329sp09hw8sol - ECE-329 Spring 2009 Homework 8 — Solution...

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Unformatted text preview: ECE-329 Spring 2009 Homework 8 — Solution March 19, 2009 1. In material media, the wave parameters are γ = p ( jωμ )( σ + jω ) and η = s jωμ σ + jω . Let us consider the medium parameters μ = μ o = 4 π × 10- 7 H / m , = 81 o ≈ 9 4 π × 10- 9 F / m , and σ = 4 S / m . a) If f = ω 2 π = 10 3 Hz , the propagation constant is γ = r ( j 2 π × 10 3 × 4 π × 10- 7 )(4 + j 2 π × 10 3 × 9 4 π × 10- 9 ) = 2 π × 10- 2 p j 8- 9 × 10- 6 = 0 . 126 + j . 126 m- 1 , and the intrinsic impedance is η = s j 2 π × 10 3 × 4 π × 10- 7 4 + j 2 π × 10 3 × 9 4 π × 10- 9 = 4 π × 10- 2 s j 8 + j 9 × 10- 6 = 3 . 1416 × 10- 2 + j 3 . 1416 × 10- 2 Ω . b) Above, α = 0 . 126 m- 1 and β = 0 . 126 m- 1 , then the penetration depth and the wavelength are δ = 1 α = 7 . 958 m and λ = 2 π β = 50 m . c) If f = ω 2 π = 10 9 Hz, the propagation constant is γ = r ( j 2 π × 10 9 × 4 π × 10- 7 )(4 + j 2 π × 10 9 × 9 4 π × 10- 9 ) = 20 π p j 8- 9 = 77 . 48 + j 203 . 8 m- 1 , and the intrinsic impedance is η = s j 2 π × 10 9 × 4 π × 10- 7 4 + j 2 π × 10 9 × 9 4 π × 10- 9 = 40 π s j 8 + j 9 = 33 . 85 + j 12 . 87Ω . In this case, α = 77 . 48 m- 1 and β = 203 . 8 m- 1 , then the penetration depth and the wavelength are δ = 1 α = 1 . 291 × 10- 2 m and λ = 2 π β = 3 . 083 × 10- 2 m . 1 ECE-329 Spring 2009 2. The magnetic field of a plane wave propagating in a non-magnetic material ( μ = μ o = 4 π × 10- 7 H / m) is given by H = 25 e- z cos(8 π · 10 6 t- √ 3 z- π 3 ) ˆ x A m ....
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This note was uploaded on 11/16/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.

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329sp09hw8sol - ECE-329 Spring 2009 Homework 8 — Solution...

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