SMOOTH LINES AND SIMULATING NETWORKS 25 



network in Fig. lid has much higher simulative precision than that 

 in Fig. 6c. These considerations suggest the possibility of attaining 

 still higher precision by connecting in parallel several such networks, 

 having constants R x \ C/; R x " t G"; R x "' , 6Y", .... 



Fig. 12 represents the two limiting forms of the network in Fig. 11, 

 corresponding to the limiting values and 1 of the parameter D 

 occurring in the design-equations (32), . . . (37). For D = the 

 limiting form is that represented in Fig. 12a, and this will be recognized 



(a) »-^wwwv 



D=0 R t c 4 =c 2 =c i 



CfOrCj 



i D hANVW 



D=l R 



ft 



'6 



I WVVVVVVVVWAM 



r\_.4 ' 'VWWWWVW Irp- 1 



Fig. 12 — The Two Limiting Forms of the Networks in Fig. 11, Corresponding to 

 the Limits and 1 of the Parameter D. Networks (b) and (c) are Potentially 



Equivalent 



as the simple 2-element network already shown in Fig. 6c; while for 

 D — 1 the limiting forms are the two potentially equivalent 3-element 

 networks represented in Figs. 12b and 12c, and are thus of the same 

 forms as two mentioned below, under the heading Modifications for 

 Very Low Frequencies, as being capable of furnishing approximate 

 simulation extending down to zero frequency. The values of the 

 elements of the network in Fig. 12c in terms of the elements of the 

 network in Fig. 12b, for equivalence of these two networks as regards 

 impedance, are 



R 6 =R 1 -\-R i =SR 1 , (41) 



Ri = R 1 (l+R i /R 3 )=3R l /2, (42) 



^ _ C* _ 4Cg / .ry. 



^~{1+R,/R,Y ~ 9 • { 6) 



Thus the network in Fig. 12c requires only four-ninths as much 

 capacity as the network in Fig. 12b. 



