SMOOTH LINES AND SIMULATING NETWORKS 



27 



original network, as indicated by Fig. 13a, where the altered values of 

 J and R[ are denoted by J' and /?/ respectively. 



R 



(a) « — wwww 



r; 



j' 



S' 



(b) o-p^vvvvwvv — o — j v 



WVWi 



S" 



Fig. 13 — Two Potentially Equivalent Modifications for Extending Range of Simula. 



tion Down to Zero Frequency, (a). Modification by Shunting the Excess-Simulator 



J', (b). Modification by Shunting the Complete Network R\"-\-J" 



Fig. 13b represents an alternative but potentially equivalent form 

 of modification, obtained by shunting the original form of network 

 (Fig. 5c) with a resistance S" '; and the conditions for equivalence are 



S f, = S , -\-Ri\ (44) 



R 1 " = R 1 '0.+R 1 '/S'), (45) 



J" = J'(1+R 1 '/S') 2 . (46) 



Since the shunts S' and S" are potentially equivalent in their effects 

 their simultaneous application would be potentially equivalent to 

 the application of either alone. 



Thus far the suggested modifications have been stated only with 

 reference to the excess-simulator regarded abstractly. When the 

 specific structure of the excess-simulator is regarded, the modifications 

 can take several different forms which, for any one excess-simulator, 

 are equivalent as regards impedance. Certain of these are noted in 

 the following paragraphs: 



Among the modified excess-simulators will evidently be found one 

 having the limiting form already depicted in Fig. 10b. 



Fig. 14 represents by (a) and (b), respectively, the 3-element 

 excess-simulators in Figs. 7a and 7b modified by the shunt resistance 

 S', and thereby converted to 4-element excess-simulators. Figs. 14c 

 and 14d represent two other 4-element excess-simulators that are 

 potentially equivalent to those in Figs. 14a and 14b as regards im- 

 pedance. 



