90 



BELL SYSTEM lECIIMC.lL JOiRXAL 



The c(|uivalciKe of these foiir-lerminal meshes makes it possible 

 to derive the relations which must exist for corresponding ecjuivalent 

 three-element mesiies, with and without mutual inductance. For 

 example, if in I'ig. 31A, the capacity Ci is of infinite value, the mesh 

 reduces to that shown in Kig. 32A and the formulae given above are 

 applicable for the e(iui\alence of the meshes of Figs. 32A and B. 



The remaining meshes of Figs. 17C and U have similar potential 

 equivalence to meshes of the same fundamental type but ha\ing mutual 

 inductance between the respective pairs of coils. 



Three-Terminal Equivalent Meshes. Three terminal meshes con- 

 taining mutual inductance will now be discussed. It has been shown 



l'. 



(B) 



Kig. 32 — Kquivaleiit Two-Terminal Reactance Networks, Only One of Which 

 Contains Mutual Inductance 



that two coils, with nintii.ii inductance between them (I'ig. 2nA), are 

 ecjuivalent to certain 7' and tt structures containing only tangible 

 inductances (Figs. 2'.(B and C). Referring to Fig. 2'.)B, it is seen that 

 two coils, with series opposing mutual inductance between them 

 (corresponding to the upper alternative signs in Fig. 29B), are etjuiva- 

 lent to a 7" network ha\ing three positive inductance arms, provided 

 the mutual inductance .1/ is less than Li' and L;'. The values of 

 these arms are respecti\ely, Li' — M, Lt' — M, and M. If .1/ is larger 

 than Li', one arm of the ec|ui\alent T network is a negative inductance 

 while the other two arms are positive inductances. Similarly, if M 

 is larger than L/, a different arm of the T network will be a negative 

 inductance while the two remaining arms will be positive inductances. 

 It is [)hysically impossible for the \alue of ^1/ to be greater than both 

 Li' and Li'. Hence, it is impossible for more than one arm of the 7" 

 network, shown in Fig. 2*>tB, to be a negati\e inductance. 



When two coils ha\e series aiding mutual inductance between them 

 (the lower of the alternative signs in Fig. 2'.tB) they are equivalent 

 to a 7" network in which two of the arms consist of positi\e inductances 

 viz., Li'+M and 1.2+ M, while the third arm consists of a negative 

 inductance of the value — Af. 



