390 



BELL SYSTEM TECtlNlCAL JOURX.IL 



Now, as s is \'aried, the first term is constant. In the second term 

 the first factor is constant and the second factor \aries only in angle. 

 since the numerator is the conjugate of the denominator. The first 

 term, therefore, is the center, and the absolute value of the first 

 factor of the second term is the radius, of the circle in which w moves 

 as z takes all imaginary \alues. 



One X'ariaiu.k Rk.u tam k (iIvinc; Circli.ar Locus 



The significance of the equations may he made apparent 1)>' a 

 study of Fig. 2, which shows the imjjedance S when one of the re- 

 actances, say Z3, is made zero. We have, then, 



5 = 



A+AiiZt a+bZi 



■4 ll+i4 11.22^2 Cl + biZi 



(10) 



and the trixial case abi — aib = is excluded. This is of the t\pe of 

 (6). When 7.2 \aries over all pure imaginary values, S traces out a 



Ki^. 2--L0CUS of llic lMi|Hil.nm- .V wiili ( )nc \aii.ililc Kf.ictaiue 



circle, which ('.)) shows h.is its ( riiu-r on ilie resistance axis. Its inter- 

 cepts on the resistance axis are 



and 



.S"= =R,„ sav, when /. = () 

 «i 



S= T- =Jii; when ^2 = 00. 



(11) 

 (12) 



