516 R ELL SYSTEM TECUXICU. JOCKWIL 



increasing the damping, the rate of change of this phase shift is 

 reduced. The several curves correspond to different values of the 

 \oltage amplitude at the point ,1. 



The phase relation between the \c)ltage wa\e imjiressed upon the 

 input to the amplifier and the wave delivered by it is indicated in 

 Fig. 7 by the single straight line. That is, we are assuming that 

 the phase displacement of the wave transmitted through the ampli- 

 fier \aries but little o\er the frequency range co\ered by the diagram 

 and that ii is independent of the power which is being deli\ered 

 b\- the amplifier. The numbers associated with the sc\"eral cur\es 

 have the same signilicanre as those used with the jjower ratio 

 families. 



From these two sets of lines it is possible to determine a series of 

 values of the voltage at the junction A and of the frequency for which 

 the resultant phase displacement around the loop is zero; exactly as 

 we determined a series of values for which the resultant power change 

 was zero. These values are plotted in Fig. 6 as shown by the line P. 

 If the condition for zero phase shift were the only one which the system 

 had to satisfy, it is obvious that it would be in equilibrium at any point 

 on this ciir\e. .Since, however, the .system is called upon to satisfy 

 two conditions, one defined b>- the ciirxe .1 and the other b>- the curve 

 P. an\ intersections which ihey ma\' ha\e are the onK' points at 

 which the system can be in equilibrium. 



This method of analyzing the relations between the characteristics 

 of the several members of an oscillating s\slem, and their mutual 

 adjustment to an ctjuilibrium condition may be summarized in general 

 terms. The system is considered as a regenerative transmission 

 circuit di\ided into two [jortions. For each of these portions a family 

 of curves is plotted showing the relation between the rate at which 

 energN' crosses one of the junctions, which will be used as a reference 

 point, the r.itio belwi'cn tlu- r.ites at which energy crosses the two 

 junctions .iiid tiu' lie(|iKiic\ . .\n\ two of these variables may be 

 chosen as the coortlinates for these families of ciirxi's, tiie rt'inaining 

 variable being the parameter. The intersections of ,i <iir\e in one 

 family with the cur\e of liie same parametei in liir oilur lamily 

 define jiairs of \ahies of tiie frequency and of tiie power ,ii liu' refer- 

 ence jiimiion for whicii the system is in energy e(|uilil)riiiin. 



lor I'.u'ii |)orti()n of tiie regenerative system, a second f.iniiK' of 

 curves is jilotted showing the relaiiim lietwcin tin- power at the 

 reference junction, the phase displa( iinent of the tr.m^niiited wave 

 between the two junctions and fre(|iien( y. In tensed ions of a curx'c 

 in one of these families wiiJi the cin\e ii,i\ing the same parameter 



