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2-14 Refraction changes path length
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EM wave propagation phenomena 25 The value of N tends to vary from about 280 to 320, and both n and N vary with altitude In nonhomogeneous atmospheres (the usual case), these parameters will vary approximately linearly for several tenths of a kilometer All but a few microwave relay systems can assume an approximately linear reduction of n and N with increasing altitude, although airborne radios and radars cannot There are two methods for calculating N: N= and N= where P is the atmospheric pressure in millibars (1 torr = 13332 mbar) T is temperature in kelvins es is saturation vapor pressure of atmospheric water in millibars Hrel is the relative humidity expressed as a decimal fraction (rather than a percentage) Ray path curvature (K) can be expressed as a function of either n or N, provided that the assumption of a linear gradient dn/dh holds true: K= 1+ or K= 1+ 1 dN /dh 157 [222] 1 rodn dh [221] 776 T 373 105es T2 [220] 776 T P+ 4810esHrel T [219]
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For the near-surface region, where dn/dh varies at about 39 10 8 m, the value of K is 133 For most terrestrial microwave paths, this value (K = 4 3 = 133) is called a standard refraction, and is used in calculations in the absence of additional data For regions above the linear zone close to the surface, you can use another expression of refractivity: Na = Nse where N1 is the refractivity at 1 km altitude hr is the height of the receiver antenna ht is the height of the transmit antenna
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26 Radio-wave propagation Ce = Ln(Ns /N1) Na is the refractivity at altitude Ns is the refractivity at the earth s surface For simple models close to the surface, you can use the geometry shown in Fig 2-15 Distance d is a curved path along the surface of the earth But because the earth s radius ro is about 4000 statute miles, and it is thus very much larger than a practical antenna height h, you can simplify the model in Fig 2-15A to that in Fig 2-15B The underlying assumption is that the earth has a radio radius equal to about 4 3 (K = 133) of the actual physical radius of its surface
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2-15B Simplified geometry
EM wave propagation phenomena 27 The value of distance d is found from the expression d= where d is the distance to the radio horizon in statute miles ro is the normalized radius of the earth hft is the antenna height in feet Accounting for all constant factors, the expression reduces to d = 1414 h ft [225] 2rchft [224]
all factors being the same as defined above Example 2-1 A radio tower has a UHF radio antenna that is mounted 150 feet above the surface of the earth Calculate the radio horizon (in statute miles) for this system Solution: d = 1414 (ht)t = (1414)(150 ft)1/2 = (1414)(1225) = 1732 mi For other units of measurement: dnmi = 123 and dkm = 130 hft km [227] hft nmi [226]
Surface-wave communications The surface wave travels in direct contact with the earth s surface, and it suffers a severe frequency-dependent attenuation because of absorption by the ground The surface wave extends to considerable heights above the ground level, although its intensity drops off rapidly at the upper end The surface wave is subject to the same attenuation factors as the space wave, but in addition, it also suffers ground losses These losses are caused by ohmic resistive losses in the conductive earth, and to the dielectric properties of the earth In other words, the signal heats up the ground Horizontally polarized waves are not often used for surface wave communications because the earth tends to short-circuit the E-field component On vertically polarized waves, however, the earth offers electrical resistance to the E-field and returns currents to following waves (Fig 2-16) The conductivity of the soil determines how much energy is returned Table 2-1 shows the typical conductivity values for several different forms of soil
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