Prelim 2

# Prelim 2 - ECE 486 PRELIM#2 SPRING 2006 1(9 points Suppose...

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Unformatted text preview: ECE 486 PRELIM #2 SPRING 2006 1. (9 points) Suppose we have a dielectric slab waveguide with thickness d: 1.0 mm surrounded by air on both sides. Take ed = 260, Jud = #0: and assume the wave frequency to be 350 GHZ. a) What modes propagate in the guide? b} For the lowest order TE mode, graph the two curves that a: and 5% must satisfy. c) Estimate am ﬁx, and then the wave phase velocity in the z—direction and compare it quantitatively to the intrinsic wave phase velocity in the air and dielectric {the intrinsic wave velocities in unbounded media}. d) What is the highest frequency that can be used with this guide without exciting multiple propa— gating modes? («.4 0x Q: a We. ’ We Melon} m: DH?! nous: WWI:— ”yd/z ‘9 n if}: ”It; "" 4.4/1 “ A; "k“ —:;: 6‘ h“ *4" 4‘“ “‘“L “FM w \ a "' 1 “5—C\ r(3-6¢\ é-F'usc-k‘sohc. 'FBI' ﬂy 33-1/1 Bg-Vz. 3-". ha“! in M“ J-‘f‘vf "z“ 3-YC 1-3.5 C. d): capo (W {ll (by: was TTT ‘1 4 rs: 4‘ * ”/61.- l ,ﬁlb M J0 r w/ﬂ) : 2.1km M’s c > _.._.. c 3. 04, M I"; (at M :5 ISO age-t (rut M00668 1 ”"5 W "15. 7". BOTH Eran-'63:» Rf" aw) mangaa/ 2. (8 points) The Arecibo S—band radar transmitter operates at 2.38 GHZ with a peak power of 2 MW. Evaluate the idea of using a 500—In long section of aluminum waveguide (CrC = 3.54 X10T S / In) to deliver power from the transmitter to the antenna. Consider using a rectangular waveguide with dimensions 10 x 5 cm to carry the T1310 mode. a) If we desire single mode propagation, is this waveguide suitable for this operating frequency? 13) Determine the loss, in dB, for the signal passing through the waveguide. Neglect dielectric losses. Is the loss signiﬁcant? c) Suppose we want to transmit pulses with a pulse length of 6.66 ns Wraith-0W) Will the effects of dispersion be signiﬁcant? (1) Calculate the maximum power handling capability of the waveguide, given that the breakdown ﬁeld of moist air is 15 kV/ cm. Can the waveguide handle the required power? G A Sew = a: 1.5 cpl-,5, my Ln!» 1». org my (2\ c, 1:30, .= 11-: 3 («H-:5 6" r 'F‘Izo Ir-FM. . a“ 0— WF") '7‘ W W ‘05'3- 0.02} I'll czar 4.5-2, e : r. : 0-2:] : -c.n an gain swans (1] .J—..J- ._ a— 7 c. M“ ac‘iy Vat-\' 2;? (%;'"m\ 5.: ‘C 5")" “g. F 15b MW! It 1, 9 C.- V on .33:— (hsr'falxcsl g a.“ as 7 so M!) 14’ n.1,; as 3. (8 points) Consider a step index optical ﬁber of silica cladding 0121.500) outside a SiOg core ﬁber (n21.504) of 10 ,um diameter. a} Suppose you do not want to excite the 91 = 2 axisymmetric modes in the ﬁber. Calculate the highest frequency that can be used. State your answer in terms of optical wavelength. b) Using a frequency 40% that found in part (a), ﬁnd the effective index of refraction and estimate the phase and group velocity for the HEM mode in the ﬁber. The graph provided may be helpful here. c) From the points of View of dispersion and lossiness, is the mode you found in (b) a good choice for long distance, high bandwidth communications? Below are listed the 5th zeros of JD (3:), which may be useful. J0(zc) 1:1 1:2 1:3 2.405 5.520 8.554 a. \$47., «fa: 1E: “ue‘M‘ g '1 s D. 613M (L\ a. mu.» run-2,1, '>~ar l—SS/K U\ stop: «I 0.»: “Lu...— "’ "51’: f‘ \ U4, .- 39.“ x L 44-1 mo" Ms, (‘3 taupe; 3 \$6; 1,: " ﬁt Va z {"74 ”w" ”/3 0 \ ...
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• Spring '06
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