LAMINATED TRANSMISSION LINES. II 1181 



3.59 Mc-soc~ , wliicli is only ?()..") por cent of liie fi-('((U('ii('y '^Wow l)y 

 (517). An ordinary air-filled coaxial cable of tlu; same size would lia\e an 

 attenuation constant equal to ann at about 50 kc-sec~' and equal to 

 a,n (= 2aoo) at about 200 kc-sec~'. 



It should be borne in mind that in the pi-ecediuii; examph^ we ha\e 

 ne;>;lected the effects of (helecl ric loss and of stack uoiuuiiformity. Neither 

 of these effects can l)e completely eliminated in a physical Clogston 

 cable, and both will exert iiuncvisinKly adver.sc influences on the attenua- 

 tion constant as the frequency is raised. 



Xn. EFFECT OF NONUNIFORMITY OF LAMINATED MEDIUM 



In the previous analysis of laminated transmission lines we have 

 treated only perfectly unifoi'in structures, in which every conducting 

 hiyer is identical to every other conducting layer in thickness and in 

 electrical properties, and all the insulating layers are similarly identical 

 to each other. In practice, however, it will not be possible to lay down 

 large numbers of absolutely identical thin layers, and we therefore need 

 to know the effect on transmission of slight nonuniformities in the 

 himinated stacks. Some indication that stack uniformity will be a very 

 ci'itical problem in laminated cables which are expected to give large 

 improvements in attenuation over conventional coaxial cables of the 

 same size may be obtained from the results of Section VI, which showed 

 that in a Clogston 1 line, where the phase velocity is determined by the 

 Me procluct of the main dielectric, this product must be controlled very 

 accurately to maintain the desired deep penetration of current into the 

 laminated stacks. In a Clogston 2, where the main dielectric has been 

 replaced by extensions of the stacks, one might expect similarly stringent 

 requirements on the uniformity of the laminated material if the desired 

 current distribution is to be maintained. 



In this section we estimate the effects of stack nonuniformity by 

 studying some particular idealized cases of nonuniformity in a parallel- 

 plane Clogston 2 with infinitesimally thin layers, in which the average 

 electrical properties of the stack vary only in the direction perpendicular 

 to the layers. The principal conclusion is that if one attempts to realize 

 with a Clogston line an attenuation constant Avhich is a small fraction, 

 say of the order of one-tenth, of the attenuation constant of a conven- 

 tional line of the same dimensions at the same fi-equency, then hmg- 

 range \'ariations in the properties of the stack (as distinguished from 

 short-range random fluctuations) must be controlled to within a few 

 parts in 10,000. The price is less steep if the overall improvement sought 



