244 BELL SYSTEM TECHNICAL JOURNAL 



Ao) 



than equation (37) would indicate. The quantity calculated for —ttf from 



equation (37) multiplied by the factor 1/cos a is a parameter which specifies 

 the dependence of frequency on load. It may be specified at any value 

 of load admittance Y ^ , that is, for any position on the r plane. Generally, 

 however, one considers the rate of change of frequency with susceptance 

 at matched load, for which F^, is equal to the characteristic admittance Yo 

 of the output line at the point in question. Using the parentheses ( )o to 

 indicate that the quantity enclosed is measured at the match point and in- 

 corporating the factor 1/cos a, one obtains from (37): 



/ Acq \ ^ IfMVo^J^ ,.. 



\AB[)o 2\lJ Yoccosa' ^ ^ 



The quantity ^^, I 



as it stands is not a convenient one to measure. 

 For this reason it is customary to specify the total excursion of frequency, 

 A/ = — - , resulting from a standard variation in ABl , namely, that obtained 



ZTT 



by the total possible phase variation of a standing wave of 1.5 voltage ratio 

 in the line at the point in question. This is equivalent to traversing the 

 p = 0.2 circle on the reflection coefficient plane, shown on Fig. 33. It can 

 be shown that such a variation of load admittance results in a variation of 

 susceptance of ± 0.41 times the characteristic admittance of the line, Yo , 

 corresponding to a total susceptance variation of 0.82 Yo . When deter- 

 mined in this way the total frequency excursion is called the pulling figure, 

 PF. Hence by equation (42) 



(?) 



.82 Fo 1 



Foc cos a 



2 



= 0.41 /o 



(43) 



cos a 



Since Fo = (Gl)o, the quantity ( y j Fo in this expression is recognized as 



(Gl)o , the load admittance at the primary terminals of the ideal trans- 

 former when the line is matched at the point in question, namely, the 

 secondary terminals. Using this fact and equation (23) the pulling figure 

 is seen to be: 



Pf = 0.41/„<).«-L 0_lli2_^. (44) 



Foc cos a (C/extjo COS a 



