578 BELL SYSTEM TECHNICAL JOURNAL 



Considering the pair as a whole, the resistance when concentric is 

 R = R„ -\- Rb, and the increase due to eccentricity is AT? = ARa + ARb 

 thus giving a percentage increase, 



It is obvious that, so long as h and / are small compared with a, 

 this percentage increase is very small. 



From the well-known formuhe for the inductance and the capacity 

 between parallel cylindrical conductors, we find that the characteristic 

 impedance of a nearly coaxial pair is given in terms of the characteristic 

 impedance of the coaxial pair by 



e2^2 



Z = Zo 



1 



{k'' - 1) log ^ J' 



(149) 



where the "eccentricity" e is defined as the ratio of the interaxial 

 separation to the inner radius of the outer conductor and k as the ratio 

 of the inner radius of the outer conductor to the outer radius of the 

 inner conductor. Combining (149) and (148) we have for the attenua- 

 tion of the nearly coaxial pair: 



= ao 



1 + 2l> ^''' 



k ' (^2 _ 1) log k _ 



(150) 



References 

 ■ Papers 



1. John R. Carson, "Wave Propagation Over Parallel Wires: The Proximity 



Effect," Phil. Mag., Vol. 41, Series 6, pp. 607-633, April, 1921. 



2. John R. Carson and J. J. Gilbert, "Transmission Characteristics of the Sub- 



marine Cable," Jour. Franklin Institute, p. 705, December, 1921. 



3. John R. Carson and J. J. Gilbert, "Transmission Characteristics of the Sub- 



marine Cable," Bell Sys. Tech. Jour., pp. 88-115, July, 1922. 



4. John R. Carson, "The Guided and Radiated Energy in Wire Transmission," 



A.I.E.E. Jour., pp. 908-913, October, 1924. 



5. John R. Carson, "Electromagnetic Theory and the Foundations of the Electric 



Circuit Theory," Bell Sys. Tech. Jour., January, 1927. 



6. S. Butterworth, "Eddy Current Losses in Cylindrical Conductors, with Special 



Applications to the Alternating Current Resistances of Short Coils," Phil. 

 Trans., Royal Soc. of London, pp. 57-100, September, 1921. 



7. H. B. Dwight, "Skin Effect and Proximity Effect in Tubular Conductors," 



A.I.E.E. Jour., Vol. 41, pp. 203-209, March, 1922. 



8. H. B. Dwight, "Skin Effect and Proximity Effect in Tubular Conductors," 



A.I.E.E. Trans., Vol. 41, pp. 189-195, 1922. 



9. C. Manncback, "An Integral Equation for Skin Effect in Parallel Conductors," 



Jour, of Math, and Physics, April, 1922. 



10. H. B. Dwight, "A Precise Method of Calculation of Skin Effect in Isolated 



Tubes," A.I.E.E. Jour., Vol. 42, pp. 827-831, August, 1923. 



11. H. B. Dwight, "Proximity Effect in Wires and Thin Tubes," A.I.E.E. Jour., 



Vol. 42, pp. 961-970, September, 1923; Trans., Vol. 42, pp. 850-859, 1923. 



