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329fall10hw12sol

# 329fall10hw12sol - ECE 329 Fall 2010 Homework 12 Solution...

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Unformatted text preview: ECE 329 Fall 2010 Homework 12 - Solution Due: Dec. 8, 2010 1. a) (i) z L = Z L /Z = 2 . Locating the point z L on the Smith Chart, we can nd the corresponding Γ L = 0 . 333 . (ii) (iii) Rotating along the constant | Γ | circle towards the generator (clockwisely) by a distance l = 0 . 2 λ , we nd Γ( l ) = 0 . 333 ∠ θ , where θ =- . 2 λ . 25 λ × 180 o =- 144 o , and z ( l ) = 0 . 54- j . 24 . Then, Z ( l ) = Z · z ( l ) = 27 .- j 12 . 0 (Ω) . b) V ( l ) = Z ( l ) Z ( l ) + Z g V g = 27 .- j 12 . 27 .- j 12 . 0 + 50 × 10 = 3 . 66- j . 99 = 3 . 79 ∠- 15 . 1 o ( V ) . c) V ( l ) = V + e jβl + Γ L e- jβl = V + ( e j . 4 π + 0 . 333 e- j . 4 π ) , ∴ V + = 1 . 54- j 4 . 77 = 5 . 01 ∠- 72 . 1 o ( V ) . d) V (0) = V + (1 + Γ L ) = V + × (1 + 0 . 333) = 2 . 05- j 6 . 36 = 6 . 68 ∠- 72 . 1 o ( V ) . e) I (0) = V (0) Z L = 0 . 0205- j . 0636 = 0 . 0668 ∠- 72 . 1 o ( A ) . 1 ECE 329 Fall 2010 2. a) VSWR = | V | max | V | min = 8 . 4 ( V ) 2 . 1 ( V ) = 4 . b) Adjacent voltage minimums are separated by a distance of . 5 λ , and d . 5 λ = 5+ . 092 λ . 5 λ , therefore d min = 0 . 092 λ. c) Draw the constant | Γ | circle crossing the point A : z = VSWR (corresponding to voltage maxi- mum) on the real Γ axis. Then the other crossing point B (opposite to the point A ) corresponds...
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