SINGING ON TWO-WIRE CABLE CIRCUITS 623 



Where all values of Ak are the same, and equal to A, 



/I — Aim\ 



Sa = 10 logic ( \ _^, j (28) 



FiN, T) = 10 logic ( L^' k-'' ) • (29) 



Where all values of " 4 " are the same and equal to " /," 



F{N, T) ^ 10 logic ( \~^~_T ) • (30) 



This is the case where all the gains are equal and all the losses are 

 equal at all points. 



In the case where ^ = 1, i.e., 7" = db, 



F{N,0) = lOiologA^. (31) 



APPENDIX II 



Distribution of Two Active Return Losses in Series 



Assume two return losses in series, the two being selected at random 

 from groups of return losses (active or passive) having distributions 

 represented by ^n + Sf and vSi2 + Sf, respectively. What is the 

 distribution curve of the two in series? 



Let 



Pi = ^,e-^^'''''^\ (32) 



^2=^,g--^/2^^\ (33) 



where p\ is the relative probability of obtaining a returned current ii 

 from the first line (^u + Sf) and ki corresponds to I\ in Appendix L 

 The quantities with subscript 2 are the same for the second line 

 (5i2 + Sf). Now if iiii = H, the probability that iz exceeds a certain 

 value / is 



P{U > I) = r r pidnp2dH. (34) 



Substituting from Equations (32) and (33) and letting 



^2- / 



X = TTT-T, , a = 



e-unav.))dx, (36) 







P{U > I) = 2aK,{2a), (37) 



