Fall2023 ECE3120 Homework4 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 #4 Solution September 28, 2023 1. An EM wave propagating in a certain medium is described 𝐸 ⃗ = 25 sin(2𝜋 × 10 6 ? − 6?)?̂ (𝑉 𝑚) ⁄ (a) Determine the direction of wave propagation (b) Compute the period ?, the wavelength ?, and the phase velocity ? 𝑝 . (c) Sketch the wave at ? = 0, ? 8 ⁄ , ? 4 ⁄ , ? 2 ⁄ . Solution:
2/5 2. A certain material has a dielectric constant of 4.2 and a conductivity of 1.26 × 10 −3 ? 𝑚 ⁄ at 20 𝑀𝐻?. Calculate its complex permittivity. Solution: 3. For a wave characterized by the electric field 𝐸 ⃗ (?, ?) = ? ̂𝑎 ? cos(𝜔? − 𝑘?) + ? ̂𝑎 ? cos(𝜔? − 𝑘? + ?) identify the polarization state, determine the polarization angles ( ?, 𝜒) , and sketch the locus of 𝐸 ⃗ (0, ?) for each of the following cases: (a) 𝑎 ? = 3 𝑉 𝑚 ⁄ , 𝑎 ? = 4 𝑉 𝑚 ⁄ , and ? = 0. (b) 𝑎 ? = 3 𝑉 𝑚 ⁄ , 𝑎 ? = 4 𝑉 𝑚 ⁄ , and ? = 180°. (c) 𝑎 ? = 3 𝑉 𝑚 ⁄ , 𝑎 ? = 3 𝑉 𝑚 ⁄ , and ? = 45°. (d) 𝑎 ? = 3 𝑉 𝑚 ⁄ , 𝑎 ? = 4 𝑉 𝑚 ⁄ , and ? = −135°.
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4/5 4. The electric field of an elliptically polarized plane wave is given by 𝐸 ⃗ (?, ?) = [−? ̂10 sin(𝜔? − 𝑘? − 60°) + ? ̂30 cos(𝜔? − 𝑘?)] (𝑉 𝑚) ⁄ Determine (a) the polarization angles ( ?, 𝜒) and (b) the direction of rotation.
5/5 5. The magnetic field component of an EM wave propagating through a nonmagnetic medium ( ? = ? 0 ) is 𝐻 ⃗ = 25 sin(2 × 10 8 ? + 6?)? ̂ (𝑚𝐴 𝑚) ⁄ Determine the below. (a) The direction of wave propagation. (b) The permittivity of the medium. (c) The electric field intensity. Solution:

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