329fall08hw13sol - ECE-329 Fall 2008 Homework 13 —...

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Unformatted text preview: ECE-329 Fall 2008 Homework 13 — Solution December 13, 2008 1. Problem 1 r=2 r=0 r=1 r= ∞ x=1/2 x=0 x=1 x=2 x=-1/2 x=-1 x=-2 1 ECE-329 Fall 2008 2. Problem 2 a) Normalized load impedance z L = 100 50 = 2 Load reflection coefficient Γ L = 2- 1 2+1 = 1 3 Generalized reflection coefficient Γ( l ) = 1 3 e- j 4 π/ 5 = 1 3 e- j 2 . 513 Normalized input impedance at the generator z ( l ) = 1+Γ( l ) 1- Γ( l ) = 0 . 539- j . 237 Input impedance at the generator Z ( l ) = 50 · z ( l ) = 26 . 93- j 11 . 87Ω b) Voltage phasor at the generator V ( l ) = 10 · Z ( l ) 50+ Z ( l ) = 3 . 78 e- j . 262 V c) Voltage phasor of incident wave V + = 5 e- j 2 π/ 5 = 5 e- j 1 . 257 V d) Voltage phasor at the load V (0) = V + (1 + Γ L ) = 20 3 e- j 2 π/ 5 = 6 . 66 e- j 1 . 257 V e) Current phasor at the load I (0) = V (0) Z L = 1 15 e- j 2 π/ 5 = 0 . 066 e- j 1 . 257 A Γ(0) Γ ( l ) 3. Problem 3 a) Normalized load impedance z L = 50 50 = 1 Load reflection coefficient Γ L = 1- 1 1+1 = 0 , Generalized reflection coefficient...
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329fall08hw13sol - ECE-329 Fall 2008 Homework 13 —...

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