MUTUAL INDfCT.IXCr. IX ll.lll- FILTERS <J1 



\\'lii-iu-\i'r, ill ail f(iiii\.ili'iit /' iirlwork, our of llic .inns is a |)ositivc 

 (t>r lU'jjativc) ituliutami.'. a lorrospoiulinn arm of the tt network will 

 also In- a positi%r (or lu-iiativi') iiidurlatuo. C'onsi-ciuently, as in the 

 rase of the e(iiii\alent 7" network, the eciiiivalent ir network shown 

 in Fii;. 21K' nuu- consist of three positive inductances or two posi- 

 tive iiuluctances anil one iiei;ati\e iiKliictaiice, (Ii'peiuliiig upon tlie 

 si^n anil inagniluile of M. 



It is interesting to note that, in I'ig. 2913, point 1) is in reality a con- 

 cealed terminal, i.e., it cannot be regarded as physically accessible. 

 There are, therefore, oiil\- three accessible terniiiials to the e(|iii\a!ent 



(A) (B) 



Fig. ii — Equivalent 7" Networks of Inductance 



7' network. In the w network shown in Fig. 29C there is no such 

 concealed point. There are, however, as in the preceding case, three 

 accessible terminals A, B and C. 



When the mutual inductance, M, is equal to either one of the self 

 iniluctanccs, Li' (or L;')i and the windings are connected in series 

 opposing, the equivalent Tand ir networks of the transformer coalesce 

 to the same L type network. For example, if Li' = M in Fig. 29A 

 both the T and the ir networks of Figs. 29B and C resolve into an L 

 network whose vertical arm has the value M and whose horizontal 

 arm is Lz' — M. 



A problem of practical importance is the ec|uivalence of T and tt 

 meshes, containing three coils with mutual inductance betw'een all 

 of the elements, to similar 7" and jt meshes containing no mutual 

 inductance. The T networks of Fig. 33 are potentially eciuivalent. 

 The formulae governing their equivalence are 



L4=L, + il/,2-|-.U,3-.l/=3, (80) 



LB=L2+il/.s-.V,3 + il/23. (81) 



Z,C=Z.3-M,2-|-3/.3 + ^l/23. (82) 



In the above formulae, the signs correspond to the case of a series 

 aiding mutual inductance between all the pairs of coils. When the 



