Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

|xCOMMON- AND ADJACENT-CHANNEL INTERFERENCE 323long as several seconds. This might even cause the program to changesuddenly from one station to the other during these short intervals.Analysis of Fundamental CaseThe most elementary case of frequency modulation interference is thatproduced when two unmodulated radio-frequency carriers, having nearlythe same frequency, are added together. This gives the usual heterodyneenvelope as the two voltages beat together. In addition there is a variationin the phase of the resultant which is equivalent to frequency modulation.If the difference in frequency of the two carriers is now variedsinusoidally by changing the frequency of one, keeping the two amplitudesconstant, the result is common-channel interference or adjacent-channelinterference, depending upon the way the one frequency is varied. It isthus evident that, if the most elementary case is properly analyzed, thefrequency modulation interference is merely a generalization of theresults.Heterodyne Envelopee 2As shown in Appendix I, if two radio-frequency carriers e t sin wi andsin (w + 2ir{L)t are added, the heterodyne envelope is given bywhereEnvelope = e^y/l + x 2 + 2x cos 2t\jjI (1)e i= amplitude of first carriere 2 = amplitude of second carrierx = e 2 /eiw = angular frequency of first carrier, radians per second[a = difference in frequency, cycles per secondThis is the voltage that will be obtained if the resultant signal is sentthrough a linear rectifier and filtered. Figure 1 shows the variation of theenvelope over one beat-note cycle as the ratio of the amplitudes of thetwo signals, x, is changed. For small values of x the envelope is approximately,Envelope = ei(l + x cos 2ir\i.t) x«l (2)As the ratio x is increased gradually, the higher harmonics increase inamplitude; so the peaks become broader and the hole in the carrier becomesdeeper and narrower. In the limit, as x—»1, the envelope becomesa series of rectified cosine waves, or:Envelope = 2e i |cosir[it= 1 (3)Average Value of Envelope. If the resultant heterodyne voltage is sentthrough a linear rectifier, the direct-current voltage across the rectifieroutput increases gradually as x is increased. Figure 2 shows that this