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BELL SYSTEM TECHNICAL JOURNAL 



lines, the entire impedance function is found in the fourth quadrant of the 

 complex plane. When this is so, the generating function is reduced to a 

 resistance in parallel with a condenser. 



Graphical Representation of Functions 



As a first step in utilizing the graphical procedure, it will be advisable to 

 acquire some familiarity with the generating function in its general form 



RLCX2+LX+R 



(B) R 



L 



Z(X) = 



RLX 



(E) 



Cf) 



(G) 



R C L 



r 



A-K)= 



LC X^-fRCX+I 



CH) R^ po^VW-o— I 



o-V\AA-o-<M |-<>-<>'TJ5?r-o--<> 



RgLCX + R2 

 ^^^^"'■^ LCXS+RCX+I 



Fig. 1. — The impedance loci, Z{\), for several networks. 



and some of its special cases. Plots of various cases are given in Figs. 1(a) 

 through 1(h) together with the network configuration and the impedance 

 function thereof. Obviously the summation of the properly selected gen- 

 erating functions corresponds to the addition of the partial fractions de- 

 rived by Brune's method. For an accurate solution these partial fractions 

 when combined should approximate the given Z(X). 



Figure 1 (A) shows the impedance locus of the parallel R, L, C generating 



