Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

6 FREQUENCY MODULATION, Volume 1to determine mathematically the fidelity with which the noise is transmittedfrom the radio-frequency branch, in which it originates, to themeasuring instrument as a function of frequency. To do this, the wavespresent at the receiver input will be assumed to be the frequencymodulated carrier and the spectrum of noise voltages. This wave andspectrum will be combined into a single resultant whose amplitude andphase are functions of the constants of the component waves. Theresultant will then be "mathematically" passed through the limiter toremove the amplitude modulation. From a determination of the instantaneousfrequency of the resultant, the peak frequency deviationeffected by the noise will be found. A single noise component of arbitraryfrequency will then be substituted for the resultant of the noisespectrum, and the modulation factor at the output of the convertingfilter will be obtained. This noise component will then be varied infrequency to determine the over-alltransmission of the receiver interms of the modulation factor at the sloping filter output. The areaunder the curve representing the square of this over-all transmissionwill then be determined. By comparing this area with the correspondingarea for an amplitude modulation receiver under equivalent conditions,and taking into consideration the pass band of the intermediate- andaudio-frequency channels, a comparison will be obtained between theaverage noise powers, or the average root-mean-square noise voltagesfrom the two receivers. 4The peak voltage characteristics of the two receivers will be comparedfor fluctuation noise by a correlation of known crest factors withthe root-mean-square characteristics. (Crest factor = ratio betweenthe peak and root-mean-square voltages.) The peak voltage characteristicsof impulse noise will be determined by a separate considerationof the effect of the frequency modulation over-all transmissionsupon the peak voltage of this type of noise.After a comparison between the noise output voltages from thefrequency and amplitude modulation receivers has been obtained, therespective signal output voltages willbe taken into consideration sothat the improvement in signal-noise ratio may be determined.In the process of determining the over-all transmission of the noise,the frequency modulated wave may be expressed bye, = C sin {ut + {F d /Fm ) cos pt] (3)4Stuart Ballantine, "Fluctuation noise in radio receivers," Pboc. I.R.E.,vol. 18, pp. 1377-1387; August, (1930). In this paper, Ballantine shows that theaverage value of the square of the noise voltage "... is proportional to the areaunder the curve representing the square of the over-all transimpedance (or of thetransmission) from the radio-frequency branch in which the disturbance originatesto the measuring instrument "as a function of frequency . . . .