■ FREQUENCY-MODULATION 401 



to a good approximation. Introducing this approximation into Pn 

 as given by (23) and writing 



m = 7V,2 + N,^lc^WM\ (24) 



we have 



i'. = ^..^=(.+3(^)%3^(^?), (25) 



Ps = \^s\ 

 Now from the inequality, necessary for rectification, 



X 



COi > 



\ -\- m 



it is seen that as the parameter m is increased, coi may be reduced by 

 the factor 1/(1 -\- m). In accordance with this, we replace coi by 



coi/(l + m) in (25) and get 



Ps = XV. 



i+z,-f^i(^r+(„^y^)]. (26) 



(1 + m)- \\ COa 



The noise power Pat can be still further reduced by eliminating oji 

 from (26) by a circuit arrangement explained in Ref. Section III; if 

 this is done we get, instead of (26), 



P^=LjN^(l^3j^^^I^J^ 

 3 _ \ (1 + my , 



Ps = X252. 



We have now to compare the relative noise and signal powers of the 

 feedback with (1) straight reception without feedback and (2) reception 

 with amplitude limitation. 



For straight reception (without feedback) we have (see equation (68), 

 Ref.), corresponding to (26), 



P;.=^c.„W^(l+3('^V+3^^ 



Ps = X252, 

 and corresponding to (27) 



1 



(28) 



..v==3..3^^(l+3(Ay 

 Ps = X'sK 



(29) 



