REDUCTION OF SKIN EFFECT LOSSES 499 



--(7)^7(7 + ^"-^^) 



As before, co€i is completely negligible compared to a, and furthermore a,j is 

 negligible compared to coe. We have therefore for a, (the subscript stands 

 for zero thickness) 



«o 



= =^ yu [^' - ^'^«' + ^*^^°^ (7) T (t + 0. 



(11-23) 



This situation is rather surprising. Let us suppose conditions are such 

 that most of the energy of the wave is flowing in the region outside the 

 stack of laminations. If this region is filled with an insulator of dielectric 

 constant €1, k^ will be very nearly equal to co^juoei . Then ao will be given by 



= V!-»[(:-'-')+'(?)(t)] '"-» 



K €1 is made equal to e, q;o becomes 



W 

 ao = 



w + r ("-^)- 



= r+W¥ '''-''' 



where X is the longitudinal wavelength. Thus, under these conditions the 



wave will penetrate into the laminations to a depth ;r" ( -^ "^ w ) before it 



has decreased by a factor 1/e. This distance is of course enormous com- 

 pared to ordinary skin depth. 



We will see in the next section that the finite thickness of the laminae 

 limits the penetration of the waves for ci = € to a distance much smaller 

 than that implied in equation (11-26) but still large compared to conven- 

 tional skin depths. In any case, we see in this simple way the suggestion of 

 a method for obtaining great penetrations and consequently considerably 

 reducing the attenuation of a transmission line. 



The analysis of this section, carried out by assuming the medium to be 

 anisotropic but homogeneous, can be given more physical meaning by 

 examining a Uttle more closely how the fields vary through the laminations 

 shown in Fig. 5. From equations (II-8) and (11-9) one finds for a general 

 case 



dE. 1 r. 2 . ,21 



dy io)€y + o-j 



[ioj/xoCy — 03 fxa^y -f- k]Hz (11-27) 



