164 BELL SYSTEM TECHNICAL JOURNAL 



experimental evidences, will result in a root-mean-square law of addi- 

 tion. Thus, the overall near-end crosstalk from m sections will be 

 equal to the crosstalk from a single section multiplied by the square 

 root of m. 



On the contrary, in a system using similar coaxial pairs transmitting 

 in the same direction and employing repeaters at the same points, the 

 far-end crosstalk is affected mostly by the phase differences of the 

 repeaters. If these do not vary from the average by more than a few 

 degrees, the far-end crosstalk in a system involving even a compara- 

 tively large number of repeaters will change proportionally to the first 

 power of the number of repeater sections m. Only with a very large 

 number of repeater sections (perhaps 500 or more) and random phase 

 differences of repeaters and line of perhaps 5°-10° will the far-end 

 crosstalk from single sections tend to approach random distribution. 

 In this case the root-mean-square law will hold reasonably well. 



Thus, far-end crosstalk will grow faster than near-end crosstalk as 

 the number of repeater sections increases. This, combined with the 

 relationship between the far-end and the near-end crosstalk in a 

 single repeater section as given by equation (61) and Fig. 8, leads us to 

 conclude that in long systems with both near- and far-end crosstalk 

 present the limiting factor will be the far-end crosstalk. This is 

 contrary to the experience with balanced structures stated above. 



References 



1. A. G. Chapman, "Open-Wire Crosstalk," Bell System Technical Journal, Vol, 



XIII, January 1934, pp. 19-58, and April 1934, pp. 195-236. 



2. S. A. Schelkunoff, "The Electromagnetic Theory of Coaxial Transmission Lines 



and Cylindrical Shields," Bell System Technical Journal, Vol. XIII, October 

 1934, pp. 532-579. 



3. L. Espenschied and M. E. Strieby, "Systems for Wide-Band Transmission Over 



Coaxial Lines," Bell System Technical Journal, Vol. XIII, October 1934, pp. 

 654-769. 



4. E. J. Sterba and C. B. Feldman, "Transmission Lines for Short-Wave Radio 



Systems," Bell System Technical Journal, Vol. II, July 1932, pp. 411-450. 



5. H.F. Mayer and E.Fisher, "Breitband Kabel mit Neuartige Isolation," E.T.Z. 



No. 46, Nov. 14, 1935. 



6. S. P. Mead, "Wave Propagation Over Parallel Tubular Conductors: The Alter- 



nating Current Resistance," Bell System Technical Journal, pp. 327-338, 

 April 1925. 



7. John R. Carson and J. J.Gilbert, "Transmission Characteristics of the Submarine 



Cable," Journal Franklin Institute, December 1921. 



8. John R. Carson and Ray S. Hoyt, "Propagation of Periodic Currents over a 



System of Parallel Wires," Bell System Technical Journal, July 1927. 



9. H. Kaden, "Das Nebensprechen Zwischen Parallelen Koaxialen Leitungen," 



Electrische Nachrichten Technik, Band 13, Heft 11 (1936), pp. 389-397. 

 10. M. E. Strieby, "A Million-Cycle Telephone System," Electrical Engineering, 

 January 1937; Bell System Technical Journal, January 1937. 



