610 BELL SYSTEM TECHNICAL JOURNAL 



of cases which will have lower singing point values. It was not pos- 

 sible to compute B from the measurements referred to above due to 

 incomplete information. 



From field measurements including a large group on 19-gauge B & 

 H-88-50 facilities during a Newark-Philadelphia trial, however, it 

 appears that B is about 2.5 db. As further evidence, the reasoning 

 given above concerning the " wabble " in the return loss distribution 

 when considered together with the standard deviation of 2 db leads 

 to the conclusion that the value of B must lie within a range from 

 about 2 to say, 3 or 4 db for all facilities. 



It is accordingly considered reasonable, to assume that the distri- 

 bution of singing points on passive repeater sections at a given place 

 will be a normal law of the form 5i - 2.5 -f 5q(2.0).5 The Sq (2.0) 

 law is shown on Fig. 6. 



When the singing points of several such repeater sections in tandem 

 are measured, it seems reasonable to say that the distribution of 

 singing points will be a normal law of the form Si — F(N, T) — 2.5 

 -f- SQ{2.Qi), by analogy with the distribution functions of single-fre- 

 quency return losses. 



When an end path is measured by itself, the singing point in the 

 2000-3000-cycle range will generally be a little less than would be 

 indicated by single-frequency return-loss measurements. However, 

 the difference between the two sets of measurements will probably be 

 less on the average than the 2.5 db indicated above, since the 

 " wabbles " in measurements of terminal return losses are usually 

 much less than in measurements of repeater section return loss, par- 

 ticularly for the lower terminal return losses which generally are on 

 non-loaded loops. It is accordingly estimated that the distribution 

 of singing points of the end paths is 



^21 - 1 + Sq{2.Q) = 6 -t- £i + 5q(2.0). (8) 



When an end path through a terminal return loss is added to the 

 intermediate paths, tests have shown that the singing point of the 

 resultant will in each case be approximately as if the currents of the 

 singing points of the intermediate paths and the end path added 

 directly. A group of such measurements is shown in Appendix III. 

 The singing point of the resultant will therefore have a distribution of 



^ It is interesting to note here that in an article in Electrical Communication for 

 July, 1934, entitled "The Prediction of Probable Singing Points on Loaded Cable 

 Circuits," the law is given as effectively Si — 2.5 -|- SQ{\.lh). The difference be- 

 tween these equations is generally within the limits of experimental error. It may 

 be a real difference, however, since there are certain differences in adjustments of 

 building-out condensers which might be expected to affect the standard deviation. 



