FREQ UENC Y-MOD ULA TION 397 



The second term of (3) is suppressed by the band-pass filter.^ 

 Then writing wc — co.v = coc, it follows that the effective output 

 wave is 



CiEM exp ( iwct + i I {\s — ix(7)dt j 



(4) 



oic isthe intermediate carrier frequency and is always < ojc, the trans- 

 mitted carrier frequency. The constant Ci is a parameter depending 

 on the characteristics of the modulator. 



The wave (4) is transmitted through the band-pass filter, and the 

 wave arriving at terminals 2, 2 is then 



C1C2EM exp f iojcf + i I (X5 — ijLa)dt j . (5) 



The parameter C2 (taken as a constant) depends on the transmission 

 characteristics from the modulator to terminals 2,2. 



Assuming an ideal frequency detector (see Ref.) the output to the 

 terminals of the rectifier (or demodulator) is 



CiC-iCsEM ( 1 + ^'^ ) exp ( io)J + i I (ks - fxa)dt j 



(6) 



Here the parameters C3 and coi depend on the characteristics of the 

 frequency detector. 

 Finally assuming that 



>^i^^ < 1 (7) 



the low-frequency output of the rectifier ^ is 



c.ccscEM (^\ + ^^ "/'' )• (8) 



If the constant term of (8) is suppressed and a fraction tj of the rectified 

 output is fed back to the oscillator we have, finally, 



m \s ' . . 



a = — - — ■ , (9) 



fx I -\- m 



^ Indeed the principal function of the band-pass filter is to suppress frequencies in 

 the neighborhood of wc + ^m- 



" More generally a demodulator. In the present paper a straight-line rectifier is 

 postulated for mathematical simplicity but the theory applies equally well to other 

 forms of detection or demodulation. 



