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BELL SYSTEM TECHNICAL JOURNAL 



Similar results can be obtained by using the image impedance 

 parameters of a dissymmetrical filter. For a dissymmetrical filter the 

 most general relationship between the input and output voltages and 

 currents can be written in the form 



ei = e\A — iiB; U = iiC — eiD where AC — BD = 1. (23) 



In terms of these parameters the image transfer constant Q and the 

 image transfer impedances are given by the relationships "^ 



cosh e = 4AC; K, = yj^ ; K, = ^^ • (24) 



The transformation ratio between the two ends of the network is then 



1 = 3=-' (^=) 



in agreement with the results of equation (22). 



Applying these results to equation (20) we find for the most general 

 case 



cosh 6 = cos 



Ki 



ol\ 



7 , w/i 



Zn, tan — 



'Oi 



1 + 



V 



7 . (^h 

 Zo, tan — 



V 



coll 

 tan — 



V 



coll I ^02 . (^h 



tan h -~ tan — 



V Zqi V 



. Zoo , 0)li C0/2 



1 — -7— tan — tan — 



7 . w/i 

 Zn, tan — 



1 + 



Z02 tan 



oih 



(26) 



Two special cases are of interest here: the first when Zoi = Zoj, and 

 the second when h = h. The first case corresponds to the transformer 

 disclosed by P. H. Smith, ^ which can be used to transform over a wide 



^ These relations were first proved for wave transmission networks in a paper of 

 the writer's, B. S. T. J., April 1927. See equations 67 and 68, page 291. They are 

 proved by other methods in "Communication Networks," E. A. Guillemin, p. 139. 



^ See reference 1, p. 431. 



