PROPORTIONING OF CIRCUITS FOR ATTENUATION 



269 



same as if its return were coaxial. Hence the high-frequency resistance 

 of each conductor is 



Rt = -J- -I /^ abohms per cm. 



(43) 



The high-frequency resistance of the shield can be shown to be 

 Sch' U 



Ro = 



c' - ¥ 



abohms per cm. 



(44) 



The high-frequency attenuation of the shielded stranded pair, found 

 by substituting equations (41) to (44) in (1), is, with zero dielectric loss, 



ni If 4\n(T- 1 



2^\XiL^ "^ w(l - oJ 



log, 2v 



1 



1 +a~ 



4 Iog« 2 J' 



1 



1 + <j^ 



+ 2L 



■] 



nepers per cm. (45) 



The optimum proportions of the shielded stranded pair at high 

 frequencies depend, therefore, on the two quantities m/yn and Li. 

 For any given shield radius c, the values of h and b which give minimum 

 attenuation may be found by setting 



^ = 0- 

 dh ' 



and 



db 



= 0. 



By imposing the first condition it is found that 



dM jc' - h^y ^ 2 log. J/(4 loge M + 2Li) 



dh Schic'h') ^ 8 loge M + 2Li m 



+ 71 



4ch^ 



(46), (47) 



(48) 



Imposing the second condition we find that 



^2 M ^ 2 log. iV/(4 loge A/ + 2L.) 

 b ^ 8 log, M + 2Li 



\nb ^* ~ ^'' 



1 

 m A:ch} 



\nb ^ 



(49) 



h' 



where M = 2un - 0/(1 + a'). 



Upon equating the left hand members of (48) and (49), and sub- 

 stituting the values of the derivatives, the following expression results 



P = 



8(r2(l + a') 



^(1 



(50) 



0(1 - 4(t2 



