VARIABLE FREQUENCY ELECTRIC CIRCUIT THEORY 



533 



If this wave is subjected to amplitude limitation, the amplitude 

 variation is suppressed, leaving a pure frequency-modulated wave, 

 proportional to the real part of 



exp 



\i( C ^dt-\- An sin ( C ^ndt \ 



(73) 



(but drastically reduced in amplitude). 

 After frequency detection the wave (73) is, within a constant. 



ndt 



exp ( * I ^dt + ^ „ sin ( i 0„i 



X 1 + — ^ ( ^ \ sdt + Ansml f Qndt 

 Consequently, since 



J9,ndt = (Jint ■\- Bn — \ I Sdt, 

 Jo 



the amplitude of the wave (74) is 



1 H I X5 + (cOn — \S)A „ COS ( I 9,ndt 



(74) 



(75) 



(76) 



This is the amplitude of the low frequency wave after rectification; it is 

 obviously proportional to 



X5 + (aj„ — \s)An COS 





Q,ndt 



(77) 



which is a special case of (64) and may be used in calculating the 

 relative signal and noise power with amplitude limitation. Hence we 

 have, by aid of (65) and (66), 



Ps = XV, 

 Pn = iojaWl 



(78) 



(These are, of course, relative values and take no account of the 

 absolute reduction in power due to amplitude limitation.) 



Comparing (78) with (68) it is seen that, for detection by straight line 

 rectification, the ratio of the noise power with to that without amplitude 

 limitation is 



^- = — ; (79) 



1 + 3cOiVcOa2 + SXh'/cOa'' 



