518 BELL SYSTEM TECHSICAL JOL'RXAL 



Another question concerns the effect upon the amphtude at which 

 the system operates as its frequency is altered by readjustment of 

 the frequency control elements. If, for example, the capacity in 

 the series resonant circuit is increased, the resonance curves of Fig. 5 

 will move to the left. Their shape also will be altered very slightly. 

 Since the power ratio curves defining the operation of the amplifier 

 are horizontal straight lines there will be a correspondingly slight 

 change in the shape of the curve indicating the possible conditions 

 for energy equilibrium. It will, of course, be displaced to the left 

 by the same amouni as are the resonance curves. If, howe\er, the 

 resistance of the resonant circuit varies directly with frequency, as it 

 might through changes in hysteresis and eddy-current losses, the 

 current through the series resonant circuit and through the resistance, 

 R-i will be increased. This increases the ratio of the xoltage across B 

 to the voltage across A and consequently lengthens the ordinates of 

 the resonance curves shown in V\g. 5. The shapes of the cur\es will 

 also be changed due to the change in the ratio of the reactance to re- 

 sistance. Under these conditions the energy equilibrium curve, in 

 addition to beini; nioM'd tii tiu' left, will i)f incrt-asrd both in height 

 and in breadth. 



The |)ii,isi- (iir\c> (if the frecjuencx' icinirol unit — I-ig. 7 — will 

 be nui\f(l to tin- lilt iiy tiie same amouni as the resonance curves. 

 Due to the slope of the phase famih" of tlu' ampliliiT which we ha\e 

 assumed to be coincident straight lines, tlu' intersections ot the two 

 phase families must ni(i\-e awa\' Irom tiie |)()int cil /i-ro phase dis- 

 placement. Tlu- si-paratioii between thi- nii'UibiTs ol the ])hase 

 famih' of the fre(|uenc\' control unit is greater lure .uid ((nisiciuiiitly 

 the ]jhase eciuilibrium curve is less nearly \erti(al tiiau liitdif. Tlu- 

 slojje of the phase faniiK' ol tiie anipiiiiiT also causes the phase 

 equilibrium curxf to mox c ici ilie ielt by a slighiK' greater amouni 

 ijiaii the displacement of the resonance point nf tiie tuned circuit. 

 It is appareiTt. therefore, since the phase e(|uilil>iiuiii lurxc iiioxes 

 farther than the amplitude equilibrium curve, ili.it tluir intersection 

 will mo\e to a position corresponding to a iowrr \,ilur ol the voltage 

 at the jivnction A. This is true of couisi', oiiK il ihc riiange in the 

 shape of the amplitude ecpjilibriuni ( ui\e due to ilu- t ii.inge in resist- 

 ance of the inductance coil is small. It is .ilso I'xident tli.it the 

 change in the fri'quency of llii' luneiit deli\i'ieil ii\ tiie osiili.ilor is 

 greater than tlu' cliani^e in liie ri-son.ini lre<|ueii(y ol ilu- indiu'i.nu'c 

 and capacity. 



These two examples ari' undouiitedU' sufiicii'iit to demonstrate how 

 a change in the constants of a single element of an oscillating system 



