PROPAGATION FACTORS IN THE INTERFERENCE REGION 



67 



and propagation over land, there is practically no 

 difference in intensity between a horizontally and a 

 vertically polarized radiation field. For X < 1 meter 

 there is, similarly, no difference for propagation over 

 .sea water. When there is a difference, as for low 

 antennas, horizontal polarization gives a smaller 

 gain; but as the antennas are raised, the two cases 

 approach equality (see Section 5.7.4). 



PROPAGATION FACTORS 

 IN THE INTERFERENCE REGION 



5.2.1 



Propagation Factors 



The factors affecting gain in the region where the 

 methods of geometrical optics may be applied are 

 discussed in Sections 5.2 to 5.5 inclusive. 



5.2.2 



Spreading Effect 



From the formula of equation (1) in Chapter 2, 

 for the field intensity components of the radiation 

 field, it follows that for distances from the transmit- 

 ter large in comparison to the wavelength, the domi- 

 nant term falls off inversely as the distance from the 

 transmitter, or 





(24) 



where Ei is the field strength at unit distance. This 

 means that the power per unit area in the radiation 

 field varies inversely as the square of the distance. 

 This spreading effect is the consequence of the fact 

 that the energy of the wave is distributed over larger 

 and larger areas as the wave progresses away from 

 the transmitter. 



5.2.3 



Interference 



When a wave travels over a conducting surface, 

 constructive and destructive interference occurs 

 between the direct wave from the transmitter and 

 the wave reflected by the surface. This is illustrated 

 in Figure 8, which is drawn for a plane earth. If 

 there is no energy lost in reflection, the direct and 

 reflected ^^aves are of equal intensitj'', and their 

 resultant varies from zero to twice the free-space 

 value, depending upon the phase difference between 

 the two components. The reflected wave lags the 



direct wave bj^ an angle 5 + c/), where 8 is the phase 

 retardation caused by the greater path length 



BECT ba;^ 



Figure 8. 

 earth. 



Geometry for radio propagation over a plane 



traversed by the reflected wave and cj) is the phase lag 

 occiu'ring at reflection. 



Figure 9 shows the vector diagram for the case 

 where the phase shift at reflection is <^ = 180 degrees. 



i,Eo 



Eo=Er 



Figure 9. Vector diagram showing tlie addition of 

 the direct and reflected waves iovcp = 180° and p = 1. 



This condition holds for horizontally polarized 

 radiation of frequency above 100 megacycles, re- 

 flected from sea water at grazing angles of less than 

 10 degrees. The resultant electric field is equal to 



E 



=V" 



Eo- + E/ - 2EoEr cos 5 



= y^{E,- Er)- + ^E,ErSin^- 



(25) 



If the reflection is complete, as from a conductor of 

 infinite conductivity, 



Er = E,, E = 2Eosm~. (26) 



^■^■* Imperfect Reflection 



In general, the strength of the reflected wave E, 

 is less than that of the incident wave £,-, partly be- 

 cause of diffuse reflection and partly because some 

 energy is refracted into the surface and absorbed. 



