1170 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



cable of the same size. Since the lower crossover frequency was found 

 at the end of Section VIII, we shall then know the theoretical limits of 

 the frequency range over which a gi\'en Clogston cable can have lower 

 loss than the corresponding standard coaxial. 



According to eciuation (317) of Section VIII, a conventional coaxial 

 cable of radius h and optimum proportions has an attenuation constant 



1.796 _ 1.796 VTTMigi/ 



VAto.^eo fi'i^i^ Vmo/co git> 



(490) 



We shall assume that the upper crosso^'er occurs in the high-frequency 

 langc where the attenuation constant of a Clogston 2 is approximately 

 pi-oportional to / . Then for the pth mode in a cable with no inner core 

 (a = 0), equation (485) gives 



2Th\TlfAglf 



TT'tifilgf 



(491) 



A little algebra shows that the two attenuation constants are equal 

 ^vhen 



/ = 



1 



10.7" 



TT^igi L2Tit'i 





(492) 



If the conventional cable is air-filled, then assuming copper conductors 

 and no magnetic materials, Ave find that equation (492) becomes, nu- 

 merically, 



1 



h 



33.02 



(2Ti),nils(/l)mils 



1 - 



(493) 



If we consider a 3/8-inch Clogston cable AAith 0.1-mil copper conduc- 

 tors, 0.05-mil polyethylene insulators, and no inner core, then 



b = 187.5 mils 



2Ti = 125 mils 



h = 0.1 mils 



e = 2/3 

 62. = 2.26 



(494) 



We found in Section VIII that the lower crossover frequency for this 

 cable is about 50 kc-sec~\ while from equation (493) the upper cross- 

 over frequency turns out to be 15 Mc-sec~ . 



We next discuss the problem of maximizing the frequency band over 

 which the attenuation constant of a Clogston cable of given diameter 



