Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

=280 FREQUENCY MODULATION, Volume IThe path difference corresponding to t is 6.2 miles. Zero degrees correspondto full deviation on one side.Since the audio signal is a cosine function, it varies slowly at first,then more rapidly as it goes through 90 degrees, and then slows downas it approaches 180 degrees. Figure 1 shows how the spacing of thepeaks and dips of the carrier envelope corresponds to this variation.Zero degrees corresponds to the slowest rate of change, and the peakis very wide; at 90 degrees, the variation is most rapid, and the peakis narrow. The amplitude can be represented by the resultant of tworotating vectors R as shown by Figure 2 If E 2 were to rotate at auniform rate, the resultant R (which corresponds to the instantaneousvalue of the envelope) , would go through identical cycles, and the peaksof Figure 1 would be evenly spaced. When the carrier wave is modulatedsinusoidally, however, the vector E 2 does not rotate uniformly,but rocks back and forth, with a sinusoidal variation of the angle 8.Fig. 2—Resultant of two signals.Under the conditions represented by Figure 1, the vector E 2 startswith 6 — 0.18 degrees and makes two revolutions (4tt radians) whilethe carrier frequency varies from maximum deviation to the meanundeviated frequency. Each time it goes past point B it gives a holein the carrier envelope, and when it goes through A it gives a peak.Figure 3 shows what happens when the frequency is increased from30 cycles per second to 5000 cycles per second. The equation of thisenvelope isei + e 2\V1.81 + 1.80 cos {12 cos (2ir/*i - 30°) }. (8)Since ir/ui = it/6 radians = 30 degrees, the curve is shifted over approximately30 degrees from that in Figure 1, corresponding to onehalf the fraction of the audio cycle by which one wave is laggingbehind the other.