1180 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



cable is given by 



ao = 



0.521\/e^ 



0.728 X 10' V^ 



nepers -meter" 



(509) 



for any value of 6, wliile if 6 = 2/3, we have 



1.353 "x/cz 



db-mile \ 



ooo = 



7 2 



1.891 X lO'V^ 



Omils 



nepers -meter 



db-mile^ . 



(510) 



The frequency /,„ as a function of the ratio am/aoo is 

 (1 - d)i a„ 



_ 44.93 r 



\J m7Mc — /, \ 7 



2.598 



«00 



for any 6, and when 6 = dm the expression for /,„ becomes 



KJmJ^lc — 



44.93 



('l)mils,^mils 0, 



' 2 - 3dr, 

 2 — dm 



(511) 



(512) 



where the factor invoh'ing dm is plotted against a„,/aoo in Fig. 21. 



If we consider a 3/8-inch Clogston cable with 0. 1-mil copper conductors 

 and polyethylene insulation (e-ir = 2.26), we find 



«oo = 0.809 db-mile~\ 



If we set 



a,„ = 2aoo == 1.018 db-mile~ , 

 then it turns out that 



dm = 0.3745, 



(513) 

 (514) 

 (ol5) 



so that the insulating layers should be 0.167 mil thick. The low-fre- 

 quency attenuation constant for dm is 



ao = 1.300a„o = 1.051 db-mile~\ (516) 



and am is reached at a freciuenc}' 



/,„ = 4.70 :Mc- sec"'. (517) 



If we had used d = 2/3, we should have reached a,„ at a frequency' of 



