530 BELL SYSTEM TECHNICAL JOURNAL 



where 



Ri = 



h = 



1 - 2X2ti ' 

 XV2 



1 - 12X^2 

 and ' 



2w /„(?") 



1 - 



z /„_i(z) 

 The relations 



Joi'z) — ber .r + i bei jc 

 and 



1 

 /i(s) = ■:^^ (ber' X + i bei' .v), 



where 



z — xV— -i 



give the expressions in equations (13) and (14) for t\ and T2. 

 For the asymptotic values we have 



• — I, when .r — » 00 , 



so that 



or 

 and 

 where 

 Also, 



In 



Ti — > 1 — V -\- iv 

 T2 ^ 1 — 2v -\- i2v, 



1 - 2X2 V 1 _ 2x2; ' "(1 - 2X7'^' 



U2 X^ { , 2. \ , . 2X4,/ 



and 



(1 - 2X2)2 V 1 - 2X2/ ' "(1 - 2X2)3' 



; X^ /, 2v \ , ■ 2\'v 



1 - 12X4 V 1 - 12XV (1 - 12X4)2 



Thus equations (15) and (16) readily follow. 



In addition, the high frequency value of the self impedance, Z„ is 

 given by 



vm ov /1 , 4X2 \ , ,. /, V2c 2X2 "2X2^ \ 



Z/°> = 2Z>^l+^-^j+4;..(^log— --^-^^^+-p:,4^,j 



