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450fall09hw12 - ECE 450 Homework 12 Due Tue 5 PM 1...

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ECE 450 Homework 12 Due: Tue, Nov 17, 2009, 5 PM 1. Rectangular waveguides are commonly used in “X-band” microwave circuitry. X-band is defined to be the 8.2 GHz f 12.4 GHz portion of the electromagnetic frequency spectrum. The standard X-band rectangular-waveguide has the dimensions of a = 2 . 29 cm and b = 1 . 02 cm (see photo below). Construct a cuto ff frequencies table of TE mn and TM mn modes for the X-band waveguide for 0 m 3 and 0 n 2 and identify which modes would be propagating (rather than evanescent) within the X-band. 2. Given that k 2 = ω 2 μ o o , show that H x = E z y + jk z E y - j ω μ o and E y = H z x + jk z H x - j ω o imply H x = - jk z H z x - j ω o E z y k 2 - k 2 z and E y = - jk z E z y - j ω μ o H z x k 2 - k 2 z . 3. An air-filled rectangular, metallic waveguide is used for the transmission of a microwave signal of frequency 4.5 GHz. The guide cross-sectional dimensions are 15 cm and 6 cm.
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