Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

-324 FREQUENCY MODULATION, Volume Ivoltage increases 27.3 per cent when x changes from zero to one.in Appendix I, this voltage is given by:Average voltage = 2(1 + x)e, E 2yx1 + XAs shown(4)where E ] [is a complete elliptic integral of the second kind with1 + xmodulus2VxRoot-Mean-Square Value of Envelope. If a square-law rectifier instead of alinear rectifier is used, the root-mean-square value of the rectified envelopecan be read with an average-reading direct-current voltmeter. The rootmean-squarevoltage will increase more rapidly with x than the average2nyt —Fig. 1—The heterodyne envelope.Fig. 2—Harmonic content of theheterodyne envelope.voltage, as shown by Figure 2.The voltage is given by:Root-mean-square voltage = e,-\/l + x 2 (5)and it increases 41.4 per cent when x increases from zero to one.Fourier-Series Analysis of Envelope. If the heterodyne envelope is rectifiedwith a linear rectifier, and the radio frequency is filtered out, the resultantaudio signal (shown by Figure 1) can be expanded in a Fourier series.The coefficients of this series are given in Appendix I and the zero-frequencycomponent is the same as the average value which is shown byFigure 2. The fundamental component increases almost linearly withincreasing £ to a maximum value of % of the corresponding direct currentvoltage. The second harmonic increases slowly until it equals 20 per centof the fundamental when x = 1 , and the third harmonic has a maximumvalue of 8.6 per cent of the fundamental.