226 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



(iii) Let the 6-th branch begin at node nt and end at rib . Let Vb = 

 Enf, — E„l . Then for each b, one of 



Vb = Rbh, Rb > (a) 



h = Cb~, Cb>0 (b) 



at 



Vb = ^ Lbb' -TT (c) 



6' at 



holds, where the matrix Lb,b', is real, symmetric, and semi-defi- 

 nite. 



Cauer has shown how an ideal transformer can be defined as the 

 limiting case of a finite passive network. It is indeed no more nor less 

 ideal than an open circuit {Rb = °o or Cb = 0) or a short circuit (Rb = 

 or Cb = 00 ). 



4.02 We seldom deal with networks in the detail which is implicit in 

 (iii) above. We are usually interested in the external characteristics, so 

 to speak, of such networks as viewed from a relatively small number of 

 terminals (nodes). These multi-terminal devices, however, we continue 

 to incorporate into larger network diagrams. It is usually clear how 

 Kirchoff's laws are to be applied in these cases, and what the differential 

 equations of the resulting system are. We are obliged, however, to make 

 these matters precise before we can deal intelligently with the most 

 general physical properties of networks. 



4.1 We have seen the two kinds of constaint that a multi-terminal de- 

 vice imposes on the branch currents and node voltages in a network in 

 which it is incorporated: the topological ones contained in Kirchoff's 

 laws and the dynamical ones described by differential equations. Cor- 

 respondingly, there are two aspects to the concept of general 2n-pole. 



4.11* In its relation to Kirchoff's laws, a general 2n-pole is indicated as 

 an object with n pairs of terminals {Tr , Tr), 1 < r < n. Each terminal 

 can be made a node in an arbitrary finite diagram constructed out of 

 network elements and other general 2m-poles, with arbitrary values of 

 m. This diagram is not an oriented linear graph, so we have no basis 

 for the use of Kirchoff's laws. From it, however, we construct an ori- 

 ented linear graph, called the ideal graph of the diagram, by the follow- 

 ing rule: 



The nodes of the ideal graph are those of the original diagram. Every 



* Technical paragraph as explained in Section 2.91. 



