452 BELL SYSTEM TECHNICAL JOURNAL 



where c = \, usually. In the very special cases of networks Ila and 

 life, wherein Zu is an inductance, c may be less than unity and approach 

 zero as a limit. For the latter values the negative inductance may 

 be obtained physically as a negative mutual between the series coils. 

 When c = 1, networks Ila and lib become physically identical, as do 

 also networks lie and 11^. If Zn is a reactance, there will he no attenua- 

 tion. Again, we shall find by applying the proper rule directly that 

 when the four general sections are closed by resistances R there will 

 result two pairs of inverse networks of impedance product R-, respec- 

 tively Ila, lid and life, lie. 



R 



O •t;^ o-'\y\yV^-o —^ O 



Fig. 7 — Unbalanced lattice type constant resistance section. 



A Special network of the unbalanced lattice type may be mentioned 

 briefly. This symmetrical structure as shown in Fig. 7 plays no 

 direct part here as a distortion correcting network but is closely related 

 to some of the other types and possesses interesting properties, among 

 others that of conjugacy as in an ordinary balanced Wheatstone bridge. 

 Its open-circuit impedance X and short-circuit impedance Y are both 

 equal to R, hence its iterative impedance, -^XY, is also R. Since 

 tanh r = -ylY/X = 1, r = oo, which means that no current would 

 flow in a terminating resistance R due to an e.m.f. applied through a 

 sending resistance R, these two impedance branches being conjugate. 

 The network containing four resistances R, which is obtained by 

 terminating this section at each end by a resistance R, may likewise be 

 derived directly from the limiting case (c = 1) of the bridged-T (I) 

 section which has similarly been terminated, merely by a rearrange- 

 ment of form. It has these properties: 



1. Opposite resistances are in conjugate branches. 



2. Each of the four resistances is faced by a resistance R. 



These properties can be seen as a result of the symmetry and also from 

 a comparison with the full-series and full-shunt ladder type sections 

 when terminated by resistances R. It is known that for one direction 



