NETH'OKKS CONIAIMNG 7110 Ix'li.lCr.l.VCliS ,w; 



It may furilu'rinore be assiimf<l without loss of vti-niTality, since it 

 is nuToK' .1 matter of l.ihellinn the re.irtaiues Z-i and Z^, that Rk^R,- 



Hence, the four critical pniuis of the imped. nice .ire .dw.us in the 

 folldwim; order ; 



R^^Ri<,R,<. Rj. 



(20) 



These circles are shown in Fig. 4. By means of the appropriate scale 

 factors K each may be marked in terms of the reactance which is left 

 in the circuit. 



Now suppose Zi is kept constant at some \alue which is a pure 

 imaginary, and Z: is varied over the range — /» <Z2^+'^. We 

 may rewrite (4) in the normal form ((5): 



5 = 



a+cZ3+{b+dZ3)Zi 

 a 1 + C1Z3+ {hi +diZ3)Zi 



(21) 



^e r Bound a^ 



Fijj. 4 — The Region to which 5 is Restricted and the Critical Circles 



The locus of S is one of a family of circles, each circle corresjionding 

 to a \alue of Z3 and completely traced out by complete \ariation of Z-. 

 The properties of each circle may be found by substitution in (9). 



