311ps2sol - ECE311 Autumn 2011 Problem Set 2 Solutions...

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Unformatted text preview: ECE311 Autumn 2011: Problem Set 2 Solutions Problem 1 a) Model microstrip as a parallel plate line. Neglecting any loss, we then have Z = √ µ/ϵ d w ≈ η d w = 377 √ 3 . 9 1 . 6 × 10 − 4 w = 90 Ω Solve to find w ≈ . 339 mm b) λ = 2 π β = 2 π ω √ µ o ϵ = 2 π (3 × 10 8 ) (2 π (5 × 10 8 )) √ 3 . 9 = 0.304 m c) Phase velocity, v p , = 1 √ µϵ = 3 × 10 8 √ 3 . 9 = 1 . 5192 × 10 8 m/s. To go 0.08 m at this speed take . 08 1 . 5192 × 10 8 = 0.527 nS d) R ′ = 2 w √ πfµ c σ c = 2 3 . 39 × 10 − 4 √ π (5 × 10 8 )(4 π × 10 − 7 ) 5 . 7 × 10 7 = 34 . 72 Ω/m L ′ = µd w = (4 π × 10 − 7 )(1 . 6 × 10 − 4 ) 3 . 39 × 10 − 4 = 0 . 59 µ H/m C ′ = ϵw d = 3 . 9(8 . 854 × 10 − 12 )(3 . 39 × 10 − 4 ) 1 . 6 × 10 − 4 = 0 . 07 nF/m G ′ = 0 Find complex propagation constant γ = √ ( R ′ + jωL ′ )( G ′ + jωC ′ ) = 0 . 1928 + j 20 . 6955 Attenuation constant = 0.1928 Np/m = (0.1928)(8.6859) = 1.6746 dB/m This would have 4 dB attenuation in...
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311ps2sol - ECE311 Autumn 2011 Problem Set 2 Solutions...

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