REDUCTION OF SKIN EFFECT LOSSES 



497 



Let us imagine that we have a semi-infinite volume of material arranged as 

 shown in Fig. 4 where the 2-axis is pointing out of the paper. If Hzq is the 

 value of Hi dit y = 0, it is clear from equation (16) that Hz must depend 

 upon y according to 



H, = H^^e~ 



where 



a = ±|/: 



i03€y + (Ty 



[icO/Xo (Ty 



CO JUoCj/ + k ] 



(Il-U) 



(n-12) 



and the sign is chosen so that the real part of a is positive. 



We can now consider the case when the material under consideration is 

 an ordinary conductor such as copper or silver. In this case we must let 



► X 



(Tx = (Ty 



solid) 



and 



Fig. 4 — Orientation of solid conductor. 



= €y — e. Then a becomes (the subscript S stands for 



OLS 



= d= v ico/ioo" — coVoc + k'^ 



(11-13) 



Now, under any practical circumstances the propagation constant k will 

 certainly not be more than a factor 100 larger than the propagation con- 

 stant of free space k = \/co^/ioeo . This applies also to the factor \/co-)Uoc. 



CO/XoO" (T 



Consider then the ratio — = — . For the metal copper, for instance, 



C0€o 



w^oeo 



a = 5.80 X 10^ mhos/meter and the dielectric constant of free space €o = 

 .885 X 10~^^ . If we consider frequencies as high as 10,000 megacylces the 

 ratio is still as great as 10^ . Thus, the second two factors under the square 

 root sign in equation (11-13) are entirely negligible and we have 



as = dc -s/ioiyLQC (11-14) 



