524 



BELL SYSTEM TECHNICAL JOURNAL 



Network 8 

 fn/4 



Cn = 



aobi — ai ' 

 aobi — ai 



Tr{aoOi — ai) 



i?]4 = 2a qR. 



^irao'R ' 



-lVlliv21 = L12IC22 = Z/2'!/w3 = RuRn 



R^ 



F = e" 



10 



'^ Fo + P2P + FoQ.r 



1 + Q2P + QJ' 



Fo(f= 0) = FM= ^); ^0 = A^. 



Attenuation Linear Equation: 



-P2 + FQ2 -f(Fo - F)Q, = (Fo - F)ip. 



In physical solutions ^ Q2 + 2yJQi = n ^ P2 + IF^^lQi = m. 

 If P2 < FqQ2 {A has a minimum) : 



1. ao = tanh (^o/2); &2 = V(24; 



^' I = Kl - tanh (^o/2))(V^ T V^). 



1'. ao = coth (^0/2); ^2 = V^; 



^' I = i(coth (^0/2) - 1)(V^ =F V^). 



If Pi > F0C2 (-4 has a maximum) : 



2. ao = coth (^0/2); &2 = V^; 



/f = tan 5 = 



^1 } = i(coth Uo/2) - 1)(V^ ± V^). 



2'. The same formulae as in 1'. 



2{a,h, - aM- f + hP) 



(1 - ao') - (ai2 - bi' + 2(1 - cH')b2)P + (1 - ao-)/>2y' 



