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BELL SYSTEM TECHNICAL JOURNAL 



spending ratios formulated in (Ref.) for straight reception and also 

 reception with amplitude limitation. In this way, as regards reduc- 

 tion of noise and "fading," the feedback circuit is found to have ad- 

 vantages comparable with those attainable by amplitude limitation."* 



I 



The receiving system operates as follows (see sketch) : 



INCOMING 

 HIGH-FREQ. 



MODU- 

 LATOR 



BAND- PASS 



FILTER 



/'MID-FREQ.= \ 



2 



KH 



FREQUENCY 

 DETECTOR 



DEMODU- 

 LATOR 



VARIABLE- 

 FREQUENCY 

 OSCILLATOR 



LOW-PASS 



FILTER 

 /CUT-OFF'i 



LOW-FREQ. 

 OUTPUT 



Feedback receiving circuit. 

 The incoming frequency-modulated wave at terminals I , I is taken as 



E exp ( iwct -\- i\ \ s dt\ , (1) 



where E is the wave amplitude, wc the carrier frequency, X the modu- 

 lation index and 5 = s{t) is the low-frequency signal which it is desired 

 to recover. 



This wave is impressed at terminals 1, 1 on one pair of terminals of a 

 "product" modulator; on the other pair of terminals of the modulator 

 there is impressed the output of a local variable-frequency oscillator: 



M exp ( iwMt + iix 



j\dt) 



(2) 



Here cojv/ is the "carrier" frequency of the oscillator, /z (a positive real 

 quantity) is the index of modulation of the oscillator and a = a{t) is 

 the low-frequency current fed back to the oscillator. 

 The output wave of the modulator is then equal to 



Ci£Af exp ( i{wc — i^M)t + i I (X5 — tJi(j)dt \ 



4- CiEM exp ( i{oic + w.v)/ -f i I (X^ + ixa)dt J . (3) 

 * Armstrong, Proc. I. R. E., May 1936, also see (Ref.). 



