LAMINATED TRANSMISSION LINES. I 



909 



(letermiiKMl l)>- tlic i)i()i)(Mties of tlu> mniii dicloclric, as discussed in Sec- 

 tion II, and \v(> nuiy use tiie intrinsic propaj^ation constant of the main 

 dielectric in calculating the svu'face impedance of tli(> boundaries. This 

 aj^proximation simplifies the analysis of C'logston 1 lines a {^reat deal. 

 We siiall treat the general case, in which an arbitrary fraction of the 

 total space is filled with laminations, in Section IX of Part II, as a part 

 of our study of Clogston 2 lines. 



In this section we shall assume that the laminae are infinitesimally 

 thin, so that the stacks may be completely characterized by their average 

 l)roperties e, fi, and g. The case of finite laminae will be taken up in the 

 next section. We shall also assume throughout that dielectric and mag- 

 netic dissipation may be neglected except, as in Section VII, where the 

 contrary is explicitly stated. 



In general the current density and the other held (|uantities in a plane 

 stack of infinitesimally thin layers will be linear combinations of the 

 functions sh Tfij and ch Tdj, where y is distance measured into the stack, 

 and T( is the propagation constant per unit distance, as given by (93). 

 The qualitative behavior of the fields in a cylindrical stack will be similar. 

 In particular, if the stack is thick enough the current density and the 

 fields will fall off as e"^'^, and we can define an "efTective skin depth" A by 



A = l/(Re r,). (100) 



Cloiiston's fundamental observation was that in order to minimize the 



Fig. 6 — Coaxial Clogston 1 transmission line. 



