696 



BELL SYSTEM TECHNICAL JOURNAL 



TABLE II 



No. 



15 



Semi-infinite smooth line (resistance R 

 and capacity Cper unit length). Cause: 

 Voltage applied through capacity Co- 

 Effect: Current at distance x from end. 



= x^RC, n = CliRC^). 



Admittance Y{p) 

 Illustrative System 

 Cause and Effect 



Y{p) = 



Copexpj- yylp) 

 1 + V^ 



Cause: Unit Impulse 

 Effect: 9nY(p) 



Co(y - 2yH/x - 2/ + 4^/") U 

 4fi yirt 



Xexp(-|;) 



— Co/i^exp {yyln + ixt) 



Xerfc(-^+V^Y 0</ 



810 



16 



Y{p) = 



Cop 



1 + Vp//x 

 Same as 15, except x 



- C 



544^ 



. ff^ ,Co(2nt-l) |^l 

 - Co/x'e"' erfc ^7i, < / 



17 



YiP) 



w 



>2"+i[V(/> + X)2 + 7i;2 + (/) + X)]-2" 



je-^'An{wt), 



k^l{p -\-\y -\-'uf' 



Semi-infinite artificial line (series element: 

 resistance R and inductance L; shunt 

 element: conductance G and capacity C; 

 R/L = G/C; mid-series termination). 

 Cause: Applied voltage. Effect: Current 

 in wth section. 

 k = (L/0^ \ = RIL = GIG, w = 2{LC)-K 



< / 



575 



1 



y{p) 



2(2a)» / 



P + 2a 



X (V^+2a+ V/?)-«" 

 ISemi-infinite artificial line (series element 

 resistance R\ shunt element: capacity C; 

 mid-series termination). Cause : Applied 

 voltage. Effect: Current in nth section. 

 a = 2KRC). 



^ e-'-'lIn-riat) - 21 .(at) -f /„+i(a/)], 

 K 



< / 



573 



