PROPORTIONING OF CIRCUITS FOR ATTENUATION 261 



This is the same as the internal inductance at zero frecjuency of a sohd 

 tube of the same dimensions. 



Since either the inner or outer conductor of a coaxial circuit, or both, 

 may be stranded, and since, in addition, the dielectric loss may either 

 be ncgii^il)le or may be appreciable, there are six different cases of 

 optimum proportioning which might be considered.'^ Only one case, 

 however, that of a coaxial circuit with only the inner conductor 

 stranded and with negligible dielectric loss, will be taken up here. 

 The high-frequency attenuation of such a coaxial circuit is 



m If / 



H ) x/tx-j NO 1 or 1 nepers per cm. (25) 



m / \ (4 \oge py + 2Li \oge P 



While the value of m varies with frequency and with the design of the 

 stranded conductor, this value is, for a particular frequency and a 

 particular design, definitely determinable. As has been noted, it is 

 generally desirable to proportion a transmission circuit so as to mini- 

 mize the attenuation at the highest frequency to be transmitted. 

 Furthermore, the value of m will not vary rapidly with changes in 

 conductor diameter provided the number of strands be changed as the 

 conductor size is varied. It therefore becomes possible to treat m as a 

 constant in deriving the relation for optimum proportioning. 



Using p to designate c/b, the condition for minimum high-frequency 

 attenuation is found to be 



2 — p log. P 

 Vw ^ 4 log, p + Li .^^. 



m , . 2 log, p -f Li * 



-pp + 1 

 ■\n 



Figure 6 shows graphs of equation (26) for two values of Li, namely, 

 Li = 0.5 abhenry per centimeter, which corresponds to the case where 

 the cross-section of the inner conductor is completely stranded, and 

 Li = 0. When the stranded inner conductor is of annular cross- 

 section the optimum value of the diameter ratio lies somewhere be- 

 tween the two curves shown. The useful range of m probably lies 

 between about 0.5 and unity and that of n between about 1 and 15. 



As to the practical use of stranding, it is apparent from the resistance 

 ratio curves of Fig. 5 that in order to take advantage of stranding it 

 would be necessary to limit the transmission band to a maximum 

 frequency well below that possible with non-stranded conductors. 

 Further drawbacks to the use of stranded conductors are their greater 

 cost as compared with non-stranded ones, and greater mechanical 



