412 BELL SYSTEM TECHNICAL JOURNAL 



giving 



Pn 4A^V 



:ir_l_ + _^l. (92) 



Ps A^F 



Thus the additional feedback represented by the factor F2 is directly 

 effective against the noise increment accompanying modulation. Re- 

 duction of this increment brings about a still closer correspondence 

 between the limiter and feedback systems as is seen by setting F = Fi 

 in (19) and comparing with (22). 



The above discussion and the analysis given in Appendix B are based 

 upon the assumption that the carrier amplitude is large compared 

 with that of the disturbance. A rigorous analysis, applicable to the 

 case where this ratio is unrestricted, becomes exceedingly involved. 

 However, a rough indication of what is to be expected in the presence 

 of a high level of disturbance can be obtained quite simply from (52) 

 developed in Appendix B. Assuming that modulation is not present 

 this can be put in the simple form 



1 Q'(ao + OlCOn) 



1 + J7 f p j cos UiJ. 



When Q' <^ A' the wave form of the output noise produced by a single 

 element of disturbance is very closely a sinusoid. However, when Q' 

 and A' become comparable in magnitude the output wave becomes 

 badly peaked when wj = nir. While the above expression is only a 

 very rough approximation under these conditions, a plot of the wave 

 form so obtained exhibits all of the essential characteristics of the curves 

 given by Crosby in a recent paper ^ dealing with noise in frequency- 

 modulation systems using amplitude limitation. These curves show a 

 similar peaking of the output-noise wave form when the ratio of carrier 

 to disturbance amplitude is in the vicinity of unity. The description 

 given by Crosby of the manifestations of this phenomenon observed 

 in an experimental system applies rather closely to what has been found 

 in the feedback system. A more detailed account will be found in a 

 later section. 



Examination of (52a) shows that the output wave can assume very 

 large and even infinite peak values when Q' and A' are approximately 

 equal. The existence of high peak values of noise implies both a large 

 instantaneous deviation in the frequency of the intermediate wave, and 

 a conversion-circuit characteristic of unlimited extent. The finite 



* MurrayG. Crosby, "Frequency Modulation Noise Characteristics," Proc. /. R.E., 

 vol. 25, pp. 472-514, April 1937. The curves referred to are given in Fig. 4 of the 

 above paper. 



