1196 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



3 



a. 

 1 



E 



20 



30 



50 

 C 



Fig. 30 — Real and imaginary parts of Aj/tt^ for a nonuniform stack whose 

 average properties vary as three cycles of a cosine function across the stack. 



the value -k appropriate to a uniform stack. McLachlan's formula shows 

 that this is indeed the case; in our notation, the leading terms give 



■w + 



e 



%vh 



1 + 



e 



8v2 



(570) 



assuming of course that the second term is reasonably small compared 

 to the first. 



This concludes our discussion of special types of nonuniformity. We 

 shall now attempt to get an idea of what the numerical results mean 

 in terms of the practical requirements on stack uniformity in a laminated 

 transmission line which is expected to show a specified reduction in at- 

 tenuation constant below a conventional line of the same dimensions. 

 For this purpose we shall compare a plane Clogston 2 line having in- 

 finitesimally thin layers with a plane air-filled line of the same 'width a, 

 bounded by electrically thick solid conductors. 



At frequencies for which the conductor thickness of the "standard" 



Fig. 31 — Real and imaginary parts of the first eigenfunction, w\ = Wi + iv\ , 

 for the nonuniform stack of Fig. 30. 



