EQUIVALENT CIRCUITS OF NETWORKS 



615 



time is taken into account only to a first order of approximation. It is 

 believed that, in general, these admittances should be considered complete 

 by themselves as new admittance elements, and, as already remarked, their 

 values in magnitude and phase may be found in the paper on vacuum tube 

 networks to which repeated reference has been made. 



As a further property of the networks, consider the expressions for the 

 jS's in Tables I, II and III. It is observed that each ^ij of a set of jS's con- 

 tains a common term, suggesting that the networks might be broken up into 

 at least two elementary constituents. The same observation applies to 

 each of the three sets of Z's. In Table I, for example, it is seen that this 

 constant term is represented by y22/D. The network of Fig. 19a can thus 

 be thought of as arising from the superposition of two networks, one of which 

 is determined by the parameters 



(25) 



(26) 



The admittance coefficients given by (25) correspond to the perfectly uni- 

 lateral active network shown in Fig. 22a, while the admittance coefficients 

 in (26) correspond to the ''passive" network in Fig. 22b. The two element- 

 ary constituents thus take the general forms of these networks. It should 

 be noticed that these two network constituents are unrelated to the fact 

 that the total current entering the complete network is the sum of conduction 

 and displacement current. 



Corresponding to the Z's other elementary constituents are obtained, with 

 general forms as shown on Figs. 23a and 23b. 



These elementary constituents are merely reflections of certain mathe- 

 matical identities. For example, the networks in Fig. 22 depend upon the 

 matrix identity 



(27) 



