Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

zPROPAGATION CHARACTERISTICS 95a time lag with respect to that, traveling over the shorter path. Hencethe frequency modulated signal traveling over an earlier path may beexpressed by/ Pd \e = Ea sin I wt -) cos pt 1(1)\ F m /where co = 2wXF c ,F c= carrier frequency, Fd = peak frequency deviationdue to modulation, F m = modulation frequency, and p = 2irXFm .The signal traveling over a later path may be expressed bye = E 1 sin < cot + /3 -\ cos (pt + a)\ (2)\ F m )where /3 and a take into account the time delay imparted to the carrierwave and the modulation, respectively.Considering only a two-path case first, the two waves given by (1)and (2) may be combined into a single resultant wave by means of thecosine law resulting in/ JTd E,e= X E + E{ + 2E E - 2 Icos \cos (pt + a)+p cos pt'I F mF msinsin < — cos (;j/+«)+(3 cos ptFj [F m F mcot-\ cos /;/+tan -1F m E LFd Fa(-cos < — cos (pl-\-a)-\-j3 cosptE, -'-'1 \F W m F* m(3)Applying the sum and difference formula for the cosine, calling Eo/Ei= li, and 2F,i/Fm sin a/2 = Z, givessine= A/E 2 + E l-+ 2E E 1 cos jzsin (pt + — J-/3Jsin