608 BELL SYSTEM TECHNICAL JOURNAL 



circuit, the more chance there is that the return loss of that Hne 

 happened to be measured at the top of a " wabble." 



When singing points ^ are measured, however, it may be said that 

 when singing takes place above, say, 2000 cycles, very nearly the 

 minimum value of return loss minus gain is obtained. The distribution 

 of singing points on a large group of lines, therefore, will be lower (in 

 decibels after correction for gain characteristic) for a given percentage 

 than the distribution of single-frequency return losses even at the 

 frequency which has the lowest computed values of any within the 

 transmitted band (say, 2900 cycles for a repeater cutting off about 

 there). Following the reasoning concerning the " wabble " given 

 above, the amount by which the singing point will be lower will be 

 small for the lower return losses and singing points of a given group 

 of lines, and will tend to increase more and more as the value of return 

 loss becomes higher. 



Figure 6 shows the Sf curve plotted on a scale which makes all 

 cumulative normal law distributions come out as straight lines. It 

 may be seen that the differences just described will tend to make the 

 singing point distribution more nearly a normal law than the Sf 

 curve. Field measurements show that such singing point measure- 

 ments do approximate a normal law much more closely than they 

 approximate the Sf curve. Measurements of singing points on about 

 900 19-gauge H-172-63 side circuits at 18 places during completion tests 

 gave standard deviations about the average of the group at each 

 place which, when added together as the weighted root mean square, 

 gave a general standard deviation of 2.02 db. About 400 similar 

 measurements on 16-gauge H-44-25 side circuits at 16 points gave a 

 standard deviation of 2.05 db. Similar measurements on 233 19-gauge 

 H-88-50 side circuits and 77 19-gauge H-88-50 phantom circuits gave 

 standard deviations of 2.13 and 2.03 db, respectively. It therefore 

 seems reasonable to conclude that a standard deviation of about 2 db 

 is substantially correct for the distribution curve of singing points at 

 a given place. It should be realized that if singing points for a given 

 type of facility from a large number of places are grouped together and 

 a standard deviation of the entire group obtained around the average 

 of the entire group, it may be considerably larger than 2 db due to the 

 differences in average values of the different groups. Such com- 

 putations on about 7500 measurements on one type of facilities showed 

 a standard deviation of about 3 db for the entire group. 



* The singing point of a given line is the gain which must be connected between 

 the two sides of a hybrid coil to just cause singing, when the line terminals of the 

 hybrid coil are connected to the line in question and the network terminals are 

 connected to the normal balancing network circuit. Unless otherwise specified, the 

 singing point is expressed in terms of the 1000-cycle gain. 



