Dr. Campbell's Memoranda of 1907 and 1912 



Introductory Note 



AS mentioned in the preceding article by Dr. Jewett, the first and 

 second of the three following memoranda were the basis of 

 methods of designing transpositions for voice-frequency circuits. They 

 applied particularly to non-loaded circuits but the theory was readily 

 extended to cover loaded circuits. In an earlier and more general 

 study written in 1904, Dr. Campbell considered the involved equations 

 necessary to an exact solution of the crosstalk problem and deduced 

 simplifying approximations and convenient artifices for avoiding 

 lengthy derivations. 



He first assumes a line having the circuits substantially perfectly 

 balanced to each other by means of very frequent transpositions. 

 He then considers the effect of an unbalanced condition in a short 

 length of line such as might arise from an irregularity in wire or 

 transposition spacing or an unbalanced series impedance which might 

 be due to a poor joint. Dr. Campbell refers to such effects as "slight 

 alterations in the impedances, mutual impedances and admittances of 

 the system." He shows how the crosstalk can be readily computed if 

 these alterations in impedance and admittance are known. 



He then considers the case of a short untransposed length in which 

 the coupling between circuits is systematic rather than accidental. 

 He shows that the crosstalk in such a short length can be computed in 

 terms of mutual impedances and admittances in just the same manner 

 used for accidental coupling in a short length nominally perfectly 

 balanced. He shows that the mutual impedance per unit length 

 (which is substantially proportional to the mutual inductance) is a 

 measure of the crosstalk effect of the magnetic field of the disturbing 

 circuit and can be computed from a knowledge of the spacing and 

 diameters of the wires of the disturbing and disturbed circuits. The 

 mutual admittance per unit length is a measure of the crosstalk effect 

 of the electric field of the disturbing circuit and is shown to be pro- 

 portional to the "direct capacity unbalance" which may readily be 

 measured or computed from measurements of the individual direct 

 capacities. This notion of direct capacity unbalance which was 

 deduced in the earlier memorandum of 1904 has been of the greatest 

 usefulness in crosstalk problems both in open wire and in cable. The 

 mutual admittance defined in this way takes account not only of the 



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