HW11 - ECE604 Homework 10 Out Tuesday(Session 25 Due...

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ECE604 Homework 10 Out: Tuesday, April 13, 2004 (Session 25) Due: Tuesday, April 20 (Session 27) [Students with tape delays: due according to session number] Problem numbers are from the text by Ramo, Whinnery and Van Duzer (3 P rd P edition, 1994). 1. 8.7a 2) 8.7g 3) 8.8d 4) Start with the gaussian function f(t) given by Eq. 8.16(13). Using this in Eq. 8.16(10), show that the envleope broadens with z as given by Eq. 8.16(14). Hint: Use the following Fourier transform identity: ( ) ( ) 1/ 2 2 j t 2 exp t e dt exp / 4 − ω π −Γ = −ω Γ Γ 5) 10.3d Hint: Review section 6.4 and note equivalence between σ and ′′ ωε . 6) 10.4a 7) A simple air-filled transmission line resonantor may be constructed by shorting both ends of a transmission line, as pictured below left, for ideal (lossless) resonator. The ideal resonator supports resonant modes such that m half-wavelengths fit within the resonator, i.e., m L 2 λ = , where m is a positive integer. a) What is the frequency of the m th resonance?
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