276 BELL SYSTEM TECHNICAL JOURNAL 



noted, the proximity effect between conductors is less completely 

 neutralized by the shield currents than is the case for the circular 

 shield. It appears that these two effects may approximately balance 

 one another, and that the circuit resistance is approximately the same 

 for both oval and circular shielded circuits. 



It is found that a circuit of approximately optimum proportions 

 comprising two solid round wires surrounded by an oval shield has 

 about 12 per cent lower attenuation than a circuit with circular shield 

 of equal cross-sectional area. 



When the conductors enclosed within the oval shield are stranded 

 there is no increase of conductor resistance due to proximity effect. 

 On this account it is desirable to bring the conductors closer together 

 in order to reduce the shield loss and the optimum spacing ratio will 

 be less than for the case of solid conductors. With stranded conductors 

 the attenuation reduction as compared with the circular shield is 

 greater than in the case of solid wires; for example, if the resistance 

 ratio (w) is .7, the attenuation with oval shield will be about 25 per cent 

 less than that of the circular shield. 



The circular form of shield is ordinarily the most convenient and 

 practical one. A disadvantage of an oval shield as compared thereto 

 is unequal stiffness or resistance to bending in different directions. 



Shielded Pair — Quasi-Elliptical Conductors 



It has been suggested at different times that the ordinary round form 

 of conductor, while well adapted for manufacturing purposes, may not 

 be the theoretically optimum shape for many types of high-frequency 

 transmission circuits. Speculations in this respect have differed 

 greatly, and a large variety of non-circular shapes of conductors have 

 been proposed, including flat strips, strips with concave or convex 

 faces opposite one another, angular forms, etc. However, except in 

 the case of the coaxial circuit, for which the circular form is clearly the 

 optimum, there has been, so far as the authors are aware, no exact 

 analytical determination of the optimum conductor shape for a given 

 type of circuit. 



A complete treatment of possible problems of this kind would extend 

 to great length. It is worth while, however, to consider a single 

 problem, namely, that of determining what shape and spacing for a 

 pair of conductors with circular shield will result in minimum high- 

 frequency attenuation. This problem is of particular interest inas- 

 much as the circular shape is ordinarily the most convenient and practi- 

 cal one for a shield. 



In attacking this problem the fundamental principles which deter- 



