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Unformatted text preview: 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 cutoff frequencies table of TE mn and TM mn modes for the X-band waveguide for ≤ m ≤ 3 and ≤ 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- jωμ o and E y = ∂H z ∂x + jk z H x- jω o imply H x =- jk z ∂H z ∂x- jω o ∂E z ∂y k 2- k 2 z and E y =- jk z ∂E z ∂y- jωμ 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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