DETECTION OF TWO MODULATED WAVES 13 



ratio of the carriers by K = e/E the equation of the curve along which 

 the value of K is constant is given by: 



^ ,-, = f:%-..,. (8) 



This equation is based upon a convenient form of the Austin-Cohen ^ 

 formula for the intensity of the field radiated from a radio transmitter. 

 This formula is: 



in which X is the wave-length in meters, d is the distance from the 



transmitter in miles and a is an attenuation constant which may range 



from zero up to 0.01 or even more. In writing down equation (8) we 



have used the abbreviation: 



101. Sa^i ,.^x 



From (8) there have been computed curves for the case in which 

 Pi = P2 and for various values of K and a. X has been taken as 300 

 meters and D, the distance between the stations, as 1,000 miles. 



In Fig. 5 are shown several curves for a = 0.001. For small values 

 of K, the curves are practically circular and are of small area. As K 

 increases, the curves become oval shaped and it can be readily shown 

 that for values of K greater than a certain critical amount, the curves 

 will not close but will be of a shape which is roughly hyperbolic. 



In Fig. 6 are shown curves corresponding to a value for a of 0.002. 

 It is to be noted that an increase in a enormously increases the area 

 inside of which the ratio of the carriers is less than a certain value. 

 The effect of a will of course be dependent upon the magnitude of the 

 distance between the stations and will be more pronounced the larger 

 this distance. For the present case in which D = 1,000 miles, there 

 is not much point in considering values of a larger than 0.002, since the 

 attenuation would be so great as to make the effect of one station on the 

 service area of the other of very little consequence. 



If we specify that the carrier beat must be at least 40 db down from 

 the speech output due to a 10 per cent modulated signal, then curve 1 of 

 Figs. 5 and 6 will represent the areas inside of which this requirement 

 will be met, while if we call for an interval of 20 db between these two 

 components, curve 5 of Figs. 5 and 6 will represent the areas in which the 

 condition is satisfied. It is evident that if a rigid restriction is placed 

 on the permissible beat note interference which may be allowed, and if 

 the attenuation is of a small value then the area in which the beat 



- L. VV. Austin, Proc, I. R. E., Vol. 14, p. 377. 



