Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

33dFREQUENCY MODULATION, Volume IThe beat-note envelope produced in this case is shown by Figure 20.The characteristic peaks and holes in the resultant carrier amplitude arepresent, but some of them are modified in shape because the two audiofrequencies are present simultaneously.Near 40 degrees and again near 130 degrees the two voltages start togo out-of-phase,but the two vectors then begin to reverse themselvesand only a small decrease in amplitude occurs.If this signal is sent through a receiver with a perfect limiter and lineardiscriminator, the resultant audio output will be as shown by Figure 21.Two cycles of the desired signal are shown as a dotted curve. This correspondsto one cycle of the undesired signal. As x increases toward one, thebeat-note interference increases inthe pulses become very narrow and long.amplitude until in the limit as x—>l,If x becomes greater than one,20° 40° 60° 80° 100° 120° 140° 160° 180°2^!-*-Fig. 20—Heterodyne envelope.the polarity of the pulses is reversed (as shown by Figure 22) and thisundesired signal gains control. When x becomes very large, only theundesired signal is received, as shown by the dotted cosine wave of unitamplitude.The equations for the envelope and the beat-note interference arederived in Appendix III. If Di and D 2 are the two deviations and [ju and[j.2are the corresponding audio frequencies, the envelope of the carrier is:Envelope = Ei VI + x 2 + 2x cos {Z>i/[J.i sin 2-iry.xt - ZVfAs sin 2irM}(22)and the audio output from a receiver with limiter and balanced discriminatoris: