402 BELL SYSTEM TECHNICAL JOURNAL 



When noise reduction is effected by amplitude limitation the corre- 

 sponding relative noise and signal powers (see equation (78), Ref.) are 



PM=\o,a'N\ (30) 



Ps = X252. 



If we assume as above that — 1 < 5 — 1 and s- is of the order of 

 magnitude of 1/2, then in practical applications X/co„ ;» 1 and wi > X. 

 On this basis comparison of (26) with (28) and (27) with (29) shows 

 that, when m^ \, the noise power with feedback is very much smaller 

 than without feedback, the ratio of the noise powers in the two cases 

 being approximately 1/(1 + w)^. (This assumes, of course, that iV^ 

 is approximately equal in the two cases.) 



Comparing, however, the noise power with feedback to that obtain- 

 able by amplitude limitation, it will be seen that in order to reduce the 

 former to the order of magnitude of the latter it is necessary that 



^^/""^ <1. (31) 



(1 + w) 



From the preceding it is seen that the performance of the feedback 

 circuit and the reduction in noise-power ratio obtainable depend in a 

 fundamental manner on the parameter m, defined above by the formula 



m = C1C2C3C4 (32) 



If the characteristics of the modulator rectifier and variable- 

 frequency oscillator are stipulated, it is possible to calculate m in terms 

 of these characteristics and the constants and connections of the network. 

 It is experimentally determinable (among other ways) as follows: 



Let the feedback circuit be opened between the low-pass filter and 

 the variable-frequency oscillator, and let the filter be closed by an 

 impedance equal to that of the oscillator as seen from the filter. Then 

 m = (since there is no low-frequency feedback to the oscillator) but 

 m/iJL is finite. 



Denoting the value of a under these circumstances by cri, it follows 

 from (9) that 



(Ti = — X5. (33) 



M 

 Consequently dividing ai by a, as given by (9), we have 



\ -\- m = (Ti/a, 



m^^-^^^- (34) 



