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329fall09hw13 - ECE 329 Homework 13 Due Tuesday December 8...

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ECE 329 Homework 13 Due: Tuesday, December 8, 2009, 5 PM 1. A T.L. with characteristic impedance Z 0 = 50 Ω and length l = 0 . 2 λ is terminated with a load Z L = 100 Ω . a) Using a Smith Chart, determine (i) the load reflection coefficient Γ L , (ii) the generalized reflection coefficient Γ( d ) at d = l and (iii) the input impedance Z ( l ) at the generator end. Hand in your marked Smith Chart. Hint: Start by finding the normalized load impedance z L = Z L /Z 0 on the Smith Chart. Express Γ L and Γ( d ) as complex numbers in polar form - i.e., as | Γ | θ . b) Using Z ( l ) from part (a), determine the voltage phasor V ( l ) at the generator end if the generator has an open circuit voltage phasor V g = 10 V and a Thevenin impedance Z g = 50 Ω . c) Given the result of (b), determine V + such that V ( d ) = V + ( e jβd + Γ L e - jβd ) . d) What is the load voltage phasor V (0) given the result of (c)? e) What is the corresponding load current I (0) ? 2. Repeat problem 1 if Z L = 50 Ω . Note, in this “trivial” problem where the load is matched to the T.L., you hardly need a Smith Chart (and don’t need to hand one in for this problem).
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