DISCONTINUITIES 423 



wave just to the left of the lossy section. Then, by equating velocities and 

 convection currents at the start of the lossy section, we obtain 



Fi/5x = Vi/8r + Vn^Sjj (9.24) 



and, from (9.21) and (9.22) 



Vr'8, = (-j/k)(Vr- Vn) (9.25) 



Similarlv 



So that 



Vi/8l = Vi/b)j+ Vnb]i 

 V,/8\ = -{\^}^{Vj+ Vr 



(9.26) 



(9.32) 



Vi = j{VJ2){k/b,){jk/h + 1) (9.27) 



Vu = j{Vy/2){k/b,){jk/h - 1) (9.28) 



At the output of the lossy section we have the voltages Vi and Vu 



V'jj = Vne-^'^'^e-'''"'''' (9.30) 



Thus, at the end of the lossy section we have 



V = Vr+ V'u (9.31) 



(;-«oC/77)z; = V'jlh + V'nihn 



(jUoC/v)v= (-j/k){Vr- V'n) 

 and similarly 



{-2V£Vlo)i = {-\/h?){y'j + v'n) (9.33) 



From (9.27) and (9.28) we see that 

 y'j -f v'u = -{k/b^\+{k:b^ cos lirkCX + sin 27ry^C.Y] Fif-^^x.v (934) 



V'j - v'u = j{k bi)\-{k bi) sin lirkCX + cos 2x;feCY]^i<^" '-'•'' (9.35) 



Whence 



V = -(k/bi)[+{k/bi) coslirkCX + smlTkCNWie-''^'^'' (9.36) 



(jmC/v)v = (l'bi)[-{k,bi) sin IwkCX + COS 27rK'-V]lV-^-'-'' (9.37) 



(-2FoC7/o)i = (l/5i)[(l/5i) cos IirkCX + (1 k) sin 2TrkCX]Vie~ ''"''■''' (9.38) 



These can be used in connection with (9.4) in obtaining \\ , the value of 

 Vi just beyond the lossy section; that is, the amplitude of the component of 

 increasing wave just beyond the lossy section. 



