0- = 5.8 X 10^ mhos/meter for copper, we obtain PT = 3.5 X 10~^ cm. Thus, 

 for any practical purpose we can ignore the failure of equation (111-40) to 

 have the proper limit for W jh = 0. 



By definition, the fields decrease into the stack according to e~'^v>^ . Let 

 us define the distance at which the fields have decreased by X/e to be the 

 effective skin depth 5^.. Then we have 



— = Real part (a,^) 



From equations (III-30) and (III-37) we find 



For €1 = e equations (III-43) and (III-42) give us finally 



5.(€i = ^) = V3 (1 + 1^) (^) 5 (ni-44) 



