Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

::208 FREQUENCY MODULATION, Volume IAmplitude-Modulation Signal-Noise Ratio vs.DistanceThe following empirical formula has been given by H. H. Beverage"for calculating the field strength when the receiver is within the opticaldistance of the transmitter88 VTV ahE (r-m-s volts per meter) =(1)where W = effective watts radiated = power in antenna times antennapower gain over a one-half wave dipole,a — the receiving antenna height in meters,h = the transmitter antenna height in meters,D = the distance in meters,A = the wavelength in meters.This formula is to be used for calculating the field strength for distanceswithin the horizon only. For distances bsyond the horizon,Beverage used a graphical method of plotting the curve of fieldstrength versus distance. In this graphical method the field strengthversus distance curve according to equation (1) was plotted for distancesout to the horizon and then the curve was continued for distancesbeyond the horizon, but with a slope of l/D H instead of 1/D 2 .The exponent "n" was determined empirically and varies with frequencyin the manner shown in Figure 1 which is reproduced fromBeverage's paper.In place of the graphical construction of the curve for distancesbeyond the horizon, the formula given by (1) may be revised to beapplicable to all distances, whether they be within or outside of thehorizon, as follows:88 VWahD,"-"-E (r-m-s volts per meter) =(2)XD"in which the exponent "n" is equal to two for distances within thehorizon and is chosen from the curve of Figure 1 for distances beyondthe horizon. D h is the distance to the horizon in meters and is equalto 2.21 \f~h + 2.21 \fa where a and h are the receiving and transmittingheights in meters. Thus, where D < D h, n = 2, and where D > D h ,n is taken from Figure 1.When the units of the formula given by (2) are converted to feet,microvolts, miles, and megacycles, the formula becomes0.01052 \fWahf D h"- 2E (r-m-s microvolts per meter) =- (3)D"