VARIABLE FREQUENCY ELECTRIC CIRCUIT THEORY 531 



necessary in one way or another to make a frequency analysis of the 

 wave (63). This is done in Appendix 2, attached hereto, where 

 however, instead of dealing with the special formula (63), a more 

 general expression 



\s(t) + (coi + w„ + us) An cos I Q„dt, (64) 



r ^ndt, 



is used for the low frequency current. This will be found to include, 

 as special cases, several other important types of rectification, as well 

 as amplitude limitation, which we shall wish to discuss later.^ Then, 

 subject to the limitation that the noise energy is uniformly distributed 

 over the spectrum, it is shown in Appendix 2 that 



Ps = XV, (65) 



Pn = iW + "i' + (1 + py\'?)o,aN\ (66) 



V = mA, (67) 



N"^ = mean high frequency power level. 



These formulas are quite important because they make the calcula- 

 tion of low frequency noise-to-signal power ratio very simple for all the 

 modes of frequency detection and demodulation which we shall discuss. 



Applying them to formula (63) we find for straight line rectification 



Pn = (iy + coi2 + XV)co,iV2, (68) 



Ps = XV. 



It is known that in practice cor ;^ XV and XV ^ coj. Consequently 

 in the factor (^Wa^ + wi^ + X^^^) the largest term is wi^. Therefore 

 it is important, if possible, to eliminate this term. This can be 

 effected by the scheme briefly discussed at the close of section III; 

 parallel rectification and differential recombination. For this scheme 

 the low frequency current is found to be proportional to 



XS + COnvlnCOS ( f fi„</M . (69) 



r fin. 

 'Jo 



Consequently, for parallel rectification and differential recombination, 



Pn = (W + XV)a;„iV2. (70) 



^ The formula is also general enough to include detection by a product modulator, 

 which however is not discussed in the text as no advantage over linear rectification 

 was found. 



