260 



BELL SYSTEM TECHNICAL JOURNAL 



from the curves of Fig. 5. It will be seen that there is ordinarily a 

 frequency at which the resistance ratio is a minimum. Above this 

 frequency the improvement due to stranding rapidly vanishes, the 

 performance thereafter being worse than that of the corresponding 

 non-stranded conductor. The minimum value of resistance ratio 

 attained in the range of some hundreds of kilocycles may be in the 

 order of 0.6, a very substantial improvement. In order to secure any 

 marked advantage in the frequency range above 700 or 800 kilocycles, 

 the number and fineness of the individual strands would be such as 

 practically to preclude their use. 



Another result obtained with stranding is an increase in the internal 

 inductance of the conductors, which likewise serves to reduce the high- 



ly of 0.9 

 O O 

 Z I- 



<<J 



a 5 



O 100 200 300 400 500 600 700 800 



FREQUENCY IN KILOCYCLES PER SECOND 



Fig. 5 — Resistance ratios of stranded conductors. 



frequency attenuation. For a round conductor which is completely 

 stranded, the internal inductance at all frequencies where the current 

 is uniformly distributed over the conductor cross-section approximates 

 .5 abhenry per centimeter, which is the internal inductance of a solid 

 round wire at zero frequency. In general, this value of internal 

 inductance will hold up to frequencies somewhat above that for which 

 the resistance ratio m is a minimum. The internal inductance of a 

 stranded conductor of annular cross-section, for all frequencies where 

 the current is uniformly distributed over the cross-section, is 



z, = "' - ^"^ + 



la 



lib'' - a") ' (&2 



—rr-^ log, - abhenries per cm. 



a^Y a 



(24) 



