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COMPILATION OF OLD FIELDS TEST 2

COMPILATION OF OLD FIELDS TEST 2 - Summer 2004...

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Unformatted text preview: Summer 2004 Name: /U/bhflh¢? (AMA-’3" Signature: 71"": Test 2g EE 3320 2,5 6 % 100 points 00 Friday, July 16, 2004 / /0’0 A portion of your grade comes from your ability to communicate technically; credit will only be given if work ”supports answer. Include units where appropriate. Important note: For this test assume that a loss tangent greater than 10 characterizes a highly conducting medium and less than 0.] characterizes a slightly conducting medium. 1. (15 pts) Find the minimum thickness of a certain material necessary to shield a room from a lMHz EM wave if 5 skin depths are required for total shielding. This material has the following properties: u=uo,e’=eo,andc=4x106%n. V : ~ -5 .p’! leer) flaw/MM : a”; _.. Arm w :fi.]q7 XI >>f u- ( : H7 - ”/5; IKO‘MM 8 85x15 " 04 “’ {KOVWJQR'Eme’fléXga 4/",111 "L... :115177x 94 391'311‘2’2» *3 3;ch : «3.55% Sl-ryjrmlf S l.l§53駑$>cf0 m _ M, ”5.5.... _.n-— nwmwfi w .w _.. ..—‘n 2. (10 pts) If the 10 s tangent of a medium is greater than l0 what does this tell you about the relationship between the displacement current density, J d , and the conduction current density, Jc ? 3' ifs/M8 flaw. cfimexs 50L sum/bl eel/w [/4 \ (fag; fie I 3 a 1.) A g”: _. "1/ Z M if 1&1 am Ava/3K , 24% 4 _ é > 0 @6962; VJ W / 3;: J? 3. 8. (10 pts) An EM wave is incident at an angle? 6 =17° from air onto the boundary of a lossless dielectric that has a permittivity of 480 . Calculate the angle of reflection and the angle of transmission. / " 7". _. . , 1— ,. “0“”) ~fl1 : ‘4le .4 \[T : l ,I (y)? .. UN [6% Aydwllgzjc> {2 ”Jazz: _ J'— Firm HflMN/Q = A in (<% 5dr: Am 9, \ \n.-fl)).\-'-‘ IND} j : an” )/, / bin )7” i1“. «31/. '" g"; ' {'3’ n "W? figy/e 4. (20 pts) Determine the polarization state of the electric field represented by E = [j3fi— (2— j2)2]e_jky . Be sure to show the standard form and how you found it. Label the two Cartesian axes on the chart below and place an X in the approximate location of the polarization. Assume that the inner dotted circle represents A =1 and the outer represents A = 5. Is the wave propagating into or (:21: of/the page? P fiflfl MW] my in ‘. "Lg dbl/“7523,21 {.571 ‘ a axis . This chart pertains to a , I ’ ’ K " x \ wave traveling out of _ - l a . 0c ' {m 43-» 7' 015) 0x {7, f ~, 3 r' \l 9 ~— 3 ,1 , _ ' 0 . 9 9a {MC-g): '15 #48:) £135 ‘ 'm-m (math 3.. 3 (5:9 ‘1 §+J§€j ‘7 I 5. (10 pts) A wave starts at point a, propagates 10 meters through a lossy dielectric for which 0L =0.3—I:n-R, reflects at normal incidence at a boundary at which F: 0.2+ 30.5 and then returns to point a. Calculate the power density of the reflected wave at point a if the power density of the wave at point a was initially 10l . m2 W _- 10 9.), l 2r . 6. (35 pts) An electromagnetic wave in air is incident at the boundary of a medium described by er =15 and ur =1. The incident angle is 69.64° and the electric field is represented bya=yae-j<kxx+kzz>%- fl , may? ”:7 ""‘xfi Ir"; (f: V x a :6”; a. In terms y/the cartesian axis system in the above figure, describe the plane of incidence. jg -— >< film it? b. Fully describe in words the polarization type of this incident wave. \ Wig, GM :2: so A559 AW 21 [mm/)Ww M Ma -— t A, / . ' cm W mCW%/m4/fad W/br/iwg‘fiz/ {’1an S ,9 c. Calculate TS . (1!; .7 Z ,5 «- 0.1/3 92 :: Al‘n’(£.j:l'fl6qlé45 {3‘ ltd-.77 ' WE ; ,5,~,f{(/0,Zs q? (0:?395) ‘ ‘ 11/) —- n) Cam/liti: ; gyfl; x305 \ / /' d. What 6 entage of the electric field is reflected? £93. -) X . “if“? (5/ jug/{diam 542/5149”th e. Calculate 9B . _-l 66 4 Am( .\ 55’, ”.0: ,2. L: Wwflea, g. Is it possible for a critical ngle to exist for this wave? Explain why or why not. A/a/a W‘ :<v‘7:é),, Bonus: 1. (2pts) During ich season (winter, spring, summer, or fall) is the sun closer to the earth? 5w (9)1. 2. (3 pts) Alt ug he earth’s gravity falls off with the square of the'distance as you move away from earth, at a distance of 125 miles (about the height that the space shuttle orbits) the earth’s gravity has barely dropped from its surface value. So, then, why are the astronauts said to be “weightless” while they float around in the shuttle as it orbits the earth? Explain. (Jim/A 7A6 AféMe M46 m In A/mzfie [email protected] If x21: m”??? vy fyg M m Add {Mg/Q A; [Ate WA ‘4 MAJ/wax M Ma WWW 497$ WM %M ,5? Wufiw/g Q/aE/fice’ - flue; MQHMA it #11501- twgll/w, / .30/ Spring 2004 Name: Test 2F EE 3320 100 points Friday, April 2, 2004 A portion of your grade comes from your ability to communicate technically; credit will only be given if work supports answer. Include units where appropriate. For this test assume that a loss tangent greater than 10 characterizes a highly conducting medium and less than 0.1 characterizes a slightly conducting medium. 1. (25 pts) Determine the polarization state of the electric field represented by —. E = [— jx —(l + j2)2]ejky. Be sure to show the standard form and how you found it. Label the two Cartesian axes on the chart below and place an X in the approximate location of the polarization. Assume that the inner dottf circle represents A =1 and the outer represents A = 5. Is the wave r0 a atin into or outo the a e? _> . ‘ki . '5: ‘h‘ef’lCY—(H’flgf) / z. . i) J —aXIS This chart pertains to a k 77/ {— /’ ‘\ l . ' w A ‘ r I J \ // \\ wave traveling out of ‘ X 6“ 72,4 2‘ +(* I 1:323 / /’ \\ the page. -‘ 9' ‘ tfi ,‘ . ‘ WAX/k. lKOPnCV‘nHNC—g lN -9 D‘KELTWM (0,41, OF PA E> Maw/v HAND ELW‘YHWL. lloLARi-e-A'fmw (RHE \ 2. (10 pts) To describe the electric field component of an EM wave we’ve been using expressions such as is = Ewe—3m. Explain how we concluded that this is the mathematical form we should use. l<: q/+:)B Plujgmj qu) NAN. flipM-‘h‘om‘. l‘w" i-‘fy’ L\ 5% 'r’i. 3. (20 pts) A low flying military airplane in Iraq is searching for buried weapons in the desert using a ground search radar with an output power density of 0.1 %2 . The earth below is characterized by 8} =2.8, 3"8,=0.05, 6:10—4%. Recognizing that the EM wave fiom the radar will attenuate in the earth as it travels in either direction (both on its way to and on its way back fiom an object) determine the largest depth for which the military can hope to find weapons if we assume that the reflection coefficient fiom any buried weapon is F = 0.55 + j0.32 and the radar’s minimum signal detection limit (return signal strength) IS lmynz. E I l Sin-m "’ 0" W/Mg‘ E7 *‘ 0 05 ‘wj, l-‘>5LI«H FLY {“11me t ’ Ll [In I. 5M Max :— f " _ ’0‘ ‘2) ‘- EH 3”]:- 10,9" X J 0 \/‘\-Cl C ‘l‘ \é‘b’ui’.éi)(~fl Q3(‘a’,‘o’5;cw".") 0‘ H 3 ’ : (aMe‘ 0%) “- — v. 55+: cum , mar/4&3“: a twp 3mm = W (Sm-.109 / 9 w“ L. :(0.ema(0,;#’<i’=l: oo :0“? 0‘3 (kw e 7) . Ll-C /J 130“}: M ,wxminmm Citie(‘i“i’lt'-- STjhAE Sr : (5 0< a , 9M4] rigidity-.1 ”Mg, > “I"; / :(0 0"}6,_O<Z.)(L:o<é> i.- 0 0,46 ’qufi :\})(110 3, j .1 .— 1.3.3.1.: ”3' be _. ’7’ C—DJX-E: ODQE N; «go/g :; )y\ 0.03511‘4fii 7’; “avg“ ‘5;(;UI_T~3)— ~14: .m 4. (20 pts) A plane wave 1:: = 25 sin(l x109t—3x)§r\%1 in flee spac:encomters a lossy medium - (ur=1, 81-:5, o: 07/)[email protected]= 0 Findl“, T, ands p_ ha I)‘ v; —- 190.— 37;,31/ LoséY MEDILMVK >1/lsE i‘JrlérHLY Compucwvé K “02+ 9‘ a ,5" 1455an War” ’4'» a '0 8 , Ffi / ,— —- 0. “7,0”? (Ixruq)(Ll'lTXl0 “WV—7% OH alg— M 9317‘; 23—5. [45" 3‘ H3371 “l5" EL : (EU-+333)?” / (9.4V new?) fl : _(30't‘l30)-- 3:}? _' ‘SLI?-+” a“ —- — ’t $.15 J . _ 3o 3 313.321 -3 __ 0.355114%? " .{3:+3[:\°)7?- HOT-f +330 H.037“ {Li 310— ’Lfi—Hfi—L_ ._ _____I : l+ giggles. : -:—/ 1+ — H L _._ We totes) l - “x __.__________4 .__ __,_..‘ 5. (25 pts) A 9 GHz uniform plane wave is propagating in polyethylene (8' = 2.2680, s” 5 0, u = no). If the amplitude of the electric field intensity is 500% and the material is assumed to be lossless, find: a.) The phase constant. b.) The wavelength in the polyethylene. c.) The phase velocity in the polyethylene. d.) The intrinsic impedance. e.) The amplitude of the magnetic field intensity. 3P: ”1 M061 Hz— ?3.5 M" i .\ (Amati: : W; 9.1668. 3.3M "t Bonus question 1 (5 pts): Is it ever possible for an object possessing a non-zero mass to exceed the speed of 'ght? Explain your answer and if your answer is yes then describe a scenario. N /' ‘ik-g 2:4 Wu+ 300%le YiS, Tn ““7 WARM» ro/lLLr-i’kkm £010. 394“: VP 4 C“ Ii— Ux nutSSlVL ”bj‘lcl CA" éL accelcrfii-ci i1) 0\ 5p MU; > VP WC Rowe, it Bonus question 2 (5 pts): Determine the radar’s operating frequency in question 3. *— Jfi>2<f03 m/s w:/3V u t ' P \ 2 10053;! 3 it: W/ Jr 9x5 x103 H2. W €1.20 C C 6,319" 5. (25 pts) An 8 GHz uniform plane wave is propagating in polyethylene (8' = 2.2680, 8" E 0, u = 110 ). If the amplitude of the electric field intensity is 400‘%1 and the material is assumed to be lossless, find: a.) The phase constant. b.) The wavelength in the polyethylene. c.) The phase velocity in the polyethylene. d.) The intrinsic impedance. e.) The amplitude of the magnetic field intensity. B: Oar—Z M060 Cool/QC Ev 627H8No SW 13 mm : q < QT : 0 Omgm/ A Q73" T59» / 3 - , ~ 9. Vp~ M1109? 5;? o p MO Q 1 .11. ., 4111115 {L A? iflfi'bfl‘o’“ Q2 9.501L ‘ l J” I *— 1 , 51 5m Bonus question 1 (5 pts): Is it ever possible for an object possessing a non- zero mass to exceed the speed of light? Explain your answer and if yo E K!" r is yes then describe a scenario. \C.w 91% MMWMWWWM )f {5 1101719 WWIIWMW Bonus question 2 (5 pts): Determine the radar’ s operating frequency 1n questlon 3. 46" W W LO 37$; _ mum Lo: 80- 71141136 MM i :1 ”MW. W 1W WVWW 3 8?” i1) 3 01/" C m l RQWWHZ 3 7&5 l R 677%‘371-5H2wicmm, pafftbgfifl; > .I \ #8141]. “xi ’5“? Fall 2003 Name: [4,14% [iii/4min Signature: , .. .. Hg EE 3320 x’ ,1” TestZE 100points ' ALL 1“: Date: Monday, November 3, 2003 Credit will onl be 'ven if work su rts answer. A ortion of our ade is based u on our communication ability. Include units where appropriate and box all numerical answers. . )(15 pts) A normally incident EM wave has a power density of lily 2 just after entering a certain m lossy medium characterized by 8’ = 280, p. = [to , 0' = 2.53m , and n = 50.3+ j46.9§2. If the wave entered from air (“air =377Q) with a frequency of 1.5 GHz and the wave’s electric field is represented by if. = fine.“z cos(0)t — Bz)‘%1 , a.) Calculate the attenuation constant, 0L: :3)! 2 , / 6 ,7 ‘21)- C’ ' (1;.- / :2.va A C , . / E : /3 >7] :/ grog/(w: WA” \, N r/ _ ,_., 4/ . H’TMT = W 7 , ’8 V1.2 \ A/ " fl) ' fltjléf 7f 7”” "*'*/\ ’ «'30 --_ _; \j‘--' W ‘ 3/71} a «1.. w/ - \s walculate the power density at a depth of 2 cm into the material. ,7- ‘ '2“? fl, ,Z(/2/,‘7)/?z/D ‘/ “f (A/ U, ’35 r/'-”” 6 i'ZVV/O/TI-Fj" (If {(‘ijalculate thefiofie—i’fie - sity of the reflected wave just after reflection3 AV ' t . f, ' . ' /' /_/}/",\ 3,71! ... f) 0' ’5 .2 /,/’ f/ 5 2.19 r .' /é {J 2/}. i/ 15)“? r7 ; K —’-— __ M I .I I ‘ \ W rim IE: 4/7: He? @ /,;//r//'1]E}o" // 7* ,76) /2 :51), K X _ ,/' lbw = [— (2 + 3 fly —- jl 02]?ij as it travels through free space. Be sure to explicitly show how you came to your conclusion. Label the two Cartesian axes on the chart and place an X in the location of the polarization. Assume that the inner dotted circle represents A :1 and the outer represents A = 5. is the wave propagating into or out of the page? This figure’s labels pertain to a wave ' traveling out of the page. Write the polarization type here: AW AW! tag/WWI the three-media configuration shown below an EM wave is incident at angle 61 = 40°. The s of refraction for the three media are n1 = 1.2, n2 = 2.1, and n3 =1.4. All three media are perfect dielectrics. a. (10 pts) Find the transmission angle 93. ’35 h" ,/ 5m {1' .7 Q1219 = 21. em 6:; .................... 9 ‘ sin. [2:71 swag: 215 “J ’ {7:}; 6m( 5m (:1. ‘3 U1 9r>j “'3- film biz) r5234 9,? - st" (n 5131157 5111(993))> ,; finr' [st/1 1:2 snip H W3”) / / 0 pts) Calculate the phase velocities of the EM wave in each of the three media and compare them inequality sngns. . o 7/ f2 I /'DI": (Jj\ J ’2 U y/pg/ V101 — 7T! ”a v > We - Wm ” .. LL #ufi' 5 ‘47:: {51? ' 3x/0J{;.y)'é ‘7 I .-" \J _ L’- 1//:‘1 > V”; > ”I“. V/ I.' A a / \. 0/1S c. (5 pts) Describe the plane of incidence for this scgyz. 7A4; 19”“ w rt" {Mm/mac r3 JLL since (rump: , d. (5 pts) At which boundaryr can a critical angle exist? ,1 Z. 4 0 W "2) \l/ 0 pts) Calculate the Brewster angle at the first boundary. If the incident wave is circular arization, in a brief discussion, qualitatively describe the composition and polarization states of the transmitted and reflected waves at the first boundary. \ 915 " sift,“ (W 5 x (1‘07? V/ ‘ \ m’ 7%: ”(fir mlew Mr Mira/r/flmwm: m" HUI/x f-{sré/mfi 41141ch 401M! (ran: “WWW a0 HM /(f ”Male/1.11115, £u1///;’r. flan/913‘ C!!!” 917/7 (1'9"? 31/! ftp/[:21flyf7Z/IA ”/5 VI, 'ML ptkPUlith/I?’ Pflr/i’f“ {I ”a (r "'4 L _ I. @ pts) Calculate PP at the first boundary (recall that n: /\/;=p' “—0 -- a”. a so: 6: —Je— // . 377 r, f ’72)“ ‘9”? my flaps 94’ ”/7,” 0059, .0 :77 : fly» / '1’}! , .- , 9 w 27/ 3H; g ’ ifz’asfiz ‘* n, “'9! j 10 pts) Find the minimum thickness of copper necessary to shield a room from a lMHz EM wave if n depths are required for total shielding, For copper, u: no , e’ = so , and 0' = 5.8x 107 ““103 .y- (3 ‘— séy/l’r ..l “a: m . 5”, L7 ' “’7"? ’7 // [ff/0 6‘” /E', // 7/1 {I’Vaé‘J‘F/fl 77/ / c Pg...’ / r, J _ // : r ff” , ./ M 4% g Mf ’ vflrlléf (1’ L" I J a , 1’ a V/ J~ 3 » 3.3 xw m Fall 2002 Name: J5“; Mm? / k, EE 3320 100 points Date: Wednesday, November 13, 2002 Credit will on] be iven if work su orts answer. Include units where appropriate and box all erical answers. £0 pts) An EM wave starts at point a, propagates 50 meters through a lossy dielectric for which 0 lNeper/Sm ,reflects at normal incidence at a boundary at which I‘ = 0.2 + j0.3 , and then returns to point a. Cal/culate the ratio of the final power to the incident power afte this round trip. . , 7 “PUB-WV /7 Zzafi/ Hz“, KIM/m // J i 7 I} , n / /_f 'er2: /C' 'L/f(/fl,/\' ,‘ , a, I w 6 - /0"9”1Q(;» (10 pts) If a 3GHz EM wave is traveling through a lossless medium characterized by ER = 4, and =uo, calculate its wavelength, 9». 15 :91/ #1, “A '1 “175:5 : 277 3 A,“ ‘7' ., ,. :31: k: Lu I/: :{1} (IL ‘4/ gw/ V L, liq/25:?» ’ ‘: 07m. L ‘(V :(3;&fi]1;\ \ '_\ 41/ ./" / he magnitude of the incident wave is Ex10=100%1. Calculate values for E;10 and Ex20' ~ _ _, 71 e 71 7/, L a, 2 f! - Jr- it >1 ' _ MOP m, //... ml". \ I L "‘21. j’:£1’/’1(jm — J 5 LYKO : 0:8 {rt/O)" 307/ \ \‘(1'0 ,/"‘" 4 ---—___,___‘7< » (éxzd 1' K0 v/h\ ‘\_ __,_____FA___:’/ 4(23) pts) Use the chart below to determine the polarization type of the electric field represented by bFEéLix 2+3 J )z]e jky as it travels through free space. Be sure to explicitly show how you came to your conclusion. Label the two Cartesian axes on the chart and place an X in the location of the polarization. Assume that the rnner dotted circle represents A— — 1 and theg outer rep rfints A: 5. Is the wave ro a atin fito or out of the a e? E _ {'4/ % 4/0 36 / u 2 . . . ' g . axis Th1s f1gure pertarns to a a wave traveling out of the 4 _ ), 6/ ,I’ f " ’T i 3. 6 / ’ é: [$é3+a0—90: /y5 3 A; £1, law I a 53/ h associated magnetic field! _H. ' .- , ' . 10 pts) An EM wave is incident 116m medium 1 (n1 =1) onto a boundary at medium 2 (n2 = 1.4 ). At what angle of incidence would he perpendicular component of the electric field be totally transmitted? .1 : I . . . 4 C d WWI“ ‘5 "J“ C Q I" 1" a 1‘ 5‘ “ L -. -r' : .4: h IA»: , 5 .17le I II l~ 0 I 7 LI '0 x' -' - ’1 / ill ’ I" .1 - (J 1 I a /// , .,. (did/”747511151114 Cam [m V P B? {' LIA, ,5". G '1 5!. ‘5) 5:. '3‘“ J 7Z¥pts) In question 6., aboy/e, what is the “perpendicular component of the electric field" p rpendicular to? Li: ITAE 6' 0}”7/3'01/16M’? ,f/an / 0f zacwtace- 'UM r/F/ ‘7V r/./ r f7 // (LIV/(61(64/ %0 / Z“? F/gragj. \./\ / " "(I .- . U , , _- /. 1/ ' . :1, ‘. 5,1,1: {9 “Hr 6'. \,@( J C, I/Iguwua/ «(-1? Hm I, ». I. . \5/ bulging." \-‘ \J ~-.[' [14“ fig +54}? / / 2 Q0 pts) An optical fiber channel has a dispersion parameter, B2 =15 954“ . A Gaussian light pulse / V at t e input of the fiber is of initial half—width T =10ps . Determine the half-width, T', of the pulse at the fiber output after the pulse travels a distance of 20 km. ...
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