LAMINATED Tli-VNSMIttSlOX LINES. II 



IKi'J 



^ [I'l/ei hgih 



7=-7 J^^ . (4<'.5) 



/5 



/ — i 



(466) 



Comparing tliese expressions with (Hjuations (25; and (20) of Section II, 

 we see that they correspond to waAcs in parallel-phme transmission 

 lines of width t^ , bounded by electrically thick solid conductors. Wc 

 shall call this range, in which a is proportional to the square root of 

 tr(M|U(nicy, the "ver}^ high frequency" range. At these frequencies the 

 propagation constant is the same in a Clogston 2 lino of finite thickness 

 as in an infinite laminated medium. 



In order to describe the various frequency ranges more precisely, we 

 shall define the three critical frequencies /i , /2 , and /s to be the fre- 

 (luencies at Avhich the approximate expressions for the attenuation 

 constants in two adjacent frequency ranges are equal. These frequencies 

 are closely related to the critical frequencies which we defined in equa- 

 tions (178) of Section V, when w^e were discussing the surface impedance 

 of a plane stack of finite layers. For a stack containing a total thick- 

 ness Ti of conducting material, we recall that the critical frequencies 

 were /i , where Ti = 8i ; f2 , w^here Ti = Ta ; and /s , where h — \/3 5i . 

 For the pth. mode in a Clogston 2 containing a total thickness 27*1 of 

 conducting material, the frequencies turn out to be 



/; = 



/; = 



/ = 



pV^M 



p~Trd 

 mgj'l 16/1 



rzr- Ji , 



2fMigitiTi 

 36m 



El 

 2 



(467) 



_(1 — 6)n-i_\ TTfj'igitl 



4^6 



h, 



where of course p = I for the principal mode. Thus the attenuation 

 (■(justant is given- approximately by (456) for ^ / ^ /i , by (461) 

 for h ^ / ^ /2 , by (462) for /.f ^ f ^ f, , and by (465) for / ^ /a . 



If we plot the foregoing approximate expressions for the atteiniation 

 constant against frequency on log-log paper, we can get a good idea of 

 the \'ariation of the attenuation of a Clogston 2 over the entire frequency 

 range. Both the approximate expressions and the exact results for a 

 particular numerical case are plotted in Fig. 20, for a Clogston 2 of 

 linite thickness and also for an infinite laminated medium. The actual 



