VARIABLE FREQUENCY ELECTRIC CIRCUIT THEORY 529 

 Formula (42) thus becomes 



I = yiiooc) • F(«a)c) -exp ii I ^dtj-l 



1+ ^' + ^' 





}• 



(cOiJ — 03 c)^ 



In order that the distortion shall be small it is necessary that 



X <3C \WR — COc\. 



If the two networks yi and y^ are oscillation circuits so adjusted that 



Ci/Li = C21L2, 



cofi^ = (1 + 5)co. = I/VlIG, 

 Wfij = (1 — d)cOc = IHL2C2, 



then the combined rectified output of the two parallel circuits is 

 proportional to 



X'J j^ C3 j^ C5 1^ 



"T 7^^ "T^ "T 7T TS -!-•••• 



5-co, ' (5-0;^)' (5-co,)5 



Thus the constant term and the first order distortion are eliminated 

 in the low frequency circuit. 



IV 



The most important advantage known at present of frequency- 

 modulation, as compared with ow;^/*7z^e-modulation, lies in the possi- 

 bility of substantial reduction in the low frequency noise-to-signal 

 power ratio in the receiver. Such reduction requires a correspondingly 

 large increase in the width of the high frequency transmission band. 

 For this reason frequency-modulation appears to be inherently 

 restricted to short wave transmission. 



In the discussion of the theory of noise which follows, it is expressly 

 assumed that the high frequency noise is small compared with the high 

 frequency signal wave. Also ideal terminal networks, filters and 

 detectors are postulated. 



In view of the assumption of a low noise power level, the calculation 

 of the low frequency noise power in the receiver proper can be made to 

 depend on the calculation of the noise due to the typical high fre- 

 quency noise element 



-4„exp {iwct + *Wn^ + iQ^- (60) 



