LOCATION OF OPENS IN TOLL TELEPHONE CABLES 29 



Includes errors which are small in comparison to the accuracy of the 

 testing equipment. Errors placed in this group obviously require no 

 compensation. Another group of errors is produced by, or is char- 

 acteristic of, certain designs of testing equipment. This class of 

 errors has been reduced to negligible magnitude by a redesign of the 

 testing equipment. One general group of errors results from faulty 

 manipulation of the testing equipment or mistakes of computation. 

 This group has been minimized by a convenient arrangement of 

 testing equipment and by outline forms for use in computation. 



Another class of errors is introduced by irregularities in the lines or 

 cables on which open locations are made. Some of these are capable 

 of compensation by constant correction factors included in formulae 

 used for computation. Other errors of this class are found to be 

 irregular functions of the length of line, and for their correction or 

 compensation curves have been prepared for each type or condition of 

 irregularity which can be used in the computation of the open location. 

 To simplify the application of the corrections, the curves are so drawn 

 that the correction is given as a simple multiplier. 



The preparation of other types of corrections will be developed later 

 in connection with the analysis and treatment of certain specific errors. 



In the development of a more sensitive and reliable method of 

 locating opens in telephone lines and cables, it was necessary to 

 make an exact study of the electrical constants of the several types 

 of conductors on which open locations are required. This involved 

 the capacitance and leakance of the conductor to ground, or to neigh- 

 boring conductors, as well as the series resistance and inductance. 

 The general formula for the impedance of a line open at the distant 



end is 



Zi = Zo coth d, (1) 



where Zo is the characteristic impedance of the line and 6 — PI, where 

 P is the propagation constant and / is the length. More fully 



P = ^i{R +ja;L)(G +jcoC), 



where R is the series resistance, L the inductance, G the leakance, 

 and C the capacitance, all expressed in terms of the same unit length, 

 and CO = It/. 

 In formula (1) 



-4 



K + jo^L 

 G + jwC 



the terms having the same significance as above. 



In cable circuits, G is usually zero, and for non-loaded lines, L is 



