572 nill.I. SYSTEM TP.CIIXIC.U. JOrRXAL 



In a large number of lines, F is the fraction of ilic whole group 

 which will ha\e a return current in excess of Ir- 



From the definition of the transmission unit liu- riiurn loss of the 

 line expressed in TU, is given by the expression 



5 = 20 log.o p = -20 log.o'p (35) 



from which 



7^=72,10-10. (36) 



Substituting in (34) 



7=- = e-2r3'" 

 Taking logarithms lo the base e and uansjMtsing 



(37) 



'I'aking logarillims to the liase 10 



5 27'= 



10-io = --^log,F. (38) 



5= 10 log. 1^27'= log.)]- (=^9) 



Sul)siituiing the \alue of 1'-^, from ctiualion (30) for I' 



5=10 1og..pi?rX,JJ (40) 



and tile wihic of Ri, from cfiuation (2o) 



5=101og,o ^Z^"«'^^^^~"'^'^^,^g^l . (41) 



By a similar process of reasoning it is e\ident that if the line contains 

 capacity de\iations only, the return loss is gi\'en by this same ex- 

 pression with lie sulistilulcd for ///. and if both types of irregularity 

 occur the rcprcscnlal i\c dc\iali(in is 



H=VHi+iri 



when He includes the effect of spacing irregularities as well as capacity 

 deviations in the cable. The foregoing exjiression can, for con- 

 \cnic-ii(f, be put in lln> form 



S = Sn + Su, + SF-SA (42) 



