400 BELL SySTEM TECHNICAL JOLRXAL 



The numbering of the sheets is, of course, arbitrary. If the upper 

 half of the Zj = circle is put on Sheet I, the arcs of the other critical 

 circles are determined as follows:" 



Circle On Sheet I On Sheet II 



Zi = Upper half Lower half 



Zi=<x) Lower half I'pper half 



Z3 = Lower half Upper half 



Zi=oo Upper half Lower half 



Each sheet, then, is divided into four sub-regions, indicated on 

 Fig. 5 by the signs of the reactances for which S is within them. When 

 Zi and Zz are composed of single elements the sub-regions in which 5 

 falls at any frequency are as follows : 



The course of S over the complete frequency range may be shown 

 by a curve through the appropriate intersections of the Zj-constant 

 and Za-constant circles, as in the following example. 



The impedance region for a particular bridge network is illustrated 

 in the two sheets of Fig. 6. The arcs of Z;-constant and Zj-constant 

 circles in each sheet form a curvilinear grid superposed on the R,X 

 grid of the complex plane. For e.xamplc, if Z2 = '200/' and Z3 = 900j, 

 the value of 5 is read from Sheet I as 327 + '29L and 5 has this value 

 irrespective of the structure of Zj and Z3. 



An impedance cur\c (dashed) is shown in Fig. li representing the 

 variation of 5 with frequency when Zj is the doubly-resonant reactance 



' When the sheets arc numliered in this way, the point .S falls on Sheet I or Sheet 1 1 

 according to the following talile, in which kt and k; arc the critical values for the 

 product and quotient of Z2 and Zj, respectively, given in Footnote 5: 



For the network of Fig. 6, *i = 116,875 and *2 = 0.9721 11. 



