LAMINATED TRANSMISSION LINES. II 



1179 



gi\x'u to a good approximation b}' 



4aoo 



e. 



0.77 



0:00 



SVSa. 



while 



/. 



2.20Xp Oim 



Trmgiti aoo 



(507) 



(508) 



The low-frequency attenuation constant ao of a Clogston cable with 

 6 = Bm will of course be greater than aoo if Om is not ecjual to 2/3. This is 

 not really a disadvantage, however, since by assumption we only wish 

 to insure that a ^ a,„ over the operating band, and the nearer a ap- 

 proaches to am oxev the whole band the less serious will be the equaliza- 

 tion problem. It may be showTi that the ratio ao/am decreases from unity 

 toward one-half as am/ am is increased indefinitely. Physically this means 

 that the low-frequency attenuation constant of an optimum Clogston 

 cable is always at least half as great as the attenuation constant at the 

 upper end of the band, and the cable never contains more conducting 

 material than would correspond to a total stack thickness of about two 

 effective skin depths at the highest operating frequency. 



We conclude with a few numerical formulas relating to the principal 

 mode in a completely filled Clogston cable with copper conductors and 

 no inner core. The low-frequency attenuation constant ao of such a 



E 

 4 <l) 



1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 



'^m / '^OO 



Fig. 21 — Curves related to the optimum fraction Qm of conducting material in 

 Clogston cables with finite laminae, us a function of the attenuation ratio amiotm ■ 



