54 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



WXHI 



■y J 



(a) TRANSMISSION LINE MAGNETiC CIRCUIT 



T 



pAy 



hAy 



2 



vAAy 



2 





hAy 



H|lh- 



Fig. 20 



(b) DIFFERENTIAL LINE ELEMENT 

 Transmission line analogy to the field of an electromagnet. 



potential, in flux density, and (at high densities) in reluctance per unit 

 length. To treat it as a single circuit element, as in the discussion of Fig. 

 3, is thus a highly simplified approximation. An understanding of the 

 extent to which this approximation is valid may be gained by considering 

 a more rigorous analysis, in which, as indicated in Fig. 20, the core and 

 return path are treated as analogous to a transmission line with dis- 

 tributed constants. 



Transmission Line Analogy 



In Fig. 20(a), the core is shown as one side of the line, and the return 

 path as the other side. The length of the line is taken as the length of 

 the winding, which is assumed to be distributed uniformly. It is assumed 

 that the line is terminated at its ends by lumped reluctances, (Ri and (Ro . 

 The characteristics of the line and the applied magnetomotive force are 

 expressed in terms of the following quantities: 



/ = mmf difference between the two sides of the line, 



^ = reluctance per unit length of line, 



p = leakage permeance per unit length of line, 



h = impressed mmf per unit length of line. 



Instead of trying to represent the entire magnetic circuit by a simple 

 network of a few lumped reluctances, it is assumed only that an infinitesi- 

 mal length (dy) of the magnetic line can be represented by the "7"' 



