This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 halfwavelengths 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 ‘ ’ ...
View
Full Document
 Spring '08
 Staff
 Electromagnet

Click to edit the document details