564 BELL SYSTEM TECHNICAL JOURNAL 



At the farther end of the listening circuit, the approximate expression is 



The total crosstalk due to the admittance and mutual impedance 

 unbalance Y and Z is thus: 



A7 = 



A7' = + £ 



e "^^^ at the transmitting end, 

 e~'^^ at the receiving end, 



from which we see that the ratio of the crosstalk due to the two kinds 

 of unbalance is independent of the location of the point on the circuit 

 at which these unbalances are introduced, and the two will be nu- 

 merically equal in case: 



4 



or 



Y = 



(667) 



;Z = 9-10 ^Z, on non-loaded open wires. 



Appended tables give the direct capacity unbalances and the mutual 

 impedance unbalances for a 40-wire lead of No. 12 wire. The relative 

 importance of the two in producing crosstalk is shown below for a few 

 typical cases: 



Unbalance per Mile 



Direct 



Capacity 



Unbalance 



mmf. 



Mutual 



Inductance 



Unbalance 



mh. 



Ratio 

 9 10-«Z 



Pairs adjacent on same cross-arm 



1/2 and 3/4 



3/4 and 5/6 



Pairs adjacent in vertical plane 



1/2 and 11/12 



3/4 and 13/14 



5/6 and 15/16 



Pairs separated by two steps 



1/2 and 5/6 



3/4 and 7/8 



1/2 and 13/14 



3/4 and 15/16 



1/2 and 21/22 



5/6 and 25/26 



-1014 

 -1469 



602 

 409 

 704 



116 



84 



93 



150 



136 



46 



- 93 

 -143 



72 



72 



147 



31 

 19 

 2 

 4 

 20 

 43 



0.8 

 0.9 



1.1 

 1.6 

 1.9 



2.4 



-2.0 



-0.2 



-0.2 



1.3 



8.4 



