Mvnwi. i.\i>( i i.i.w I i.\ ii.nT. vii.rr.Rs w 



tiiic. 111(1 thcftri</i;«/-7" t>pcstrui-ture. Typiciil series-shunt, liridned-?", 

 and lattice type structures are illustrated in I'Ir. '21A, B and C", 

 res(H>ctively. Tiie three circuits shown are electrically eciuivalent, 

 except for balance helwei-n the series arms, if the following relations 

 hold: 



Z..i = (l+/^.)/.. /.H = {l + -2K)Z,, Zc=Z,, (71) 



Z.' = Z,. Z,' = (i+A-)Z, + Z:. (72) 



In the previous discussion of ecjuivaleiit networks no reference has 

 been made to networks containing mutual inductance, many of w'hich 

 are of particular interest and importance. These will lie now discussed 

 in detail. 



I'.XKr II 



W.WE Filters Using Mutual Inductanxe 



Before considering the cc|uivalent meshes which may be formed by 

 the use of mutual inductance between pairs of coils, and the types of 

 wave filters which may be obtained by the use of these equi\alent 

 meshes, it will be necessary to define certain general terms. 



The self impedance between any two terminals of an electrical net- 

 work is the vector ratio of an applied e.m.f. to the resultant current 

 entering the network when all other accessible terminals arc free from 

 external connections. 



The mutual impedance of any network, having one pair of input 

 terminals and one pair of output terminals, is the vector ratio of the 

 e.m.f. produced at the output terminals of the network, on open cir- 

 cuit, to the current flowing into the network at the input terminals. 

 Since mutual impedance is a vector ratio, it may have either of two 

 signs, depending on the assumed directions of the input current and 

 the output voltage. The sign of the mutual impedance is, in general, 

 identified by its effect in increasing or decreasing the vector impedance 

 of the meshes in which it exists. It is usually convenient, in this 

 case, to consider either a simple series or a simple parallel mesh of 

 two self impedances between which the mutual impedance acts. For 

 the purpose of determining the sign of the mutual impedance, we shall 

 confine our discussion to a sinifile series combination. Consequently, 

 the mutual impedance will be calletl either series aiding or series 

 opposing. 



When a mutual impedance, Z,\t, acts between two self impedances 

 Zi and Z2, (Fig. 22) connected in scries in such a way as to increase 

 veclorially the impedance of the combination, it is called a series aiding 



