BAND WIDTH AXD TILiNS. MISS ION PERFORMANCE 583 



For marginal interference E ^ 2 y/l A and 



This equation shows that S/I varies as (B/NfrY'^ for large bandvvidths giv- 

 ing 9 db improvement per octave of bandwidth. The curves of Fig. 10 

 were plotted from equations (8) and (14). 



PPM-FM 



The pulse here is transmitted by a change in frequency from /j to /i + j3 

 and back again. The total frequency swing i3 corresponds to the pulse 

 height E in the AM case. The frequency detector delivers a pulse of height 

 jS to the baseband filter. Associated with the pulse is the error caused by 

 noise or interference in the rf-band. In the case of fluctuation noise having 

 mean power P„ per cycle in the rf-medium, a baseband filter of width Fb 

 accepts the familiar triangular voltage distribution of noise with frequency 

 resulting^^ in a mean square integrated magnitude expressed on a frequency 

 scale as : 



El = Pn Fl/ZWc (15) 



where Wc is the mean carrier power. Then, on substituting /3 for E, and the 

 above expression for E\ i^i the equation for A^: 



^ = ^Ml (16) 



Taking the ratio of e- to A/^, 



^^"^' - SP.Fl W/. /• ^ ' 



The radio signal bandwidth B is approximately equal to the frequency 



swing plus a sideband at each end or 



B = ^+2Fb (18) 



Using this relation to eliminate /3, we have 



For marginal operation of the FM limiter: 



Wc = kPnB (20) 



where we shall assume k = 16 in numerical calculations. 



^ An elementary component of interference Q cos qt produces a frequency error (Q/P)f 

 cos l-rrft where/ is the ditlerence between the interfering and carrier freciuencies. The cor- 

 responding mean square frequency error \sPQ-/2F-. But Q-,'2 = P„(//and there are equal 

 contributions from u|)per and lower sidebands centered around the carrier. Also replacing 

 P^/2 by Wc, we get a mean square frequency error in band df at/ equal to P„pdf/Wc. In- 

 tegrating over frequencies from to Fb gives the above result. 



