1170 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



12 512 512 512 512 512 51 



FREQUENCY f 



Fig. 20 — Attenuation constants of a plane Clogston 2 line and an infinite 

 laminated medium versus frequency on log-log scale. 



numerical values are of no special significance, having been chosen solely 

 for convenience in plotting. 



So far as the practical applications of Clogston lines are concerned, we 

 are primarily interested in the frequency range /i ^ / ^ /2 , where the 

 attenuation constant is essentially independent of frequency. To de- 

 termine the rate at which the attenuation constant of the pth mode 

 begins to deviate from its "flat" value as the frequency is increased, 

 we write equation (459) in the form 



U\T\ 



OL = 



p-TT- 



2^il/lga 



1 + 



Sp'Tr'^i 



jp^-K- 



2yJjL/l ga _ 



1 + 



U\T\n\g\f 

 3p2 



(468) 



The two terms in the square brackets are equal, and the attenuation 

 constant is double its "flat" value, when / = /2 , a result which is in 

 very good agreement with the calculated values shown in Fig. 20. 

 The maximum permissible thickness of the conducting layers in a 



