Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

348FREQUENCY MODULATION, Volume ILet 2ityd = (3 and tan ax sin /31 + x cos (3Then k sin a = x sin /3(59)k cos a = 1 + x cos /3(60)where: fc = vl + x + 2 2x cos /3(61)x sin£I +x cos /3Fig. 24—Determination of k.Multiply equation 59 by i and add equation 60.Then: 1 + x cos /3 + ix sin (3 = k (cos a + i sin a) (62)or: 1 + x e' p = A; e ia . Takelogarithms of both sides. Then:log (1 + x e fS ) = log k + ia.Since:X2 t-3 'v> 4log (1 + Z) = X _—+—--+ ... - Kx