32 



STANDARD PROPAGATION 



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X(METERS) 



Figure 1. Nomogram for free space transmission between parallel doublets. 



"path factor." The nomogram, Figure 1, gives this 

 relation for G 1 = G- 2 = A P = 1. Often the electric field 

 at the position of the receiver is desired. It is given by 



E = ^p VPiGiA P) 



(3) 



where E is in volts per meter, Pi in watts. If E is 

 known, the power delivered by the receiving antenna 

 to a matched load is 



E°- 

 120t. 



3X 2 



Sir 



(?2. 



(4) 



The combination of equations (3) and (4) gives again 

 the general transmission formula (2). 



The lower limit of possible receiver sensitivity is 

 set by the thermal noise in the receiving system. At 

 ordinary temperatures the thermal noise power in 

 watts is very approximately 



4 • 10- 15 A/> 



(5) 



where A/ is the radio-frequency bandwidth of the 

 receiver in megacycles. 



The minimum power P mln required for intelligible 

 reception being usually in excess of the thermal noise 

 power, it is customary to use the ratio P mm /P noise 

 expressed in decibels as a measure of the receiver 

 sensitivity. Ten times the logarithm of this ratio 

 (to the base 10) is the sensitivity of the receiver in 

 decibels above thermal noise. 



As may be seen from this brief outline, the problem 

 of transmission in free space is a very simple one from 

 the engineering viewpoint. There are certain ques- 

 tions regarding noise limit, receiver sensitivity, and 

 matching of the load which constitute refinements of 

 the above procedure. They are of interest primarily 

 for those concerned with receiver design; apart from 

 these the problem of power transmission may be con- 

 sidered solved by these formulas. The most impor- 

 tant and difficult part of ultra short wave propagation 

 then becomes the quantitative determination of the 

 path factor A p as a function of the geometry of the 

 transmission path, electromagnetic properties of the 

 ground, refractive properties of the atmosphere, etc 



ss OPTICAL PROPERTIES OF THE 

 EARTH'S SURFACE AND ATMOSPHERE 



Reflection Coefficients 



In dealing with standard propagation it is usually 

 assumed that the ground has electromagnetic prop- 

 erties which are constant over the length of the 

 transmission path. Deviations from this idealized 

 behavior are treated below as diffraction phenomena. 



The electromagnetic properties of the ground 

 are completely described by its complex dielectric 

 constant, 



e c = e r - je t = e r — jQ0a\, (61 



where t r is the relative dielectric constant, a the con- 



