EARTH CONSTANTS IN THE MICROWAVE RANGE 



139 



However, the experimental setup was portable in 

 this case, which proved to be advantageous. 



It seems desirable to give first the results obtained 

 under the best-defined conditions^'- (9 cm) for a 

 variety of grounds and compare those with the re- 

 sults of the 10-cni waves obtained under less well- 

 defined conditions.^ The latter results are given al- 

 ways in graphical form. 



The grazing angle interval (0° to about 30°) ex- 

 l^lored with the 10-cm waves was quite large, and a 

 grajDhical representation of the results is well justi- 

 fied. At 9 cm only three or at most four angles of in- 

 cidence were investigated. 



The schematic representation of the experimental 

 setup is given in Figure 3. If p denotes the ratio of 



TRANSMITTER 



Figure 3. Idealized geometry of the experhnent 



the amplitude of the reflected wave to that of the 

 incident wave in the vicinity of the reflecting sur- 

 face, then at the position of the receiver the total field 

 received in case of reinforcement is 



-Emax = E -\- kpE. 

 E is the field strength of the direct wave and k is a 

 correction factor taking into account the directivity 

 of the transmitter and receiver as well as the increased 

 path length of the reflected ray as compared to that 

 of the direct ray. In case of phase opposition 



These lead to 



P' = kp 



£„i„ = E - kpE. 



(■E'max / -Emin) + 1 



Throughout the work at 10 cm this corrected reflec- 

 tion coefficient (kp) or p' has been investigated. Pre- 

 sumably A- is nearly unity so that p' = p. 



Very Dry Sandy Ground. Table 1, for 9 cm, refers 

 to very dry ground. In order to obtain a precise value 



of the complex dielectric constant of this very dry 

 sandy ground its absorption coefficient was measured 

 directly. The measurement was made by interposing 

 a filled container between transmitter and receiver. 



Table 1. Reflection coefficients of very dry sandy ground 

 for X = 9 cin.i>2 



Grazing 

 angle Vertical polarization 

 degrees Calculated Observed 



Horizontal polarization 

 Calculated Observed 



The container, a wooden trough, had ^ in. plate 

 glass ends, 18 in. square, one of which was movable, 

 thus allowing a test of the absorber up to a thickness 

 of 12 in. The most suitable values of cr (real part 

 of the complex dielectric constant tc) and conductivity 

 (J or ej = 60 a\ (imaginary part of the comijlex 

 dielectric constant) which fit the reflection and ab- 

 sorption coefficient data were found to be (.r = 2,, a 

 = 0.033 mho per meter, e; = 0.18. 



It should be mentioned here that the calculated 

 reflection coefficients were obtained by using the gen- 

 eralized Fresnel formulas for reflection of electro- 

 magnetic waves by plane dielectric surfaces. The in- 

 cident waves travel in vacuum (or air) and fall on 

 the plane surface of a dielectric at the grazing angle \p. 

 The complex dielectric constant tc is 



«c = fr — jii , 



= (r — j 60 O-X , 



where Cr is the real part of the dielectric constant and 

 ti = GOaX is its imaginary part, o- is the conductivity 

 of the dielectric medium in mhos per m, and A is the 

 wavelength, in vacuum, of the incident radiation. 

 The generalized Fresnel formulas, for horizontally 

 and vertically polarized waves, respectively, are 



sin ^ — (ec — cos^i/')^ 

 sin* + (e<; — cos- i/)' 



■i't; _ ec sin *■ — ( ec— cos- \p f 

 tc sin *■ -|- ( e,,— cos- ^ f 



P,e ' " = 



P.e 



(horizontal) 



(vertical), 



where p denotes the magnitude of the complex reflec- 

 tion coefficient and i// is the angle of lag of the 

 reflected component behind the incident component 

 of the electric field. 



The results at 10 cm and for dry sand are given 

 in Figure 4. The theoretical curves given on the 



