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prelim3sol

prelim3sol - ECE 3030 Electromagnetic Fields and Waves Your...

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ECE 3030: Electromagnetic Fields and Waves Fall 2008 Your Name: PRELIM 3 November 24 Instructions: Problem 1: Multi-layer dielectric. a. Wavelengths: λ 1 = 0 . 132 μ m (a quarter wave transformer), λ 2 = 0 . 033 μ m (3.5 wave- lengths, multiple half-wavelengths transforms the impedance back to its original value), and λ 3 = 0 . 132 μ m (5 quarters of a wavelength, i.e., another quarter-wave transformer). b. The time averaged Poynting flux exiting the right-hand side of the structure is just the same as that entering: h S i = 0 . 005 2 2 · 377 = 3 . 316 × 10 - 8 W Problem 2: Impedance matching. a. Free-space wavelength: λ 0 = 0 . 06 m. b. Normalized load impedance: z nL = 0 . 55 - j . c. Fractional wavelength label for the normalized impedance found in (b): λ 1 = 0 . 363 d. Input normalized input impedance: z in = 1 + j 1 . 5 and the fractional wavelength label corresponding to this point: λ 2 = 0 . 176 The distance is (0 . 5 - 0 . 363) + 0 . 176 = 0 . 313 wavelengths, or 1.878 cm. e. The transmission line must be at least 6 meters long to reach from the load to the matching capacitor. Add the length based on your answers to parts (a) and (d) needed for
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