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HW11-sol - Sky/«416 ECE604 Homework#1 1 Out Monday Due...

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Unformatted text preview: Sky/«416?? ECE604 Homework #1 1 Out: Monday, April 27, 2009 Due: Friday, May 1, 2009 ' Please complete on—line course survey 0 Final: Wednesday, May 6 8:00 — 10:00 AM Physics Room 203 These problems are from the text by Ramo, Whinnery, and Van Duzer (3rd edition, 1994) or are attached. 1) 10.3d Hint: Review section 6.4 and note equivalence between G and we”. 2) 10.4a 3) 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. I<-———— L -———>{ 0w M it 0h“. m an issi 111' c: I 11 1 0 1n Z0,C char. impedance Z0, velocity 6 Resonator with loss Ideal (lossless) resonator The ideal resonator supports resonant modes such that m half-wavelengths fit within the m7» resonator, i.e., 7 = L, where m is a positive integer. a) What is the frequency of the mt resonance? b) Now consider a resonator with loss, which we model by replacing one of the shorted ends with a load RL, where RL << Z0. Work out an approximate expression for the energy storage time and the Q of the mth resonance. You may assume that the resonant frequencies are approximately the same as for part (a). 0) Give numbers for the resonant frequency, the Q, and the bandwidth of the mt resonance for L = 3 meters, Z0 2 509, and RL = 19. h h IL’J‘J‘ “‘4 /¢95}‘7 fluéfc/Z/T‘IC m; A)”; ML! 7Z6 fl? “5») 7/!“ fi/Wk‘tév 6‘” CV“: vUfl V X H 4': 53””; ’1) “4’6: 3 (Agbfme 5 flaw} (:‘YJ %’v[{‘€ C1“ ¢ ”J 6 if, ‘ T/{iwm . \ ’ , , 2 / w {:7th éLmeé") “rt/6&6 ‘ €44 l0’4a. ‘Notc that wave vanishes 4'0:- TEWH, [51,3104- (I')-(5)J H: p30 or 349 both In and n=o. For TM“...P modes : Maw; vanishes H3 either- m or n=o. Resonant {are «an 'E'rom . loath) is For I cubic can} t - -E==¢%[m:’%-n‘4 ‘ffé ’ ‘ b3 0°° " a. P5 _ P Be‘ow We tabulate nonvanishing modes, with normalized monomt' {zreguencics and There are. '1 d'uWer'ent. Muendes. {W‘GX P‘néékijlfiN Cg; 1%16 {€14 :21»? th‘yc. 3“) WNW” (ELM—(33 ‘th—KQ’ WLV VV‘O‘j (31 (/9 (LIL/H ( Mu it ‘ ’ ...
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