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329sp09hw12 - ECE 329 Homework 12 Due Wed 5PM 1 Two...

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Unformatted text preview: ECE 329 Homework 12 Due: Wed, Apr 22, 2009, 5PM 1. Two T.L.’s with characteristic impedances Z 1 and Z 2 are joined at a junction that also includes a “shunt” resistance R as shown in the diagram below. R Z 1 Z 2 z v ++ v +- v- Z 1 v ++ /Z 2 v + + v- +- +- Assume that a voltage wave v + ( t- z v p 1 ) from the left produces reflected and transmitted waves v- ( t + z v p 1 ) and v ++ ( t- z v p 2 ) on lines 1 and 2 traveling to the left and right, respectively, on two sides of the junction. Using an abbreviated notation, Kirchhoff’s voltage and current laws (KVL and KCL) applied at the junction can be expressed as v + + v- = v ++ and v + Z 1- v- Z 1 = v ++ Z eq , where Z eq ≡ RZ 2 R + Z 2 is the parallel combination of R and Z 2 . a) Verify the KVL and KCL equations given above, explaining carefully how they are obtained. b) Solve the KVL and KCL equations above to obtain the reflection and transmission coefficients Γ 12 ≡ v- v + and τ 12 = v ++ v + for the junction....
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329sp09hw12 - ECE 329 Homework 12 Due Wed 5PM 1 Two...

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