710 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



3. CLOGSTON II CABLE 



3.1 Resistance 



A Clogston II cable may be looked upon as having an "inner" and 

 "outer" conductor which are separated by an infinitesimal amount in 

 which /?ac given by (20) above is an expression for the parallel connection 

 of R^ci and /?ac2 of a Clogston II cable having an outer diameter of D 

 and an inner diameter of d. That is: 



R&cl + R&c2 



It will now be assumed that (1) the currents flowing in one direction 

 through the "inner" conductor and in the opposite direction in the 

 "outer" conductor, will separate in such a way that R^d is equal to 

 R^c2 y and (2) that the currents are uniformly distributed over the cross 

 sections of the conductors. With these assumptions the respective cross 

 sections would then be equal, and the reversal of the current would 

 take place in a completely filled {d = 0) Clogston II cable at a radius 

 equal to: 



r = — ^ = 0.3535A (33) 



By substituting (32) and (33) in (20) it can be shown that: 



^ , ^ 328320 r, ^ B2w'D^FL ^ 1 u / • /o.^ 



R^i -f R^2 = ^, _ ^, I 1 + 3y^Q + • • • J ohms/mi, (34) 



where 



The above assumptions relating to division and distribution of the 

 current are not exact. S. P. Morgan has shown that the current distribu- 

 tion is not uniform and that the reversal of the current takes place at a 

 radius equal to 0.3138D. As shown in a later section of this paper, 

 the error resulting from these simplifying assumptions is not large. 



3.2 Impedance, Attenuation and Phase 



In a Clogston II cabU;, tlie main dielectric insulation between "inner" 

 and "outer" conductor has vanished. Thus the external inductance 

 approaches zero and the external capacitance becomes infinitely large. 



B2= 1 + 



