BAND WIDTH AND TRANSMISSION PERFORMANCE 



579 



APPENDIX II 



Interference between two frequency modulated waves 



This problem occurs so frequently in the present paper that its solution 

 is ai)pcnded liere for reference. Figure 36 shows a geometric figure from 

 whicli the phase of a two-component wave can be calculated. We write 



where 



P cos d -\- Q cos (f = R cos \l/ 



Ri = p2 _^ g.' ^ 2PQ cos (d - if) 

 P sin -{- Q s\n (f 



tan \p 



P cos 6 -\- Q cos <p 



± i_- 



Fig36. —Geometric solution for resultant phase of two frequency modulated waves. 



The response of a perfect frequency detector in radians/sec. is given by 



12 = dxf'/dt = - 

 at 



( t ^' 



I arc tan — 



hid' + ^') + 



sin + (? sin ^ 

 cos 6 -\- Q cos ip 



<p' P" - Q^ 



2 P2 _|_ g2 _f_ 2PQ cos {9 - if) 



