By Frank Gross

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**Sample text**

73) √ with k = ω µε = 2π/λ The reﬂection coefﬁcient R is normally complex and can alternatively be expressed as R = |R|e− jψ . 75) Factoring the direct path term out of Eq. 76) The magnitude of the second term in Eq. 76) is called the path gain factor F. F is also similar to the height gain deﬁned in Bertoni [9]. 77) This factor is analogous to the array factor for a two-element array separated by a distance of 2h1 . In addition, the point of reﬂection at y is the solution to a simple algebra problem and is given as 30 Chapter Two y = dh1 /(h1 + h2 ).

2. Both regions are nonmagnetic. εr1 = 2, εr2 = 4. 9 Modify Prob. 8 such that the loss tangent in region 1 is zero. If Ei0 = 1, use MATLAB to plot the standing wave pattern for the range −2π < βz < 0. 10 In the oblique incidence case with parallel polarization, as depicted in Fig. 14, both regions are nonmagnetic and εr1 = 1, εr2 = 6. 2 Plane wave at normal incidence on a boundary. 8284, θi = 45◦ . 11 Repeat Prob. 10 but for the perpendicular polarization case as depicted in Fig. 16. 12 Region 1 is free space and region 2 is lossless and nonmagnetic with εr2 = 2, 8, 64.

11 Dielectric boundary with electric ﬂux density. Fundamentals of Electromagnetic Fields 21 operation as in Sec. 2 can be applied to magnetic ﬁelds with the same corresponding values for the relative permeabilities achieving the same results. This is not surprising since electric and magnetic ﬁelds and electric and magnetic media are duals of each other. 7 Planewave Reﬂection and Transmission Coefﬁcients Multipath signals are the consequence of the transmitted signal reﬂecting, transmitting, and diffracting from various structures along the route to the receiver.