Exam3-sol

Exam3-sol - a, Mia Name ECE604 Midterm Exam #3 April 15,...

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Unformatted text preview: a, Mia Name ECE604 Midterm Exam #3 April 15, 2009 Notes: 0 4 problems, 50 minutes. 0 A formula sheet is supplied separately or attached at back. 0 You are also allowed your formula sheet: two sides at 8 1/2” X 11” 0 Please put your name on each page. Power reflectance (R) Name Problem 1. 25 points Consider a smooth planar interface between two transparent materials with it = uo. One material is air (n = 1); the other material has unknown refractive index n (n > 1). The power reflectance is sketched below for both polarizations as a function of incidence angle. The order of the materials is not specified at this point. a) Is the light incident from air into the unknown material or from the unknown material into air? How do you know? the WM 4%er we a 4% i when 5% ‘3»: ‘3 a: a a. @m l’\ t liWfiL’lC I iI'\ [goo Far/kl ‘5 (bCCZCflA 3’) C; a b) Clearly explain at least two different ways that n can be obtained from the supplied reflectance data. Give a number for the refractive index of the unknown material. ‘im 6ch l EM elm U A lc; m: (m M11“ incident angle Workspace for Problem 1 on next page Name Problem 1 Additional Worksheet Name Problem 2. 25 points A voltage source with RS = 509 series impedance drives a transmission line (TL) system at 3 GHz. As shown, the source is connected to the left end of TLl with characteristic impedance 21 = 509 and length (11 = 1 meter. At the right end of the TL1, two more transmission lines, TL2 and TL3 are connected in parallel. The characteristic impedances, lengths, and load resistors are as shown. All TL’s are air—filled; that is, the propagation velocity is the speed of light (3 x 108 m/sec). a) For R2 = 1009, specify values of d2 and d3 that minimize the power in the negative travelling wave in TL1. b) For R2 = 259, specify values of d2 and d3 that minimize the power in the negative travelling wave in TL1. a K . ' \ m-V ' * fl, (/vw‘r' " “ Ufm We. cbwtmkmzekwg (m it”? 14"" “(WV [a 1L mp “ . 7 Al ‘ I - ‘ V "A. i ’5 f“ (:3 (3513 05, Atom is S‘le la”? “#4 Fawn/(#6 lW‘ch‘IQr-nm AWN/“i I m .51.... A film , i , _ _ p f '8‘, QW' . , .t v A 23’ (2 (EV. é OJ Ibex“; 27p” (a 2M “’4 , V . r . g» 3 j ,, _M~(/‘ao-wmc‘> ) (at I : [Wk/M fiéawwa { [um ,\ s (U s rm: “AW 6 y, ‘ , ‘ 3: --,/~7 “M i ! Simui/M (PU/Mgr 1 ad“ fl e 5’ I , l . i P has, {Mei/«.ij 74¢ : ' M i r v (A) r; ‘ . I Em“; [IVLYL Q gig” *1" (72" {M 1‘ "‘M/ [Ix-Wt eh m we , fr , [’6 a" l i _ Workspace for Problem 2 on next page 2);,y Twain It,” Wig/pchsz I min/muyafl flu/(VA ) ad) I i I. “M ' x» "’ ' L m? 0.53% '74, ~37 g 50/} m (gags/19R ‘ Name Problem 2 Additional Worksheet 60%. (/m (Pvt/é) I fig.» 2: t§ :: /C)CL} VG U W667 0-130 (jg u “- ‘TA‘E V”? 5 a “4% I f I: M 2 : W / 0‘) r”? 5'22, x”? 6” (V Maw-WNWwa WAN,” wwww 3' [0‘3 i 2:1“: gMC) f? y (LQA 6564' LJ (:3: 6’6\ ( rum C(f (Migfigwm (\ Lav" ,~ go ( ) .Lve,.g)yc,}( S; [K/Z ) me“ C“ (A (\A‘W‘ fag) cflcm‘rewj “'AA (£63 3 0) 6/2“) l EMA/L“ «ta/ft), : (( é) 28%) L : ADO/7 v “~ ' I w :1 cw 4'11" find/I )1‘5‘1 “,2 »- C3”) i, A i {23 D C, (/0 k. i L, C M ‘ m7 125'” ,l? _ g". “3 SBA/7 F A /Z 2V V I ? #61 1A VW j: W1 I) i/ (1 Wax/(i / W flaw ‘ V ‘ h , g ‘ 1m / « (A6; '35 c; 6 / Jam :42“, 79%,. j , W), ‘ Z "I VLF“ k wif'fluk‘) on '3: #90 fl q “0 (fligr‘fmdd‘ é; is?) $2 8 Problem 3. 20 points Name Consider solutions to Maxwell’s equations for a metallic parallel—plate transmission line and a metallic rectangular waveguide. In particular, list three distinct ways in which the properties of the field (including its propagation) are fundamentally different for the waveguide solutions compared to the (lowest—order) transmission line solution. Your answers should be short but clear. You may assume that both transmission line and waveguide are lossless, air—filled, and constructed from perfectly conducting metal. /( 5 144 c: [a g s -‘ rM» {14"}; €154 $4: alt-k1,. [0‘71 ; / H as”. (0%]va 6701'“ r" a r» m 6:?” "iém 065;“ng £239 [/1 a» c. “A: 614) ‘lv’v’x 7L: 2" Km; flyufiw c/ ‘5’ {/9 A» [,4 as Jim" Val/s (3:2 , p.37 can“? afiLfLéflé/ij‘ 53"“ ’ aim/:9 im‘{;’ «@7- a 2/ a 9U ,szgw'f»; We 0km t i Ifld elf}; G65? 1:11“. I {giramm (7 l (Emma 0 mm)“ .2” l .e/tioéa £1 (AL-t; Q [71 (is (3 ‘3 flit/“C: I/) 515 )[959 00,77 (“E/Let; €17 s’LJ flxM/fl dig“ é? “Eva ad, :2 l“/[ ( up of /(S‘ [1:1 Wei/“Um Name Problem 4. 30 points (3 parts) The (+2 propagating) Tan solution for a rectangular parallel plate waveguide is written (at z = O) as: EZ =E0 sin[m—TCX—]sin Ex = —jfi[m_n]/kg E0 003(m_nx]3in a b a a b By: —jB[—n—7E]/kg Eosin mnx]cos[-rm—y Hx= jwe[£l£]/kg 13()six1{“‘—TEx cos Pit—y— b a b b a b (a, 13) (a=30cm) x=a Fig 1 In this problem we consider the TM” mode (m = 1, n = 1). Assume the waveguide is air—filled, the metal plates are perfect conductors, and the waveguide dimensions are a = 30 cm, b = 15 cm. superposition of various plane waves. The operating frequency is 2 GHz. i) How many plane waves are required? a) Within the region 0 S x S a, 0 S y S b, theFl‘Mu Eolution may be considered as the ii) If the various plane waves have the form e_jk'? (in phasor notation), completely ' specify the k vector for each of the plane waves. 7 ' 7613‘ RA H @253 teppec { "6L1? , 525mm mega/“:3 «,UL (NEW. “:QQ‘KM ‘ w; ’ i ' ‘ f «g in (T93 > {2}?" C1333 é ex» ( e: I. m “ragga b t, _ “:2 m < > bf“ (“Q‘s G“ fl ‘ 1 ' ' +0 «4 WWW. caesium men fires girl: (Continued on n‘eiitpage)JZ \ (ta/m, ‘M‘é W3\‘)§m(’ai;>& h \ ‘MQ‘WiV/éki (Nixich W Q?” “with!” SHE“ “Kim/0‘ i’ Mtg/to W;i‘l““3/b] * “$93.1 mg» e we, v “a ma W6 Name (Problem 4 continued) b) Figure 2 shows a snapshot of the TM“ electric field lines in the x =3— plane (indicated by dashed line in Fig. 1). Indicate in Fig. 2 the H field lines, as well as the surface currents and charges on the metal plates. Briefly explain your reasoning. ~ , :33 top / WM§ «few «mg L W5 ‘3» plate 4w “Jr _, “f.” w. it at ' I llllmlllnllllmlnml Cg) y = 0 _ "Ill/IIIHIIIMIIIIIIIMIH x = g— JV .5}. + w “h M "i" magmas b; w we) Fig. 2 ( ‘39 Cilxmfigy , cech4 cm W if; (D "E" “Ml; ” a, fig} C) New (441 «Q S ‘ $3 at 5;) Crew Fulani W "‘"M """""""" ' \l i geeksgrg E” K11“ WW” Vewfifim divmm c) Assuming the frequency is 2 GHz, what is the periodicity in the z direction of the field? l l ind—w Vthczlté :2 gar w‘L c: C;u;‘<'t~°’:”’~7 1"“ LF‘i'l'“ Xie‘l Seam wt “ . . my! Lei-k Q” 0:: 3739A ? CM ) " M “at?” W C): 1”!ch (lgt‘CVME ‘ awfl (Du W w Additional FigZon next page C‘AfYVQ [+15% : H 0mg “Q F‘m Em I’M up 8 ‘43” ( g Mg €XJ::?1 g3, (QC) DA Ala/«A7 Q 61% Q ( (1)134 (Ma. M4. fwd/x D {‘1 Silt f” '“ haw ...
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Exam3-sol - a, Mia Name ECE604 Midterm Exam #3 April 15,...

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