SMOOTH LINES AND SIMULATING NETWORKS 2,7 



Instead of/ as the independent variable it may be more convenient 

 to employ some quantity proportional to / (for instance, F or E) ; 

 likewise, instead of P, P , Q, M, N, some quantities proportional to 

 them (for instance, their ratios to k). 



Appendix D 



Relative Values of the Elements in the Four Precise Types 

 of Complete Networks (Fig. 11) 



The following three sets of formulas express the values of the ele- 

 ments constituting the networks in Figs, lib, lie, lid, respectively, in 

 terms of the elements constituting the network in Fig. 11a when those 

 four networks have equal impedances. These formulas involve 

 the two ratios £ and f pertaining to the network in Fig. 11a and de- 

 fined by the equations 



Z = C 3 /C 2 , t=Ri/R s . 

 For Fig. lib, 



R, ( £ \ 2 C 4 1+4 C 5 1+4 



r 3 vi+4/ c 3 4 - c 3 e 



For Fig. lie, 



*■_,., / 4 \ 2 C 6= l + £ 



R* f ^U + 4/ ' C z 4 ' 



i? 3 s ' V 5 4 / ' C 3 



For Fig. lid, 



i? 3 U+t) -2(1 + 4)' 



#9^ 2fr 



i? 3 2(1 + 4) -(h-t)' 



C 8 ^ 24-r(l + 4)U-r) 



Cz mr 



C 9 ^ f(l + 4)(ry+r)-24 

 C 3 2£fr 



t 



where ^ = 1 + 4+-, r= ' /i + e + A^ _4i. 



