HW12 - ECE604 Homework 12 Out Tuesday Due Tuesday...

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1 ECE604 Homework 12 Out: Tuesday, April 12, 2005 Due: Tuesday, April 19, 2005 Announcements: Prof. Weiner will not be available for office hours on Wednesday, April 13, 2005. Final exam will be held Monday, May 2, 2005, 3:20-5:20pm, Room to be announced Problems given by number are from the text by Ramo, Whinnery and Van Duzer (3 rd edition, 1994). 1. Consider the m,n TE and m,n TM modes of a metallic rectangular waveguide ( ) m 0, n 0 . Show that for any specific values of m and n, the m,n TE and m,n TM modes are orthogonal (use same m,n for TE and TM mode). More precisely show that ( ) ( ) * * TM (TE) TE (TM) m,n m,n m,n m,n 1 P dA Re E H E H 0 2 = × + × = ± ± ± ± Note: It is sufficient to consider only the z-component of P - i.e., the component of power along the waveguide direction. 2. 10.3d Hint: Review section 6.4 and note equivalence between σ and ′′ ωε 3. 10.4a 4. 10.4c 5. In this problem we consider data transmission in two different metal waveguide structures: (I) the parallel-plate waveguide and (II) the square waveguide. Both waveguides are taken to be air-filled and lossless.

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2 (a) We wish to transmit information using a baseband transmission scheme. Our data rate is R (units of bits/second), and each bit has duration T = 1/R. For each data bit equal to ‘1’, we simply transmit a constant DC voltage during time T.
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