# sp08hw12sol1 - ECE329 Spring 20008 Homework 12 Problem 1 Γ...

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Unformatted text preview: ECE329 Spring 20008 Homework 12 Problem 1 Γ r- r r + 1 2 + Γ 2 i = " r 2 + x 2- 1 ( r + 1) 2 + x 2 !- r r + 1 2 # + 2 x ( r + 1) 2 + x 2 ! 2 = ( r 2 + x 2 + 1 ) ( r + 1)- r ( r + 1) 2 + x 2 ( r + 1) ( r + 1) 2 + x 2 2 + 2 x ( r + 1) ( r + 1) ( r + 1) 2 + x 2 2 = h ( r 2 + x 2 + 1 ) ( r + 1)- r ( r + 1) 2 + x 2 i 2 + (2 x ( r + 1)) 2 ( r + 1) 2 ( r + 1) 2 + x 2 = (- 2 r- r 2 + x 2- 1 ) 2 + 4 x 2 ( r 2 + 2 r + 1 ) ( r + 1) 2 ( r + 1) 2 + x 2 = 1 ( r + 1) 2 (Γ r- 1) 2 + Γ i- 1 x = " r 2 + x 2- 1 ( r + 1) 2 + x 2 !- 1 # 2 + " 2 x ( r + 1) 2 + x 2 !- 1 x # 2 = x ( r 2 + x 2- 1)- x (( r + 1) 2 + x 2 ) x ( r + 1) 2 + x 2 2 + 2 x 2- ( r + 1) 2- x 2 x ( r + 1) 2 + x 2 2 = x 2 (- 2 r- 2) 2 + ( x 2- r 2- 2 r- 1) 2 x 2 ( r + 1) 2 + x 2 2 = 1 x 1 r=2 r=0 r=1 r= ∞ x=1/2 x=0 x=1 x=2 x=-1/2 x=-1 x=-2 Problem 2 Note that Z (0) = 100- 100 j represents the unnormalized load impedance while z (0) = 1 Z Z (0) = 2- 2 j is normalized load impedance. In most cases below, I've listed the unnormalized load impedance.normalized load impedance....
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sp08hw12sol1 - ECE329 Spring 20008 Homework 12 Problem 1 Γ...

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