86 BELL SYSTEM JECUSICAL JOURNAL 



losses) the arms of its equivalent T network arc composed simply 

 of positi\'e or negative inductances. Of the three inductances in- 

 volved, at least two of them must he positive while the third may be 

 either positive or negative. 



From Fig. 25, it is evident thai two windings or coils, together 

 with their mutual impedance, may be represented by an ecjuivalent 

 network which aftords a transfer of energy from one winding to the 

 other. This ecjuivalent network may, with limitations, contain 

 positive or negative inductances. 



While the two-winding transformer of Fig. 23 has been represented 

 by an equivalent 7" network in Fig. 2ti, the e(|uivalent network may 

 alternatively be (jf v form (Fig. 27) instead of T form, thnuigli the 



Z Z -Z ' 





2^2,-Zj^ <JZ.Z,-Z. 



Zz+Zm i i 2,+Z, 



2 O- 



Fig. 27 — It Network of Stlf Impedances Equivalent to the Structure of Kig. 23 



general relationships for T' or ir networks previously stated. When 

 no dissipation exists in the transformer, either eciuivalent network 

 will have at least two positive inductances while the third inductance 

 may be either positive or negative. 



From the principles previously outlined in Part I, for the ec[uivalence 

 of certain electrical meshes and for their substitution for one another 

 in any circuit, it is ol)vious that when two coils, with mutual im- 

 pcfiance between them, exist in a circuit, in the manner shown in 

 Fig. 23, either of the meshes shown in Fig. 20 or 27 may be substituted 

 for them or vice versa. The representation of the mutual impedance, 

 Zii, i)y an e(iuivalent network (l"ig. 25) makes it possible to represent 

 the transformer of I'ig. 23 by a T or jt network containing only self 

 impitlances. This afTords a great simplification in the analysis of 

 filter circuits containing pairs of coils having mutual impedance 

 between them in that it permits such circuits to be reduced to an 

 equivalent series-shunt (or lattice or bridged-?') type structure. 

 Consequently, the methods of design which have been built up for 

 the series-shunt and kindred tyi)e structures may be directly applied 

 to the solution of circuits com. lining such p.tirs of coils. 



