350 BELL SYSTEM TECHNICAL JOURNAL 



Interaction Crosstalk with One Tertiary Short- Circuited 

 Far-End 



For the sake of simplicity, and with no considerable loss of applica- 

 bility, we will postulate the restriction that e"^^^ and e'>'»' are large 

 compared with e'^\ where / is the length of the section in which we are 

 formulating the tertiary currents. 



Referring to equations (31) to (34), under the above restrictions the 

 terms involving e~'^^^ and e'~''^'^ are negligible in the region near x = I 

 and thus in this region 



Ii = - SigTi^ - 77262^^^^ + L(pi - gi) + V2(p2 - g2)>-T^ (36) 



l2= - vibie^''' - bicy^- + IviiPi - gi) + (p2 - g2)>-^^ (37) 



+ \iKr(p, + qi) - viK2(p2 + q2)le-y\ (38) 



V2 = - mKihiCy^ + Kibicy^'' 



+ [ - -n^KiiPy + gi) 4- K^ip^ + g2)>-T^ (39) 

 where ^ 



Pi = -;^^T^ ^( ^ ' (40) 



2Ai(1 — ■»?ii72)(7i - 7) 



7 



^' ^ 2Ki{l - vm){yi + t) ' ^^^^ 



^' ^ 2X2(1 - :7i'72)(72 - 7) ' ^^^^ 



^' 2X2(1 -^l'?2)(72 + 7)" ^ ^ 



If, now, X is measured from the far end, and the following substitu- 

 tions are made as a matter of convenience: ^ 



ai = 6ie(Ti+^)', (44) 



a2 = b2e^y^+y^', (45) 



equations (36) to (39), multiplied by e"*^' so that the currents and 

 voltages are given for unit received current in the energized coaxial, 

 become 



Ji = - flie-Ti^ - 772026-^^^ + [(^1 - gi) + 772(^2 - g2)>^^ (46) 



I2 = - rjiaie-Ti- - aoe-y^^ + ImiPi - gi) + (P2 - g2)>^^ (47) 



^ The terms involving e~y^ here are identical with the corresponding terms in 

 equations (31) to (34) except for the change in nomenclature, which in each case has 

 been chosen so that the a's and b's will be given by simple functions of the parameters 

 employed (^'s and q's here: i^-'s in the previous equations). 



3 a\ and 02 here have no relation to Oi and ai in equations (31) to (34). 



