434 

 where 



BELL SYSTEM TECHNICAL JOURNAL 



H = aABbi and 



= — kpi 



Inserting these values in (37) and writing (1 — ^j8) = F, the receiver 

 output becomes, with feedback, 



(42) 



(43) 



cr = aAB[b,p,S + h^ipiSy + &3(pi5)3]. (44) 



APPENDIX B 



Analysis of Noise Reduction 



In the following analysis it is assumed that the amplitude of the 

 disturbance producing the noise is sufficiently small compared with 

 that of the incoming signal wave so that the principle of superposition 

 will apply. Hence the manner in which the effect of a single disturbing 

 component is modified by feedback will first be developed. Then the 

 effect of a disturbance consisting of a continuous spectrum is derived 

 by direct summation. 



Consider first the case where there are impressed upon the grid of 

 the modulator the incoming wave and the local oscillator voltage ^^ 

 as defined by (31) and (32), plus a single disturbing component 



Q cos [(coi + co„)/ + 0„]. (45) 



Then the intermediate-frequency product will be 



aAB cos coq/ + p\ I Sdt — Pi I kadt 



+ aBQ cos (wo + con)/ - p2 I k(Tdl + 0„ . (46) 



For simplicity assume that the intermediate-frequency amplifier and 

 conversion circuit have the ideal transfer admittance characteristic 



F(co) — a^ -\- ai(w — Wo). 



(47) 



" Arbitrary phase constants will be omitted from these expressions since they do 

 not affect the final result. 



