94 



BELL SYSTEM TECIIXtCAL JOURNAL 



work composeti of three s(.-lf incluctances, it is possible to substitute 

 the one t>[K' of mesh for tlie other in any kind of a circuit williout 

 affecting the currents or voltages external to tlie meshes involved. 

 This substitution is always physically possible provided none of the 

 arms of the equivalent 7" or tt networks is a negative inductance. 



The structures shown in Fig. 35 are illustrative of the power of 

 equivalent networks as tools for the s<jlution of filter structures con- 

 taining mutual inductance. The equivalence of the structure shown 

 in Fig. 3.5B to that of Fig. \l'i.\ is evident from the equivalence of two 

 coils (Fig. 29) with mutual inductance (.l/ij) between them to three 

 inductances, L,\. Lit and Lc without iiiuttial inductance. Likewise, 



r-AAAAArn 



(b) 



Fig. 36— RalaiHfil aii<l I'libalanccd Forms of a Filter Section, ContaininK Mutual 

 Inductance 



the eciuivalencc of the structure shown in F'ig. 35C to that of Fig. 35B 

 is obtainable by successive mesh substitutions. The equivalence of 

 the structures shown in Fig. 3')I) and E to that of Fig. 35C arc also 

 obtainable from eciuivalences previously referred to. If the propaga- 

 tion and impctlance characteristics of either of the structures of 

 F"ig. 35C' or D are known, then the other structures shown in Fig. 35 

 will have the same characteristics. Furthermore, if the values of 

 the constants of any one of these structures arc known, the constants 

 of any of the other structures are readilv obiain.ililc 1)\- means of 

 transformation fornuilae. 



In a large number of wave fdlers, the structures are unbalanced; 

 that is, all of the series imiH-flances are placed in one of the two line 

 wires while the remaining wire is a short circuit. ()rdinaril>-, the 

 object in using such an unbalanced structure is to minimize the num- 

 IxT of elements re(|iiiri'd in the series arms. It should be noted, 

 however, (Fig. 30) that in case an inductance element enters into 



