STABILIZED FEEDBACK AMPLIFIERS 5 



With feedback, fi is not zero and the input to the ^-circuit becomes 

 eo + i8(£ + N +'D). The output is E + A^ + /) and is equal to 

 M[go + KE + N + D)'] + n + d{E) or: 



In the output, signal, noise and modulation are divided by (1 — miS)i 

 and assuming 1 1 — ;U/3 1 > 1, all are reduced. 



Change in Gain Due to Feedback 



From equation (2), the amplification with feedback equals the 

 amplification without feedback divided by (1 — ai/S). The effect of 

 adding feedback, therefore, usually is to change the gain of the amplifier 

 and this change will be expressed as: 



GcF = 20 logi 



1 



1 -M/3 



(3) 



where Gcf is dh change in gain due to feedback. 1/(1 — ix^) will be used 

 as a quantitative measure of the effect of feedback and the feedback 

 referred to as positive feedback or negative feedback according as the 

 absolute value of 1/(1 — m/3) is greater or less than unity. Positive 

 feedback increases the gain of the amplifier; negative feedback reduces 

 it. The term feedback is not limited merely to those cases where the 

 absolute value of 1/(1 — ii0) is other than unity. 

 From /ijS = | mi8 I [$ and (3) , it may be shown that : 



10-OcF/io = 1 - 2!m/3| COS* + |m/3|-, (4) 



which is the equation for a family of concentric circles of radii 

 10~^cf/io about the point 1, 0. Figure 3 is a polar diagram of the 

 vector field of m/? = Im/SI |$. Using rectangular instead of polar 

 coordinates, Fig. 4 corresponds to Fig. 3 and may be regarded as a 

 diagram of the field of /x/3 where the parameter is db change in gain 

 due to feedback. From these diagrams all of the essential properties 

 of feedback action can be obtained such as change in amplification, 

 effect on linearity, change in stability due to variations in various 

 parts of the system, reduction of noise, etc. Certain significant 

 boundaries have been designated similarly on both figures. 



For example, boundary A is the locus of zero change in gain due to 

 feedback. Along this parametric contour line where the absolute 

 magnitude of amplification is not changed by feedback action, values 

 of I )u/3 1 range from zero to 2 and the phase shift, $, around the amplifier 



