DISTORTION CORRECTION 465 



(39) 



5e = 5 + 5' = 0, 



then the complementary network is given by 



zi/ = i?i + -f-^-r- . (40) 



_ -I 



where Rx = 2 coth {Acl2)R, 



22 = 4 cosech2 (Ac/2)Ryzs, 

 and i?3 = 4 cosech^ {Aj2)Ry{Rs - 2 coth (^<./2)i?). 



Here 22 is the inverse network of Zs of impedance product 4co- 

 sech- {Ac/2)R^. The network in (40) is Ri in series with the parallel 

 combination of 22 and Rs. An equivalent form for Zn' is 



21/ = 7-^ T' (41) 



-R/ + 22' Rs' 



where i?/ = cosh^ {AJ2){Rs - 2 tanh (Ac/2)R), 



22' = cosh2 {Aj2){Rs - 2 tanh {AJ2)Ryizs, 



. „ , _ 2i?(coth04j2)i?, - 2i?) 

 ^""^ ^^ " (i?. - 2 coth (^e/2)i?) ' 



It will be a physical network provided Ac satisfies the relation 



1 < coth {Acl2) ^ RJ2R. (42) 



At the minimum Ac, Ri = Ri, zo = 22', and Rz = R3' = 30. 



If, on the other hand, the given section has parallel impedances 

 (similar to the preceding network of (38) whose output terminals are 

 reversed), 



211 = r- , (43) 



— + — 

 Rp Zp 



where Rp is a resistance and Zp is any impedance, any equivalent 

 transformation of which does not contain parallel resistance, then a 

 corresponding complementary network has one form given by 



2n'=-j ^ . (44) 



1 



Ri 22 + R3 



