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161_1_MT2_soln

# 161_1_MT2_soln - EE161 Midterm#2 Solutions(Fall 2006 1 In...

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EE161 Midterm #2 Solutions (Fall 2006) 1. In this problem, we use the microstrip as a quarter wavelength transformer to match the impedance of a coax line to a resistive load. (a) The characteristic impedance of the coax line is Z coax = η ln b a 2 π = η ε r ln b a 2 π = 120 π 2 . 25 ln 1 . 75 0 . 5 2 π = 50 . 11Ω (b) Parallel plate waveguide model is used to analyze the microstrip impedance trans- former, therefore, the dominant mode is TEM mode. β = k = ω με = 2 πf ε r C = 2 π × 3 × 10 9 10 . 3 3 × 10 8 = 201 . 65 rad / m u p = ω β = ω ω με = C ε r = 3 × 10 8 10 . 3 = 9 . 35 × 10 8 m / s λ g = 2 π β = 2 π 201 . 65 = 3 . 12 cm (c) The microstrip works as a quarter wavelength transformer, therefore, L = λ g 4 = 3 . 12cm 4 = 7 . 8 mm Z ms = radicalbig Z L Z coax = 18 × 50 . 11 = 30 . 03 Ω Z ms = η 0 t ε r W = 120 π × 10 - 3 10 . 3 × W = 30 . 03 W = 3 . 91 mm 2. 5GHz is the cutoff frequency of the dominant mode. (a) Since b < 1 . 5 b = a < 2 b , the dominant mode is TE 10 mode.

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161_1_MT2_soln - EE161 Midterm#2 Solutions(Fall 2006 1 In...

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