DR. CAMPBELL'S MEMORANDA OF 1907 AND 1912 



567 



II. Crosstalk Formulae for Phantom Circuits* 



There may be crosstalk between two phantom circuits, between a 

 phantom and a distinct two-wire circuit, or between a phantom and 

 one of its own side circuits. 



In the first case we may assume that each side of both phantoms is 

 perfectly balanced with respect to every part of the system, as we are 

 not here concerned with the crosstalk on the side circuits. The two 

 wires forming the side of a phantom may then be treated as a single 

 conductor. The sources of crosstalk will therefore be direct ad- 

 mittance unbalance and mutual impedance unbalance exactly as for 

 ordinary pairs. The capacity unbalance in formula? ' is found from 

 the 16 direct capacities between the two sets of four wires, and the 

 mutual impedance unbalance is found from the 16 mutual impedances 

 between the same wires, but this is to be divided by four in order to 

 allow for the division of the current between the two wires on each 

 side of both phantom circuits. 



In the second case each side of the phantom circuit may be assumed 

 perfectly balanced. In the computation of the capacity unbalance, 

 8 direct capacities enter. There are also 8 mutual impedances involved 

 in the mutual impedance unbalance, and these must be divided by 2 in 

 order to allow for the division of the phantom circuit current between 

 the two wires. 



The crosstalk between a phantom circuit and one of its side circuits 

 differs materially from the others, as the use of the same conductors to 

 form the side circuit and one side of the phantom circuit introduces 

 two additional sources of unbalance. These are: unbalance in the 

 impedance of the two conductors forming the side circuit, and un- 

 balance in the direct admittance from the two conductors forming 

 the side circuit to the system outside of the phantom conductors. 



The assumed distribution of unbalances is shown by Fig. 1. Insert 



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Fig. 1. 



* Memorandum dated October 31, 1907. 

 1 See September 14 memorandum. 



