sp08hw10sol1 - ECE329 Spring 2008 HW10 Problem 1 a = 9.3...

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ECE329 Spring 2008 HW10 Problem 1 a) C = π± 0 cosh - 1 ( d/a ) = 9 . 3 · 10 - 12 F/m L = μ 0 π cosh - 1 ( d/a ) = 1 . 2 · 10 - 6 H/m Z 0 = r L C = 359 . b) 3 inches = 0.076 m Z 0 = r L C = 1 2 π ln ± b a ²r μ 0 ± 0 a = b e 2 πZ 0 η 0 = 0 . 076 e 2 π * 50 / 377 = 0 . 033 m Problem 2 v ( z, t ) = e - αz cos( ωt - βz ) (1) ∂v ∂z = - αe - αz cos ( ωt - βz ) + βe - αz sin ( ωt - βz ) ∂i ∂t = α L e - αz cos ( ωt - βz ) - β L e - αz sin ( ωt - βz ) i = α ω L e - αz sin ( ωt - βz ) + β ω L e - αz cos ( ωt - βz ) ∂i ∂z = β 2 - α 2 ω L e - αz sin ( ωt - βz ) - 2 αβ ω L e - αz cos ( ωt - βz ) (2) ∂v ∂t = - ωe - αz sin ( ωt - βz ) (3) Next, using - ∂i ∂z = C ∂v ∂t + G v compare Eqs. 1, 2, and 3. β 2 - α 2 ω L = ω C 2 αβ ω L
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