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The magnitude of h is ZhZ 2s7.2894 107d2 1.383 109 From Eq. (5.13): p h Zh Z ax0.0527 The dot product of p and f is p f 0.0527 0 ( 0.0046) 1.356 108 km2 8.3 107 0.9986 1.35 108 ay0.0046 az0.9986 s 6.3214 106d2 s1.3812 109d2
1 dx f (x)
(1.35
cles (as in Fig. 9.3), but also not entering a zone on the table designated by a border as in the program of Fig. 9.2.
108)2
HINT:
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5.4 Cross-Polarization Discrimination The propagation path between a satellite and earth station passes through the ionosphere, and possibly through layers of ice crystals in the upper atmosphere and rain, all of which are capable of altering the polarization of the wave being transmitted. An orthogonal component may be generated from the transmitted polarization, an effect referred to as depolarization. This can cause interference where orthogonal polarization is used to provide isolation between signals, as in the case of frequency reuse. Two measures are in use to quantify the effects of polarization interference. The most widely used measure is called cross-polarization discrimination (XPD). Figure 5.11a shows how this is defined. The transmitted electric field is shown having a magnitude E1 before it enters the medium which causes depolarization. At the receiving antenna the electric field may have two components, a copolar component, having magnitude E11, and a cross-polar component, having magnitude E12. The cross-polarization discrimination in decibels is defined as XPD 20 log E11 E12 (5.17)
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In each case, we employ the chain rule to show that the derivative of the function on the right is the integrand on the left. (a) Dx x 1 tan 1 a a x 1 1 1 Dx tan 1 = a a a1+ x 2 a 1 1 1 = 2 = 2 a 1 + x2 a + x2 =
Vectors defining (a) cross-polarization discrimination (XPD), and (b) polarization isolation (I).
Does the robot always stay inside Does it ever exit the area What if you try a set of data where there is a break in the virtual wall 4. Line 31 in Fig. 9.6 has a formula that says: m 1.0*(Y2 Y1)/(X2 X1), why not just say: m (Y2 Y1)/(X2 X1) What is the reason for using 1.0 in the formula
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The second situation is shown in Fig. 5.11b. Here, two orthogonally polarized signals, with magnitudes E1 and E2, are transmitted. After traversing the depolarizing medium, copolar and cross-polar components exist for both waves. The polarization isolation is defined by the ratio of received copolar power to received cross-polar power and thus takes into account any additional depolarization introduced by the receiving system (Ippolito, 1986). Since received power is proportional to the square of the electric field strength, the polarization isolation in decibels is defined as I 20 log E11 E21 (5.18)
1 a 1 a2 [a > 0 implies a = [ u v = uv] 1
HINT: See Secs. B.7.1 and B.7.5 for details of on integer and oating-point numbers and operations on these numbers.
When the transmitted signals have the same magnitudes (E1 E2) and where the receiving system introduces negligible depolarization, then I and XPD give identical results For clarity, linear polarization is shown in Fig 511, but the same definitions for XPD and I apply for any other system of orthogonal polarization 55 Ionospheric Depolarization The ionosphere is the upper region of the earth s atmosphere that has been ionized, mainly by solar radiation The free electrons in the ionosphere are not uniformly distributed but form layers Furthermore, clouds of electrons (known as traveling ionospheric disturbances) may travel through the ionosphere and give rise to fluctuations in the signal One of the effects of the ionosphere is to produce a rotation of the polarization of a signal, an effect known as Faraday rotation.
When a linearly polarized wave traverses the ionosphere, it sets in motion the free electrons in the ionized layers These electrons move in the earth s magnetic field, and therefore, they experience a force (similar to that which a current-carrying conductor experiences in the magnetic field of a motor) The direction of electron motion is no longer parallel to the electric field of the wave, and as the electrons react back on the wave, the net effect is to shift the polarization The angular shift in polarization (the Faraday rotation) is dependent on the length of the path in the ionosphere, the strength of the earth s magnetic field in the ionized region, and the electron density in the region Faraday rotation is inversely proportional to frequency squared and is not considered to be a serious problem for frequencies above about 10 GHz.
HINT:
a2 ]
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