520 BELL SYSTEM TECHXICAL JOURNAL 



the vacuum tubes considerably liclow their overloading point, where 

 the gain changes but little as the output is increased; by operating 

 the tuned circuit at low power levels, where the damping, and con- 

 sequentK- the loss, varies but little with changes in the input; and 

 by keeping the damping as low as possible. 



The slope of the amplifier gain family is, of course, a factor, but 

 in practice it is found undesirable to permit the gain of the ampli- 

 fier to var\' with frequency. The slope of the phase equilibrium 

 curve, which determines the change in frequency corresponding to 

 a given change in transmission gain or loss, depends upon three 

 things, as may be seen from Fig. 7. These are: 



1. The distance from the point of zero phase displacement at 

 which the phase family of the amplifier intersects the phase family 

 of the frequency control unit; the less this distance, the less will be 

 the fre(|uency change accompanying a given voltage change. 



2. The slope of the phase family of the frequency control unit; 

 the more nearly vertical these curves are made, the less will be the 

 frequency change accompanying a given voltage change. 



'i. The separation between the members of the phase family of 

 the freciuencN' control unit; the less this separation, the less will be 

 th" frequency change accompanying a given amplitude change. 



If the phase family of the amplifier is not a single line, the separation 

 Ijetween its members would be a factor. The slope of the curve 

 also has a slight effect. The distance from the point of zero phase 

 displacement, at which the two families intersect, may be reduced 

 by reducing such reactive impedances as appear in the amplifier 

 circuit. The slope of the frequenc\- (oiiirol unit famiK- may be 

 increased 1)\' reducing the damjiing of the tuned circuit. It may 

 also be increased by reducing the phase displacement in the amplifier, 

 thereby operating nearer the point of zero pha.se displacement where 

 the rate of change of phase shift with frequency is greatest. The 

 separation between the members of the phase famih' of the frequency 

 control unit may be reduced b\' reducing the magnitude of such 

 changes as occur in the dam])ing. Moreo\er, since for \.irious 

 amounts of damping the several members of the phase famil\- aj)- 

 proach coincidence at the resonance |)<)int. it is again desir.ibk- to 

 reduce any phase disjilacenienl of llic ain|)iitiir in order to work 

 as near this point as possibk'. 



It has just been suggested that an>' reduction in the pha.se shift 

 through the amplifier will make the phase equilibrium curve more 

 nearly vertical. It will be noticed, however, that this causes the 

 intersection between the pha.se equilibrium curve and the amplitude 



