DR. CAMPBELL'S MEMORANDA OF 1907 AND 1912 565 



It will be noted that the two are of about equal importance for the 

 cases of most severe static exposure. For 5/6 and 15/16, which is 

 quite a severe exposure, the magnetic is twice as important as the 

 static. For the pairs which are so far removed as to bring in con- 

 siderable static shielding from the other wires the magnetic crosstalk 

 may be still more important relatively. Thus for 5/6 and 25/26 it is 

 eight times as great as the static. 



At the sending end of the system the static and the magnetic cross- 

 talks combine, while at the other end they tend to cancel each other. 

 In practice, therefore, the summation is the more important case. 



If both unbalances are pure reactances, the one being pure capacity 

 and the other pure inductance, and the line has approximately the same 

 impedance at all frequencies, the character of the crosstalk will be 

 the same whether it is produced by capacity or mutual inductance. 

 This will be approximately the case on well insulated open-wire lines. 

 On non-loaded cable circuits the line impedance decreases as the fre- 

 quency rises. On cables, therefore, the crosstalk due to mutual 

 impedance will have the higher frequencies more strongly pronounced 

 than the crosstalk due to capacity. 



For a transposed line we find the total crosstalk by integrating the 

 crosstalk throughout the entire length of the line. We will assume 

 that the lines are infinitely long and that the transpositions give the 

 system a periodic structure of lengths. Let x be the distance to 

 the first transposition, a, b, c, d---s, the distances from the trans- 

 position to the others in the periodic section. 



V 7 \ f*^' ^' ^+*' ^+''' ■■• 



)r*x, X, 1+6, X 

 «7 0, x-\-a, x+a, 

 — — ( — 4- —\ (1 — 2e-27:r I 2g-27U+a) 



- 2e-2T(-+«) + •••), 



since the periodic section 5 must contain an even number of trans- 

 positions. 



27 \16 ' 4/feV \ 1 - ^"^"^ 



or approximately 



^=-i(Ts + s^)^'-2['-2^- + v.^:i 



