CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 149 



a given frequency lyH"^ is negligible when compared with 2yl, we have 

 g-2yi = I _ 2yl + 272/2 



= 1 - 2t/, (11) 



and the expression (10) becomes 



The near-end crosstalk is therefore proportional to /. 



For very large values of yl, that is, a very high frequency or extreme 

 length or both, where the exponential expression is negligible as com- 

 pared to unity, the expression (10) becomes 



which is independent of length. 



The variation of the near-end crosstalk with length for intermediate 

 values of 7/ can be best followed if instead of the expression (10) we use 

 its absolute value 



|iVi2| = 



Here 



Vn 



IZ12I Vl - 2g-2°' cos (2/3/) -f e-'"' 

 2 1 Zi I V^M^ 



(14) 



7 = a + i^, (15) 



a is the attenuation constant in nepers per unit length and (3 is the 

 phase constant in radians per unit length. 



We observe that for a given value of / one of the factors in (14) is 

 oscillating with frequency. Thus, if we plot the crosstalk against 

 frequency, the resulting curve is a wavy line superimposed upon a 

 smooth curve, with the successive minimum points corresponding to 

 the frequencies for which the given line is practically a multiple of half 

 wave-lengths. The smooth curve is of course given by the magnitude 

 of the expression (13). The curves on Fig. 2 illustrate the change of 

 the near-end crosstalk with frequency for different lengths of a triple 

 coaxial line made of copper conductors. 



Direct Far-End Crosstalk 



In order to determine the far-end crosstalk, we have to compute the 

 induced voltage arriving at the far end of the system. Proceeding in a 

 way similar to the derivation of the near-end crosstalk, we obtain the 

 contribution dVf to the potential across the right end of circuit (2), due 



