584 BELL SYSTEM TECHNICAL JOURNAL 



The subscripts, as before, merely refer to the terminations. The G 

 and H expressions which correspond to the reflection coefficient with 

 each of the four particular types of terminations, 1, 2, 3, and 4, follow. 

 Reflection Coefficients, rmi and Vmi, with Mid-M-type Terminations. 

 For termination 1 arbitrarily assumed at b we have Wi, = K2i{m) 

 and Zr — R. Introducing for this case the subscript ms, signifying 

 il/-type and mid-shunt, it follows by (6) and (32) that 



_ K2,{m)-R 



and its equivalent 



_c _,H ^ _ \ + {\-m-){Uk + iVk)-{±Vl+Uk+iVk) ,,.. 



With termination 2, Wb=Ki2{m) and Zb = R, so that by (32) the 

 corresponding coefficient r^i becomes 



(42) 

 Since— 1 = 

 and (43) 



//ml=//m2 + T. 



Reflection Coefficients, r^o and rx\, with x-"constant k" Terminations. 

 In the case of the x--shunt termination 3, Kxi, relations (36) give 



_ K^-z^kR/{z^+{x-.S)R) 



''" K,k+z,kR/{z2k + {x-.5)Ry ^ 



Introducing (35) this is 



"■ \±{2x-\)y/u^+iVk±y/\+Uk+iVk 



The .T-series termination 4, Kx\, has a coefficient r^i detcMinined 

 by (37) which is related to rxi through (35) as 



rx,= -rx2. (45) 



It follows from the corresponding exponential expressions that 



and (46) 



//xi=7/i2 + ir. 



I 



V 



