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BELL SYSTEM TECHNICAL JOURNAL 



2.5. Relations for Equivalence of Propagation Constants 

 All of the above networks have equivalent iterative impedances 

 equal to R. It is sometimes useful to be able to transform readily 

 from one type to another which has also an equivalent propagation 

 constant, if that is physically possible. This may arise in an economic 

 study of a final network design where account is taken of all practical 

 factors, such as symmetry, line balance, number of the elements, 

 their magnitudes, etc. 



The structures which are important in this connection when dealing 

 with both attenuation and phase characteristics comprise the ladder, 

 lattice, and bridged-T (I) networks, whose propagation constant 

 formulae are given in (12), (13), and (14). For their propagation 

 constants to be identical the impedance Zn in one type must bear a 

 definite relation to that in another. In the following table, derived 

 by equating these formulae, a general impedance z is introduced. Each 

 2ii may be expressed in terms of z and R. Here z is taken as the Zn 

 for each type in succession. It then becomes a simple matter to 

 transform from one type of structure to another having an equivalent 

 propagation constant. The parameter c in a derived bridged-T (I) 

 network would be taken such as to give the minimum number of 



elements. 



TABLE II 



Relations for Equivalence 



A transformation from the Zn of one type section to that of another 

 equivalent one involves essentially only an alteration of the given 

 impedance by a positive or negative resistance element in parallel 

 with it. This will not always result in a physical network with 



