Chapter 12: Problem 7
The semi-infinite regions \(z<0\) and \(z>1 \mathrm{~m}\) are free space. For
\(0
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chapter 12: Problem 7
The semi-infinite regions \(z<0\) and \(z>1 \mathrm{~m}\) are free space. For
\(0
These are the key concepts you need to understand to accurately answer the question.
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Get started for freeRegion 1, \(z<0\), and region \(2, z>0\), are both perfect dielectrics ( \(\mu=\mu_{0}\), \(\epsilon^{\prime \prime}=0\) ). A uniform plane wave traveling in the \(\mathbf{a}_{z}\) direction has a radian frequency of \(3 \times 10^{10} \mathrm{rad} / \mathrm{s}\). Its wavelengths in the two regions are \(\lambda_{1}=\) \(5 \mathrm{~cm}\) and \(\lambda_{2}=3 \mathrm{~cm}\). What percentage of the energy incident on the boundary is \((a)\) reflected; \((b)\) transmitted? \((c)\) What is the standing wave ratio in region \(1 ?\)
A \(50-\mathrm{MHz}\) uniform plane wave is normally incident from air onto the surface of a calm ocean. For seawater, \(\sigma=4 \mathrm{~S} / \mathrm{m}\), and \(\epsilon_{r}^{\prime}=78 .(a)\) Determine the fractions of the incident power that are reflected and transmitted. (b) Qualitatively, how (if at all) will these answers change as the frequency is increased?
A \(T=20\) ps transform-limited pulse propagates through \(10 \mathrm{~km}\) of a dispersive medium for which \(\beta_{2}=12 \mathrm{ps}^{2} / \mathrm{km}\). The pulse then propagates through a second \(10 \mathrm{~km}\) medium for which \(\beta_{2}=-12 \mathrm{ps}^{2} / \mathrm{km}\). Describe the pulse at the output of the second medium and give a physical explanation for what happened.
A wave starts at point \(a\), propagates \(1 \mathrm{~m}\) through a lossy dielectric rated at \(0.1 \mathrm{~dB} / \mathrm{cm}\), reflects at normal incidence at a boundary at which \(\Gamma=0.3+j 0.4\), and then returns to point \(a .\) Calculate the ratio of the final power to the incident power after this round trip, and specify the overall loss in decibels.
A right-circularly polarized plane wave is normally incident from air onto a semi-infinite slab of plexiglas \(\left(\epsilon_{r}^{\prime}=3.45, \epsilon_{r}^{\prime \prime}=0\right) .\) Calculate the fractions of the incident power that are reflected and transmitted. Also, describe the polarizations of the reflected and transmitted waves.
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