Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

:350 FREQUENCY MODULATION, Volume IThen:ei + e 2= Ei\/ 1 + x* + 2x cos (3 sin jw< H sin 2uv.< - cpf-(74)where x = E,/Ei, /3 = — sin 2xti.< — atandtan cpx sin /31 + £ COS /3The instantaneous frequency becomes:w 1 d . x sin /3— + D cos 2ir(Ji< - ^- -r. tan 1— -2tt 27r eft 1+ x cosw „ „ x cos,+ x 2 a )s 5 ]D cos 27r[i2 - —\2w 1 + x + 2 2x cos /3 ( 2tt)= — + D cos 2-kuX - - :(0 ^ Z) COS 2irui — a/27r= — + D cos 2irui-;2x cos ? + */* + i r 75 )Envelope of Beatnote Patternis1cos pThe beatnote produced in the output of a receiver with a perfect limitergiven by:+ xOutput = D cos 2Tr\j.tD cos 2ir\Lt — cv/2ir2»£+l£ + i ( 76)cos p + Xwhere: = — sin 2ir,it —at— 6. The two envelopes of the maxima andI*minima of the beat-note pattern are obtained by setting ft= 2mr or(2n + l)ir where n is an integer. This gives the two envelopes:D oc xEnvelope = cos 2w\xt + - —1 + x 2-k X + 1(77)and:cos 2iru.t +- - (78)- X 2ir X - 1Fourier-Series Analysis of Instantaneous FrequencyIn accordance with the analysis of Appendix I, equation 65: