88 BF.LL SiSTEM TECIIMC.IL JOlKX.iL 



l"ig. 17H, u> (letiTiniiR- ilif fonsi.mis of ilic iiii'sh sliowii in Fig. 28D 

 fruiii the known \alufs of the constants of the structure of Fig. 28C. 

 The relations which must exist if the structure of Fig. 28D is to be 

 equivalent to the structure shown in Fig. 28A, or vice versa, are given 

 by the following relations 



Li'iLi'Li'-M-) 



t\ = C,',Lt 



(L2'±M)- 

 U±M\- 



.=z./. c-,=cv(^=;;^^) 



(75) 

 (76) 



rile upper and lower of the altiTnati\e signs, in the preceding equa- 

 tions, correspond respecti\ely to series aiding and opposing connec- 

 tions. The e(|ui\ alence of these four-elenieni meshes makes it possible 



L",L',-M' 



(A) (B) (C) 



Fig. 29 — E(|uivalfnt Thrcc-TtTiiiiTi.il Iinlint.iiKL- Networks 



L, 



L'. 



" C. 



LrrHH 



Kig. 30— Kqiiiv.ili-nt Two- Terminal Reactance Networks 

 (onlains Mutual Inductance 



Onh' One of Which 



to derive at once, the relalion> which must exist between certain 

 (f|uivalent three-element meshes involving mutual inductance. For 

 e.x.imple, if the capacity Cj' of Fig. 28A is zero, tiu- nush reduces to 

 the three-element nush of Fig. liOA and the fornnilae given above 

 are then ap|)lical)Ie for the e(|uivalence of the structures of Figs. 

 30A and B. 



In the s;imc way that the me&hes illustrated in Fig. 28 were shown 

 to Ik; iMJtentially e<|uivalent to each other, it is |)ossible to i)rove that 



