Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

336 FREQUENCY MODULATION, Volume Iw + a, and phase angle 6, or:e 2 = E 2sin {(to + a)t + 6} (15)then, as shown in Appendix II, the envelope of the resultant carrier isgiven by:Envelope = Ei V 1 + x* + 2x cos /3 (16)where: /3 = — sin 2ir\d — at — 6and the audio output is given by:D COS 27T[X< - a/2-TTOutput = D cos 27rui —,cos (8 + xWhen this is expanded in a Fourier series to determine the harmonicand cross-modulation distortion, the audio output is given by:Output = D cos 2ir\d+ S 2 (- a;)" j- - £- I J r (nDM cos (re - nod - w6) (18)n = l r=-o° ( TO 2lT )where s = 2ir[i£, and a;/(i; x, 6) sin {(2r) (2^)} (19)r = lwhere the C- and S-functions are defined as follows:C(m, n; x, 6) = S Jm (sn) cos s6s = l S(20)S(m, n;x, 8) = 2 -^-^-* Jm (sw) sin s0 (21)x 2^1