272 BELL SYSTEM TECHNICAL JOURNAL 



For a given inner radius of shield and jjiven dielectric constant and 

 conductor material, the diameter and spacing ratios which make equa- 

 tion (53) a maximum can be obtained by the substitution method 

 previously described. When the conductors and shield are of the same 

 material and ^ = 1, computation shows that the total frequency range 

 is a maximum when the radius ratio p equals 5.9 and the spacing ratio 

 a equals 0.33. This value oi A = \ represents an important practical 

 case, since it will, as a rule, be desirable to employ the same repeater 

 points for each circuit and permit the same attenuations between 

 repeater points. It is also of interest, however, to determine the 

 effect of other values of A . 



When A is zero, the problem reduces to that of the simple shielded 

 pair, which has been shown previously to be minimized by the propor- 

 tions given in {2>3)) and (34). 



When A becomes large, or, in other words, when the phantom circuit 

 alone is used, XjKi^ must be maximized. It is obviously necessary 

 that the enclosed conductor be in contact and, accordingly, the spacing 

 ratio must be the reciprocal of the diameter ratio. For this condition 

 the following proportions result: 



p = ^ = 6.0; a = ^ = 0.17. (55), (56) 



The above proportions are optimum only when the enclosed con- 

 ductors and the shield are of the same conductivity. The relations 

 for the case of unequal conductivities may be derived in a similar 

 manner. For practical purposes the effect of dielectric loss on the 

 optimum proportions is negligible. 



Double Coaxial Circuit 

 Another form of balanced and shielded transmission circuits may be 

 obtained by using two coaxial conductor units, the transmission path 

 consisting of the two inner coaxial conductors in series, with the outer 

 coaxial conductors serving only for shielding. Such a circuit is shown 

 diagrammatically in cross-section in Fig. 13. Usually the outer 

 conductors would be in practically continuous contact with each other. 

 A circuit of this type will handle a frequency band extending to lower 

 values than can be used with a single coaxial circuit, since it is balanced 

 and the two coaxial units can be transposed by twisting or by periodic 

 interchange of their positions. At high frequencies, where the shielding 

 of the outer conductor of the coaxial circuit becomes effective, the outer 

 conductors may be separated to any desired distance. It is essential, 

 however, that they be connected together at the ends of the circuit. 



