500 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



Let the value of H^ at the interface of a conducting lamina and a dielectric 

 lamina be {Hz)ii . From equation (11-27), one finds just within the conduct- 

 ing lamina 



^^ = ico/xo(^.)o, (11-28) 



dy 



while just with the adjacent dielectric lamina 



^' = Wo[l-^](ff.)o. (11-29) 



Thus, if the laminae are very thin, the change in Ex across the conducting 

 lamina is 



{AEx)m = ic^no{H,)oW (n-30) 



and the change in Ex across the dielectric lamina is 



(AEx), = ^a)Mo(H.)o (l - 7) ^ (11-^1) 



/ W\ 



Therefore, when 6i = €(l-| j, the change in Ex across the conducting 



lamina is just balanced by the change in Ex across the dielectric lamina. 

 This is the basic reason for the deep penetration of the fields into the lam- 

 inated structure. When ci = e, there is no change in Ex across the dielectric 



W 

 lamina. In this case we note from equation (11-24) that ao = ttt , «s , 



and we see that the waves will penetrate into the laminae an increased dis- 

 tance that is just accounted for by the spacing of the laminae. Thus, for 

 ci = €, the attenuation of a laminated line will be unchanged if the laminae 

 are replaced by solid metal. 



in. Laminations of Finite Thickness 



Let us refer again to Fig. 5 where a stack of conducting laminae of thick- 

 ness W and conductivity a are shown separated by insulating laminae of 

 thickness / and dielectric constant e. First we shall inquire as to how the 

 fields change across the conducting laminations. According to equations 

 (II-8) and (II-9) one has 



^ = ia^tMoaH. (IIM) 



£x = -— (III-2) 



<r dy 



