10 BELL SYSTEM TECHNICAL JOURNAL 



voltage at the input without feedback is free from distortion and with 

 feedback it is not and, hence, the assumption that the generated 

 modulation is a function only of the signal output used in deriving 

 equation (2) is not necessarily justified. 



From the relationship D = -Do/(l — m/^), it is to be concluded that 

 modulation with feedback will be reduced db for db as the effect of 

 feedback action causes an arbitrary db reduction in the gain of the 

 amplifier, i.e., when the feedback is negative. With positive feedback 

 the opposite is true, the modulation being increased by an amount 

 corresponding to the increase in amplification. 



If modulation in the j3-circuit is a factor, it can be shown that 

 usually in its effect on the output, the modulation level at the output 

 due to non-linearity of the /3-circuit is approximately /x/5/(l — At/S) multi- 

 plied by the modulation generated in the /3-circuit acting alone and 



without feedback. 



Additional Effects 



Noise 



A criterion of the worth of a reduction in noise is the reduction in 

 signal-to-noise ratio at the output of an amplifier. Assuming that 

 the amount of noise introduced is the same in two systems, for example 

 with and without feedback respectively, and that the signal outputs 

 are the same, a comparison of the signal-to-noise ratios will be affected 

 by the amplification between the place at which the noise enters and 

 the output. Denoting this amplification by a and ao respectively, it 

 can be shown that the relation between the two noise ratios is 

 {ao/a){l — MiS). This is called the noise index. 



If noise is introduced in the power supply circuits of the last tube, 

 ao/a = 1 and the noise index is (1 — m/3)- As a result of this relation 

 less expensive power supply filters are possible in the last stage. 



Phase Shift, Envelope Delay, Delay Distortion 

 In the expression Af = [m/(1 — m/3)] [£. ^ is the overall phase shift 

 with feedback, and it can be shown that the phase shift through the 

 amplifier with feedback may be made to approach the phase shift through 

 the ^-circuit plus 180 degrees. The effect of phase shift in the jS-circuit 

 is not correspondingly reduced. It will be recalled that in reducing 

 the change in phase shift with frequency, envelope delay, which 

 is the slope of the phase shift with respect to the angular velocity, 

 (J, = 27rf, also is reduced. The delay distortion likewise is reduced 

 because a measure of delay distortion at a particular frequency is the 

 difference between the envelope delay at that frequency and the least 

 envelope delay in the band. 



