KADIO PROPAGATION FUNDAMENTALS 615 



(which can happen only with vertical polarization) the reflection coeffi- 

 cient approaches +1. The angle for which the reflection coefficient is a 

 minimum is called the pseiido-Brewster angle and it occurs for sin 6 



For antennas approaching ground level the first two terms in (3) 

 cancel each other Qii and ho approach zero and R approaches —1) and 

 the magnitude of the third term becomes 



'^^ ^^^^'^2x^"l^ (11) 



where ha = minimum effective antenna height shown in Fig. 3 

 X 



The surface wave term arises because the earth is not a perfect re- 

 flector. Some energy is transmitted into the ground and sets up ground 

 currents, which are distorted relative to what would have been the case 

 in an ideal perfectly reflecting surface. The surface wave is defined as 

 the vertical electric field for vertical polarization, or the horizontal 

 electric field for horizontal polarization, that is associated with the extra 

 components of the ground currents caused by lack of perfect reflection. 

 Another component of the electric field associated with the ground 

 currents is in the direction of propagation. It accounts for the success of 

 the wave antenna at lower frequencies, but it is always smaller in magni- 

 tude than the surface wave as defined above. The components of the 

 electric vector in three mutually perpendicular co-ordinates are given 

 by Norton." 



In addition to the effect of the earth on the propagation of radio waves, 

 the presence of the ground may also affect the impedance of low antennas 

 and thereby may have an effect on the generation and reception of radio 

 waves.2^ As the antenna height \'aries, the impedance oscillates around 

 the free space value, but the variations in impedance are usually unim- 

 portant as long as the center of the antenna is more than a quarter- 

 wavelength above the ground. For vertical grounded antennas (such as 

 are used in standard AM broadcasting) the impedance is doubled and the 

 net effect is that the maximum field intensity is 3 db above the free space 

 value instead of 6 db as indicated in (4) for ele\'ated antennas. 



Typical \'alues of the field intensity to be expected from a grounded 

 quarter-wave vertical antenna are shown in Fig. 12 for transmission over 

 poor soil and in Fig. 13 for transmission over sea water. These charts in- 



