DISTORTION CORRECTION 455 



positive elements. The following statements can be made, however: 



1. The transformation of the ladder type to the equivalent bridged-T (/) 

 type, and vice versa, is always possible. 



2. The transformation of the ladder type, or the bridged-T (7) type, to 

 the equivalent lattice type is always physically possible; the converse is 

 not necessarily so. 



Those structures which are potentially phase networks, and thus 

 useful when requiring a non-attenuating network with a phase char- 

 acteristic only, are the lattice type again and the bridged-T (II) type. 

 Such networks are used to introduce various characteristics for the 

 time-of-phase-transmission. It will be sufficient to give the relations 

 for equivalence between these two types, obtained from (13) and (15), 

 as 



(Zll)lattlce = 1-^ 1 I ' (17) 



\2ll 4z2i/c/ bridged-T (II) 



which is ahvays physically possible if the bridged-T {II) network exists. 

 On the other hand 



(Zu) bridged-T (II) = 7(221 ± Vz2r — ci?-),attice ' (18) 



where the c which belongs to the bridged-T (II) type must necessarily 

 be taken so as to make the radical a perfect square, if a physical 

 equivalent is possible. It is to be pointed out that in the propagation 

 constant formula (15), considered as a general form, the range of 

 values for the parameter c which will give a physical bridged-T (II) 

 network is c ^ 1, usually, while the range for a physical lattice net- 

 work is c ^ 0, as seen from (17). Thus, the lattice type can give a 

 greater variety of propagation constants. 



From all the comparisons made above this conclusion may be drawn. 

 The lattice type has a greater range for its propagation constant char- 

 acteristic than has either a ladder or a bridged-T type. Hence, the lattice 

 type might well be considered as the fundamental one, when designing such 

 networks, from which other equivalent types may be obtained by transforma- 

 tions, if such physical structures are possible. 



2.6. Propagation Constants Expressed as Frequency Functions 

 In Section 2.4 the propagation constant of any of these networks 

 was given as varying with frequency only implicitly, according to 

 some function of the impedance ratio, Zu/IR. To express it more 

 explicitly as a frequency function, I shall sketch briefly a satisfactory 

 general method to be followed. 

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