So, the modi ed coherent component of the total eld intensity is Ico mod in .NET

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So, the modi ed coherent component of the total eld intensity is Ico mod
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where c is the grazing angle de ned earlier, r1 is the distance of the direct radio path between the antennas, r2 is the distance from the transmitter to the point of re ection and from the point of re ection to the receiver, that is the radio path length of the q re ected wave. The equivalent surface impedance is Z emr pe1 , with the
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relative permeability mr % 1, for all nonferromagnetic surfaces. There are six distinct cases that can be considered here, three for each linear polarization, vertical and horizontal. These three asymptotic cases are valid a) for short correlation lengths L and all grazing angles c; b) for long correlation length L and large grazing angles c; c) for long correlation length L and small grazing angles c.
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So, for vertical polarization, the effective surface impedance Z has a real part corresponding to a loss of power and an imaginary part corresponding to a reactive,
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ELECTROMAGNETIC ASPECTS OF WAVE PROPAGATION OVER TERRAIN
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stored energy near the surface. Furthermore, the change in effective surface impedance for vertical polarization is strictly reactive for short correlation lengths l ) L , resistive for large correlation lengths and large grazing angles (l ( L and c ) p1 ), and a mixture of both for large correlation lengths and small grazing kL angles (l ( L and c ( p1 ). For the case of a horizontally polarized eld the kL surface impedance and the corresponding effective permittivity can be derived in a similar fashion. In the case of low antenna elevation with respect to roughness, the criteria of s ! l and s ) l are generally valid and the Rayleigh scalar factor can be used as long as the criteria of the Kirchhoff approximation are ful lled. In this case, instead of the specular re ection coef cients, we introduce the following effective re ection coef cients [9 16] a) for vertical polarization  s 2 ! Gef GV exp 2 2p sin c V l 4:77
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h 2 i where exp 2 2p s sin c is the Rayleigh s factor; the coef cient GV is l de ned by (4.50b) in Section 4.3 and can be reduced to er GV 1 2c p er 1 4:78
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b) for horizontal polarization
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 s 2 ! Gef GH exp 2 2p sin c H l
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where GH is de ned by (4.50a) in Section 4.3 and can be reduced to 1 GH 1 2c p er 1 4:80
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So, the use of each approximation strongly depends not only on the dimensions of rough structures with respect to the wavelength, but mostly on the terminal antenna elevations as well. 4.5. PROPAGATION ABOVE A SMOOTH CURVED TERRAIN Let us now consider the case when the terrain is smooth but curved (see Fig. 4.18). In this case the degree of curvature and diffraction caused by the curved earth surface must be taken into account for the evaluation of eld characteristics. In practice, for
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FIGURE 4.18. Geometrical presentation of radio path above a curved terrain.
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land communications, it is very important to note that the in uence of the curvature of the Earth s surface must be taken into account only for radio paths longer than 20 30 km. Fock s Model. To take into account the terrain curvature and diffraction from the curved terrain, Fock, by introducing two special scales: the range scale, L lR2 =p 1=3 , and the height scale, H 0:5 l2 Re =p2 1=3 , respectively, has e determined the range of radio path, d, and the heights of both terminal antennas, hT and hR , using the dimensionless parameters x d=L, y1 hT =H, y2 hR =H. The attenuation factor with respect to the at terrain has a form [28]   1 p X exp ixtk A tk y1 A tk y2    F 2 px   k 1 tk p2 A tk A tk  p p i pRe =l 1=3 = er0 i60ls 4:81
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