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BELL SYSTEM TECHNICAL JOURNAL 



After the output as given by (20) is rectified, the constant term sup- 

 pressed, and only first powers in An and Bn retained, we get finally 



m/fjL 

 \ -\- m 



X5 + yl„ I COl + w„ — 



1 + w 



X5 I COS 



+ 



Bn 



CiCsM 



(cOi + C0„) COS 



r fin' dt 1 . 



dt 



Now the right-hand side of (21) corresponds precisely with formula 

 (64) (Ref.) on which the calculation of the relative low-frequency noise 

 and signal powers is based. Consequently following the methods 

 developed in Ref. and assuming An and Bn small we get 



mjij. 

 \ -\- m 



1 X%2 



3 (1 + my 



i^aNa 



-f (^ COa^ + C0i2 + {\S - IXaf \ C^aN.'IcWAP 



(22) 



The relative low-frequency noise and signal powers are then (omitting 



/ til I a 

 the common factor 



Pn = ^ C^a'Na' 



Ps = X'^?. 



1 + m 

 1 +3 



+ 3^^^^ 



1 O^a'Nb^ 



3 ciWM'- 



(1 -f m)2 



1 +3 



^ ^ ^ (X5 - f.ar 



(23) 



In these formulas NJ is proportional to the noise power level in the 

 neighborhood of the carrier frequency uc', it enters at the input ter- 

 minals 1, 1 (see Ref. Appendix 2). Nb^ is proportional to the noise 

 power level in the neighborhood of the intermediate carrier frequency 

 cocl it enters at terminals 2,2. oja is the highest essential frequency in the 

 low-frequency signal s(t); it is the cut-off frequency of the low-pass 

 filter. 



Formula (22) is solvable (see Appendix) but a simple approximate 

 solution, valid when the noise is small compared with the signal, is 

 made possible by observing that under this restriction 



\S — IJLCX = 



\ -\- m 



(11) 



