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Problems
c. Had you used Equation P2.1 to determine the polarization, you would get the same answer as that for (b). Check this out by drawing the diagram like Figure 2.6b or c. d. Determine the instantaneous power density S( x , t) and active power density < SR ( x) > . P2.9 A conducting film of impedance 377 Ω/square is placed a quarter-wavelength in air from a plane conductor (PEC) to eliminate wave reflection at 9 GHz. Assume negligible displacement currents in the film. Plot a curve showing the fraction of incident power reflected versus frequency for frequencies 6–18 GHz.
377 Ω/sq. PEC
Free space d = λ/4
P2.10 Calculate the reflection coefficient and percent of incident energy reflected when a uniform plane wave is normally incident on a Plexiglas radome (dielectric window) of thickness 3/8″, relative permittivity εr = 2.8, with free space on both sides. λ0 = 20 cm. Repeat for λ0 = 10 cm. Repeat for λ0 = 3 cm. Comment on the results obtained. P2.11 A green ion laser beam, operating at λ0 = 5.45 μm, is generated in vacuum, and then passes through a glass window of refractive index 1.5 into water with n = 1.34. Design a window to give zero reflection at the two surfaces for a wave polarized with E in the plane of incidence, that is, find θB2 − θB1.
θB2 θB1 n1 = 1
n3 = 1.34
n2 = 1.5
P2.12 The transmitting antenna of a ground-to-air communication system is placed at a height of 10 m above the water, as shown in the figure. For a separation of 10 km between the transmitter and the receiver, which is placed on an airborne platform, find the height h2 above water of the receiving system so that the wave reflected by the water does not possess a parallel-polarized component. Assume that the water surface is flat and lossless. [Reference 2 of Chapter 2]
h2 ε0, μ0
10 m
Water (εr = 81) 104 m
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P2.13 A source Vgs = 60∠0° with internal impedance 200 Ω is connected to a resistive load ZL1 = 200 Ω by a two-wire lossless transmission line in air (velocity of propagation c = 3 × 108 m/s) of length l1 = 10 cm and characteristic impedance
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