Fall2023 ECE3120 Homework5 Solutions

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3120

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Electrical Engineering

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Oct 30, 2023

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1/5 ECE3120 (Fall 2023) Homework #5 Solutions October 5, 2023 1. A uniform plane wave in a lossy medium has a phase constant of 1.6 𝑟𝑎?/𝑚 at 10 7 𝐻?, and its magnitude is reduced by 60% for every 2 𝑚 traveled. Find the skin depth and speed of the wave. Solutions:
2/5 2. A nonmagnetic medium has an intrinsic impedance of 240∠30° (Ω). Find the below. (a) Loss tangent (b) Dielectric constant (c) Complex permittivity (d) Attenuation constant at 1 𝑀𝐻? Solutions:
3/5 3. In a certain medium, 𝐸 ⃗ = 16? −0.1𝑦 sin(2 × 10 8 𝑡 − 𝛽?) ? ̂ (𝐴/𝑚) Find the below. (a) Propagation constant. (b) Wavelength (c) Velocity of the wave (d) Skin depth Solutions:
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4/5 4. Which of the following media may be treated as conducting at 8 𝑀𝐻? ? (a) Wet marshy soil (𝜀 = 15𝜀 0 , 𝜇 = 𝜇 0 , 𝜎 = 10 −2 𝑆/𝑚) (b) Intrinsic germanium (𝜀 = 16𝜀 0 , 𝜇 = 𝜇 0 , 𝜎 = 0.025 𝑆/𝑚) (c) Seawater (𝜀 = 81𝜀 0 , 𝜇 = 𝜇 0 , 𝜎 = 25 𝑆/𝑚) Solutions:
5/5 5. Seawater plays a vital role in the study of submarine communications. Assuming that for seawater, 𝜎 = 4 𝑆/𝑚, 𝜀 𝑟 = 80, 𝜇 𝑟 = 1, and ? = 100 𝑘𝐻?, calculate the below. (a) Phase velocity (b) Wavelength (c) Skin depth (d) Intrinsic impedance Solutions:

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