IRREGULARITIES IN WIRE TRANSMISSION CIRCUITS 551 



Then, replacing e and neglecting higher-order terms in 4> and e, 

 which are small, and putting li^ — 8^/4:, equations (7) and (8) become 



<i252 



E,r' = E,i' = ^ • (9) 



loe 



The echo Eb affects the measured impedance. If unit voltage is 

 impressed in series with the line, and a network having impedance K, 

 the current flowing, not counting the echoes, is IjlK. The echo cur- 

 rent is then (Ebll)('i.l2K), and the total current 



1 +_£i 

 2K 



The measured impedance is 



2K 



(10) 



(11) 



1 -\-Eb 

 and the part due to the line is 



Kl = 7-tV - K = K(1 - 2Eb) approximately, (12) 



1 + -C-6 



Kl-K^- 2EbK, (13) 



{KLr -Kr) = - 2EbrK, (14) 



{KLi -Ki)^- 2EbiK. (15) 



For K, the real part only is to be used as it is assumed that the 

 imaginary part is negligible in comparison with it. Where departures 

 from K are considered, however, this imaginary part may not be negli- 

 gible in comparison with the departures. 



(16) 

 (17) 

 (18) 



