NEGATIVE FEEDBACK 



437 



to satisfy both of the conditions expressed by (59). The total effect 

 is obtained by summing the output power resulting from each con- 

 tribution since the original elements have random phases. If ^2 is the 

 resistance of the output circuit the total power of frequency q becomes 



Q' 



2r2F^ 



ao + ai(mp + q) — 



A'ai^kp2mp 



+ z 



a-0 + ai{mp — q) — 



F 



A'ai^kpimp 

 F 



JJ{x) 



JmKx) 



(60) 



This is readily evaluated with the aid of tables appended to an earlier 

 paper. '^ The result is 



r2F'' 



ao' + 





+ 



aiV ] 



(61) 



The amplitude factor Q remains to be~defined. If N^ is the mean 

 disturbing power per unit band width in the vicinity of the carrier 

 frequency and ri the resistance of the input circuit, the peak amplitude 

 of any element is defined by the relation 



N^do 



2ri 



(62) 



Thus the power associated with each element becomes differentially 

 small, and if the value so obtained is entered into (61) there is obtained 

 the output noise power contained in a band extending from qto q -\- dq. 

 Then we shall have 



dW 



INhijayBY 



ao'-\- 



a i^Aw' 

 ~2F^ 



+ aiV 



dq. 



(63) 



The total noise power in a band extending to a limiting frequency qa is 



The corresponding signal power is 



_ (aT^^)^ 



(65) 



12 J. G. Chaffee, "The Detection of Frequency Modulated Waves," Proc. I. R. E., 

 vol. 23, pp. 517-540, May 1935. 



