250 BELL SYSTEM TECHNICAL JOURNAL 



conductors are designed to be substantially alike and are located 

 substantially symmetrically with respect to earth and surrounding 

 conductors. 



In the past, telephone transmission circuits have been largely of the 

 balanced type. It has been found possible to operate such balanced 

 circuits up to fairly high frequencies,^ without incurring excessive 

 interference. However, as the frequency is raised it becomes increas- 

 ingly difficult to maintain a sufficiently high degree of balance, and 

 shielding may then be desirable. The shielding may eliminate balance 

 entirely, as in the coaxial circuit, or may be combined with balance in 

 what may be termed a shielded balanced circuit, of which the shielded 

 pair is an outstanding example. 



For the simplest forms of circuits, the optimum relations may be 

 precisely derived with the aid of the propagation formulas. In more 

 difficult cases it is necessary to use approximate methods of one kind or 

 another. These methods, however, can generally be made to yield 

 sufficiently accurate results for practical purposes. 



Coaxial Circuits 



Coaxial circuits, which furnish the least difficult problems in opti- 

 mum proportioning, make a natural starting point for this subject. 



Basic Coaxial Circuit 



The first type of circuit to be considered is the basic circuit consisting 

 of two tubular conductors arranged coaxially, whose cross-section is 

 shown diagrammatically in Fig. 1. 



Before trying to find out how to proportion such a circuit, it must be 

 noted that in the design of any shielded circuit there enter a number 

 of variables, including the overall size of the structure, the type and 

 thickness of shield, the type of conductor or conductors, the type of 

 insulation, and the frequencies to be transmitted. Some of these 

 factors exert an important influence on the optimum proportioning, so 

 that it is necessary, in order to arrive at a unique solution in a given 

 case, to keep certain factors fixed. Thereafter, however, the effect 

 produced upon the result by varying these factors may be examined. 



First, therefore, let the following assumptions be made: 



1. That the tubular conductors of Fig. 1 are composed of solid material. 



2. That the dielectric is gaseous, with zero dielectric loss. This is a 



condition which may be approached in practice. 



3. That the inner diameter of the outer conductor is fixed. This is a 



convenient assumption, having for its basis the fact that it is 

 ordinarily desirable, for economic or other reasons, to limit the 



