Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

:288 FREQUENCY MODULATION, Volume IEffect of Interference on the Audio Output from the DiscriminatorAs shown in Appendix I, Equation (23), the audio output from thediscriminator is proportional to2D sin 7i-yui sin (2-rr/j.t — 7r,ui )Dcos2TTjjt + (15)1/X + COS {z COS (2ir)xt — TTjit^) + at ]X + COS {z COS (2-np.t — TTfit ) + od }The first term represents the undistorted output, and the second termshows the distortion introduced by the interference. This result wasobtained by assuming that a limiter removes the coincidental amplitudemodulation from the wave, and that the discriminator output isproportionalto the instantaneous frequency.General Case — Two Voltages Nearly EqualThe distortion term can be expanded in a Fourier series,as shownin Appendix II. The audio output from the discriminator is proportionaltoOutput = D COS 2ir[).t00- 2/x 2 (- D*C (2m + l,z; x, ,d ) (2n + 1) sin (2n + 1) ywhere00— 2,u 2 (— l) n S (2n, z; x, mt )n = l(2n) sin 2ny (16)y — 2-!Tjj.t — 7r/tt and the C and S functions are defined as followsoc(— X)*C (m,n; x, 0) = 5 Jm {sn) cossff. (17)« (-*)«S (m,n; x,8) = 2 /,„ (sn) sin s8. (18)8= 1sThe amplitude of each harmonic can be calculated from these equationsby assuming the proper value of n. The C and S functions can be commutedfrom tables of Bessel functions. Figures 14, 15, 16, and 17 showsome graphs of these functions.Figure 18 shows the distortion caused at an audio frequency of 500cycles per second under the conditions listed. The phase of the two