PROPORTIONING OF CIRCUITS FOR ATTENUATION 263 



If the internal inductance of the conductors is assumed to be zero, 

 ►which is the most usual case, the high-frequency attenuation of the 

 circuit may then be written 



a = ^ (p + r) -p^ . (30) 



2c 2 loge p 



Upon minimizing with respect to c/b the condition for mininiuni liigh- 

 frequenc\- attenuation is found to be 



log,, p = = 1 + -^ • (31) 



These relations have been found useful in certain instances. 



Balanced Shielded Circuits 

 Though arrangements of three or more coaxial conductors are 

 possible,'^ practical interest is almost wholly limited to coaxial circuits 

 employing but two conductors. With balanced shielded circuits, 

 however, the number of conductors, counting the shield as one, is 

 necessarily three and may be more. With a coaxial circuit, moreover, 

 the cylindrical shape is the natural and usual one for the conductors. 

 With balanced shielded circuits, on the other hand, there enter a 

 number of possibilities. Not only are cylindrical shapes of conductors 

 and shield to be considered, but a variety of other shapes as well. 

 More complex, therefore, than the foregoing problems in optimum 

 proportioning are those for balanced shielded circuits, now to be 

 discussed. 



Shielded Pair — Cylindrical Conductors and Shield 

 The simplest form of balanced shielded circuit is a shielded pair 

 comprising two cylindrical conductors surrounded by a cylindrical 

 shield. Such a circuit is shown diagrammatically in cross-section in 

 Fig. 7. For the present, attention will be directed to the circuit 

 obtained when the tw^o enclosed conductors are connected one as a 

 return for the other. 



Condition j or Minimum Attenuation '•'■ 



As before, it is desired to minimize the high-frequency attenuation. 

 Let it be assumed first, as in the coaxial circuit, that the area within 

 the shield is fixed, the conductors are of solid material and the dielectric 

 is gaseous. Let b represent the radius of each conductor in Fig. 7, c 

 the inner radius of the shield, h the distance from the center of either 

 conductor to the center of the shield, Xi the conductivity of each con- 



