SINGING ON TWO-WIRE CABLE CIRCUITS 621 



equation and simplifying, 



- 1.62 = X (E - 4.05) + X (E + 1.93), (18) 



p p 



which is satisfied if E = 8.8 db. 



The active balance of the circuit with a 9 db net loss at the critical 

 frequency measured from the " A " end may be computed as follows: 

 The successive paths from the line side of repeater ^' A " are (using 

 values for Sp = 0): 



1. 27.35 



2. 27.35 + 34 - 30 = 31.35 



3. 27.37 + 34 - 30 + 34 - 33.7 = 31.67 



4. 27.25 + 34 - 30 + 34 - 33.7 + 36 - 30.8 = 36.75 



5. 27,25 + 34 - 30 + 34 - 33.7 + 36 - 30.8 + 30 - 27.8 = 38.95 



6. 27.32 4- 34 - 30 + 34 - 33.7 + 36 - 30.8 



+ 30 - 27.8 + 30 - 28.8 = 40.22. 



Combining these paths as the sum of their power ratios gives 24.33 db, 

 which is the computed single-frequency return loss without the end 

 path from the line side of the terminal repeater for Sp = (i.e., which 

 will be exceeded in 63 per cent of the cases). The active singing point 

 from this point will be 24.33 - 2.5 + Sq(2) = 21.83 + Sq(2). The 

 corresponding active singing point referred to the drop side of the 

 repeater will be 21.83 - 14.4 + Sq(2) = 7 A3 + 5^(2) db. With a 

 fixed termination giving a return loss of 5 db at the circuit terminal, 

 the end path from the drop side of the repeater will be 18 + 5 = 23 db. 

 From Appendix V, for c^ = 23 — 7.43 = 15.57 db, the expected active 

 singing point including the end path is the distribution curve 7.43 

 + Sg(15.57) under average conditions. For example, by interpolation 

 in the table in Appendix V, two per cent of such circuits will have 

 lower active singing points from the drop than about 7.43 — 5 = 2.43 

 db and from the line side of the repeater than 2.43 + 14.4 = 16.83 

 db, both under average conditions. 



This answer may be computed by reading from the Sq(2.0) at two 

 per cent which gives 52(2.0) == — 4.1 db. At this percentage, there- 

 fore, the active singing point without the end path is 7.43 — 4.1 

 = 3.33 db. Combining this with the fixed and path of 23 db gives 

 3.33 - 0.9 = 2.43 db. 



