OPEN-WIRE CROSSTALK 235 



single-wire tertiary circuits with ground return could be used. Com- 

 putation with such tertiary circuits is impracticable because of the 

 large coupling between them. 



In the elaborate system of tertiary circuits described above, the 

 ghost circuit may be neglected. The voltage impressed across this 

 circuit is the average of all the voltages impressed on the various 

 wires. These voltages may be plus or minus and the average tends 

 to be small. Also, the charge per pair per impressed volt is usually 

 much less for the ghost circuit than for a phantom circuit due to the 

 relatively small capacitance between a pair and ground as compared 

 with that between two pairs. 



The pairs used for transmission purposes may usually be disregarded, 

 also, since their coupling with the disturbing and disturbed circuits is 

 much smaller than that of the phantom tertiary circuits. 



The practical method of computing the indirect crosstalk coefficient 

 is, therefore, to consider as tertiary circuits a considerable number of 

 phantoms composed of pairs used for transmission purposes including 

 the disturbed and disturbing pairs. In calculating the charge in any 

 tertiary circuit, the voltages impressed on other tertiary circuits are 

 disregarded. 



In calculating the effect of a single tertiary circuit c, the expression 

 for the indirect coefficient contained the factor TacTcb- To estimate 

 the effect of all the tertiary circuits, this factor should be replaced by : 



2 



— ZLTapTph. 



This expression assumes that there are n pairs on the line and that 

 w — 2 of these pairs are close enough to the disturbing and disturbed 

 pairs to appreciably affect the indirect crosstalk between them. The 

 subscript p indicates any phantom of the m pairs including the dis- 

 turbed and disturbing pairs. The summation is for all possible 

 phantoms each consisting of two of the ni pairs. If the voltages 

 induced by the balanced charges Q,,' of pair a are Vr and Vs for the 

 two sides of a phantom, the balanced voltage assumed to be impressed 



2 

 across the phantom is— (F^ — Vr). Other parts of Vr and Vs are 



m 



used in the "ghost" voltage and in balanced voltages across other 

 phantoms. 



Tap and Tpb are voltage transfer coefficients relating balanced 

 impressed voltage on the disturbing circuit to induced voltage on the 

 disturbed circuit. Tap involves C/ the transmission capacitance of 

 circuit a on a single pair line. Tph involves the transmission capaci- 



