LOCATION OF OPENS IN TOLL TELEPHONE CABLES 



31 



ponent of the impedance, because the resistance component of the 

 impedance is negligibly small. However, as the length of cable in- 

 creases, the input impedance can no longer be regarded as equivalent 

 to the capacitance component of the impedance between the conductor 



C Q. 



j; E 



10 20 30 40 



Miles of Wire Beyond the Break. 



Fig. 1 



and ground, because the input impedance is not proportional to the 

 capacitance but varies as the hyperbolic cotangent (Formula 1). 

 The significance and magnitudes of errors inherent in this relation 

 are analyzed and discussed below. 



In a homogeneous line, then, if Z] and Z2 represent the input 

 impedances of the bad and good wires respectively, the percentage 

 distance to the fault is most accurately determined by separating the 

 impedances into their real and imaginary parts. 



Thus 



Zi = ai — jh^ 

 and 



Zi = ai — jhi. 



If the corresponding lengths are respectively Ix and h, the true 

 distance ratio is lyjli. Assuming that feo/^i is the ratio given by 

 measurement (the shorter line having the higher capacitive reactance). 





= c, 



where c is a correction which must be added to or subtracted from the 

 ratio of capacitive reactances to secure the ratio of total capacitance, 

 i.e., the distance ratio. 



