GO 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1934 



Equivalent Magnetic Circuit 



Over the low density region, in which the magnetic circuit rehictances 

 are substantially nidependent of the flux, the expressions for the reluc- 

 tance can be simplified by a procedure analogous to that used in deri\ing 

 electrical network equivalents. Provided the gap reluctance varies 

 linearly with the gap, magnetic circuits such as those of Figs. 3 and 21 

 can be replaced by an equivalent circuit of the simple form shown in 



Fig. 23 — Equivalent magnetic circuit. 

 Fig. 23. For this simple parallel circuit, the total reluctance is given by: 



(R = 



(Rl (Ro + 



A 



(24) 



(iio + (Rl + 



A 



The simpler subscripts of these equivalent values of the magnetic 

 circuit constants are used to distinguish them from the design values, 

 applying to the magnetic circuit taken as representing the actual struc- 

 ture. In the usual case the design values apply to the two mesh circuit 

 of Fig. 21, for which the additional subscript 2 is used. When a three mesh 

 circuit is required to represent the structure, the design ^'aIues are dis- 

 tinguished by the subscript 3, as in the constants of Fig. 3. 



In the usual case in which the design values apply to the circuit of 

 Fig. 21, expressions for the equivalent values may be obtained by com- 

 parison of the reluctance given bj' (23) with that given by (24). The for- 

 mer equation may be written in the form. 



(^ = (^c + (R/.2 — 

 while (24) may be written. 

 (R = (Rz. 



A2(R/ 



A2(R02 + ^2(Rl2 + X ' 



ASil 



.4(Ro -\- A(S\l + X 



