364 KENNELLY-NABESHIMA— ESTABLISHING A 



Relations between the transmission-reflection coefficients in the 

 transient state and the position angle at B in the subsequent steady 

 state: Referring to Fig. 3, and to the load of a vector ohms at B 

 connected to a uniform line of surge impedance Sq, we know that 

 in the steady a.-c. state, the position angle 8^ at B is defined by 



tanh 5b = — numeric Z . (39) 



But 



tanh bs = ^ss 1 ^-Sb = ^ ^ ^-Ub numeric Z . (40) 



Hence 

 I — e -^B = — ■ — =:fn=2— n = i .9333 + JO.00496 



= 1-9333 ^ o''8'49" numeric Z, (41) 



-2&r ^ ~ "-^ 



— f,-~^B = ■ =fyi— 1=1— n= 0.9333 + jO.00496 



= 0.93331 Z 0° 18' 16" numeric Z , (42) 



I + t~'^B = — ^^— = 2 — m = n = 0.0667 — jo.00496 



= 0.06689 \ 4° 15' 10" numeric Z, (43) 



^-2Sb = tO__ =1— jfi=n — l = — 0.9333 ~ iO.00496 



Zo + 0- 



= 0.93331 ^ 1 79° 41' 44" numeric Z, (44) 



5b = logh Vtz:^ = logh \-^^ = 0.03451 +71.56814 



= 0.03451 + JO.9983 numeric Z, (45) 



Here m is the voltage transmission 



coefficient at junction BC 

 — (i — m)=m — I is the voltage reflection 



coefficient at junction BC 

 n is the current transmission 



coefficient at junction BC 

 — (i — n)=n — I is the current reflection 



coefficient at junction BC 



