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BELL SYSTEM TECHNICAL JOURNAL 



Figs, lie and lid represent two other complete networks that also 

 are potentially equivalent to those in Figs. 11a and lib 12 . 



Appendix D gives the three sets of formulas expressing the values 

 of the elements constituting the networks in Figs, lib, lie, lid re- 



r-H 



(b)<^WWA-Hr- 



Hh 



R, 



(O-tHF 



r7c 7 



(d). 



c^ 



R 8 ,C a 



MA/VWAM — \H 



Fig. 11 — Four Potentially Equivalent 4-Element Complete Networks Possessing 

 High Simulative Precision for Most Applications, Except at Very Low Frequencies 



spectively, in terms of the elements constituting the network in 

 Fig. 11a, when those four networks have equal impedances. 



Although the four complete networks in Fig. 11 are potentially 

 equivalent as regards impedance there is some choice among them from 

 the viewpoint of cost and space occupied. For it is readily seen by 

 mere inspection of the networks at zero frequency that, when they 

 have equal impedances, 



C% + Cz — Cs + C9 — C\ — Ce- 



(39) 



Thus the networks in Figs. 11a and lid have the same total capacity; 

 and this is less than the total capacity of the network in Fig. lib 

 by the amount C 5 , and is less than the total capacity of that in Fig. lie 

 by the amount C7. Similarly by mere inspection of the networks at 

 infinite frequency it is seen that 



G%-\-Gi — G%-\-G§ = Gi, 



(40) 



the G's being the reciprocals of the i?'s and thus being the corre- 

 sponding conductances. 



Before leaving Fig. 11 it may be noted that the network in Fig. lid 

 has the same form as though obtained by connecting in parallel two 

 networks having the same form as Fig. 6c but with elements Ry', CY 

 and R\" , C\" , say. Now it is known that, in most applications, the 



12 In connection with Figs, lib and lie the network shown in U. S. Patent No. 

 1,240,213 of September 18, 1917 may be of some interest. 



