Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

VARIATION OF BANDWIDTH WITH MODULATIONINDEX IN FREQUENCY MODULATION*!ByMURLAN S. CORRINGTONHome Instrument Department, RCA Victor Division,Camden, N. J.Summary— Equations are derived for the carrier and side-frequencyamplitudes which are obtained when a carrier wave is frequency-modulatedThe bandwidth occupied by such a frequency-by a complex audio signal.modulated ivave is defined as the distance between the tivo frequenciesbeyond which none of the side frequencies is greater than 1 per cent ofthe carrier amplitude obtained when the modulation is removed.Curves are given to show the amount this bandwidth exceeds theextremes of deviation for a range of modulation indexes from 0.1 to 10,000,for sinusoidal, square, rectangular, and triangular modulation. For moreprecise definitions of bandwidth, curves are also given for side-frequencyamplitude limits of 0.1 per cent and 0.01 per cent of the carrier-waveamplitude. For complex modulation the total bandwidth can be estimatedby computing the bandwidth that would be required by each audio-frequencycomponent, if it were on separately, and adding the residts.IFIntroductionA CARRIER wave is frequency-modulated with a sinusoidalaudio voltage, an infinite number of side frequencies is produced.The carrier amplitude is reduced when the modulating voltageis applied, and may even become zero. If the deviation is increased,additional side frequencies are produced in both sidebands, and thedistribution of the intensities of the previous ones is changed. Fora single audio tone, the distance between side frequencies is alwaysequal to the audio frequency. When two or more modulating tonesare used simultaneously, side frequencies are produced which areseparated from the carrier by all possible combination frequencieswhich can be obtained from sums and differences of harmonics ofthe modulating frequencies. 12 Thus, if there are two audio tones offrequencies /i tand /x ,2the side frequencies are separated from the* Decimal classification : R148.2.•j-Reprinted from Proc. I.R.E., October, 1947.1Murray G. Crosby, "Carrier and Side-Frequency Relations with MultitoneFrequency or Phase Modulation," RCA REVIEW, vol. 3, pp. 103-106;July, 1938.- M. Kulp, "Spektra und Klirrfaktoren Frequenz- und Amplituden-Modulierter Schwingungen," Part I. Elek. Nach.-Tech., vol. 19, pp. 72-84;May, 1942.65