STABILIZED FEEDBACK AMPLIFIERS 9 



A curious fact to be noted from (11) is that it is possible to choose 

 a value of m/S (namely, |ju|3| = sec $) so that the numerator of the 

 right hand side vanishes. This means that the gain stability is 

 perfect, assuming differential variations in \fx\. Referring to Figs. 3 

 and 4, contour C is the locus of |a£/3| = sec <l> and it includes all ampli- 

 fiers whose gain is unaffected by small variations in | ^i | . In this way 

 it is even possible to stabilize an amplifier whose feedback is positive, 

 i.e., feedback may be utilized to raise the gain of an amplifier and, at 

 the same time, the gain stability with feedback need not be degraded 

 but on the contrary improved. If a similar procedure is followed 

 with an amplifier whose feedback is negative, the gain stability will 

 be theoretically perfect and independent of the reductions in gain due 

 to feedback. Over too wide a frequency band practical difficulties 

 will limit the improvements possible by these methods. 



With negative feedback, gain stability is always improved by an 

 amount at least as great as corresponds to the reduction in gain and 

 generally more; with positive feedback, gain stability is never degraded 

 by more than would correspond to the increase in gain and under 

 appropriate conditions, assuming the variations are not too great, 

 is as good as or much better than without feedback. With positive 

 feedback, the variations in /i or /3 must not be permitted to become 

 sufficiently great to cause the amplifier to sing or give rise to instabil- 

 ity as defined in a following section on "Avoiding Singing." 



Modulation 



To determine the effect of feedback action upon modulation pro- 

 duced in the amplifier circuit, it is convenient to assume that the 

 output of undistorted signal is made the same with and without feed- 

 back and that a comparison is then made of the difference in modula- 

 tion with and without feedback. Therefore, with feedback, the input 

 is changed to e = go(l — m/3) and, referring to equation (2), the out- 

 put voltage is m^o. and the generated modulation, d(E), assumes its 

 value without feedback, d(Eo),and d(E)l{l -/i/3) becomes d(Eo) / (1 - (il3) 

 which is Dol{l — jj.^). This relationship is approximate because the 



D. |m;S| = 1. 



£. * = 90°. Improvement in gain stability corresponds to twice db reduction 



in gain. 

 F and G. Constant amplification ratio against variations in <i>. 



Constant phase shift through the amplifier against variations in |/x| and 

 l/3i. 

 H. Same properties as B. 

 I. Same properties as E. 



J. Conditions in which -r- L— -r = -r— T the overall gain is the exact negative 



I 1 — MP I I P I 



in^■erse of the transmission through the /3-circuit. 



