329fall2009_he3sol - ECE 329 Introduction to...

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Unformatted text preview: ECE 329 Introduction to Electromagnetic Fields Fall 09 University of Illinois Franke, Kim, Oelze, Waldrop Exam 3 Thursday, November 19, 2009 — 7:00—8:15 PM Name: 50 L“ “O N Section: 8 AM 10 AM 12 PM 1 PM Please clearly PRINT your name in CAPITAL LETTERS and circle your section in the above boxes. This is a closed book exam and calculators are not allowed. You are allowed to bring notes on a 3x5 index card — both sides of the card may be used. Please show all work and make sure to include your reasoning for each answer. All answers should include units wherever appropriate. Problem 1 (25 points) Problem 2 (25 points) Problem 3 (25 points) Problem 4 (25 points) TOTAL (100 points) 1. A TEM plane wave is propagating through a good conductor, with time—domain electric and magnetic field intensities given by: .c u) / ./ E(x, t) = 1006—4035 cos(47r X 10st — fix + V/m Hm, t) = see-4°z cos(47r x 10% — ,8zr + $2 A/m a.) (5 pts) What is the complex propagation constant '7? Xim+j<7. “540 S (19’? RV gonad WAMCJ'GV' K= 40+340 5 Llobfi) Wm] b) (5 pts) What is the phase velocity 1),, of the wave? yo 5 'l-‘fi- mg: 7 V? (f ‘70“ W l“bl “\ c) (5 pts) What is the complex impedance 7} of the material? .. .v- _, '17/ m'wll’gg’ ' R 11:26} Li {9:} 441=Ig 1'74 Rvojmml csmduohw d) (5 pts) What is the phase ¢ of the electric field? A! ' . 1T . Earl—«MRS :— 2?— iszel N J /’b l‘lg e u 1r 1r 9 497? <.o <l>— 754—1; 71(le e) (5 pts) Discuss how you would verify that the material is a good conductor. - 2:. 93M dew wé >7 l 5 7 IO U“ Mg “50 . 2. An electromagnetic wave with a. co—sinusoidal time variation and an angular frequency of w :2 67r x 108 rad/s is propagating in the +2 direction in free space. It is known that E(z = 0,t = O) : —4:i: V/m. ‘10“? a) (4 pts) If the wave is linearily polarized, what is E at z = 0 and cut : 32:? Z flop): Ex? so a, > o - ?(z.k)= F,ws(w1”¢2 +401)? 3? 4> =0] 5, = «Ll. 4° flaw/w) = '4ws(“/zro)§= o - 73W» RM _. 0% b) (4 pts) If the wave is right-handed circularly polarized, what is E at z = 0 and wt 2 5? -. \Ex\= IE” 40 —E>(o/T/2w> = 4+3! V/m w!" 1“72- c) (4 pts) If the wave is right—handed circularly polarized, what is E at t = 0 and flz = 77? v) _.> \ f‘ “— 1 =— 1T ' 4 E( 4”») E(o) A») Zflvwv. lo armluft ’W .. " ,_ A V ’ "Ltcpsfirvflx ~ 4X /M d) (10 pts) Write the general expression for the wave electric field E(z, t) if the wave is right-handed circularly polarized. Verify that your expression satisfies the wave description given above as well as your answers to (b) and €61.47) ; ED 50$(M’@&’+4>O/)2 + FDSCM(W't'(Ji’—hi>‘>9 7 whore Ep=~L¥ +0 SMASH E(0;°)"W ' A A A A 4“; xxy:2;vf MA was {9140‘s mat/s RH in" ; 3L, LAT-h)“ , 117 WMy,“ lExl‘lfyl Q V\° 9.“)! C? vow- mp): am); away : 4} V A J E(o,“/u) = '4w3(1T/2_)'i< v 4—Sr5m("‘/z)y = "W Ewe/03 = “Rafi/fl? Ibisméffi = +4)? \/ e) (3 pts) The time-averaged power density transported by the linearin polarized wave described 8 in part (a) is (S) = —2 W/rnz. Does the circularly polarized wave expressed in part ((1) have @smaller, 07r70tlw same value of (S)? Briefly explain your answer. <97 = (all? = < Ell) . "1° 'FW WW wmw ‘ <\€|1> =<Ibw>z79L§=r ‘% M MSW/Ame. Yowar EJEXT—l W MW; RV W WM“, M W a, (lawn fivmVxW Cw Malay (:91. was. 3. Consider a T.L. with a characteristic impedance Z0 2 50 9, length l 2 400 In, and propagation velocity v = 2 X 108 m/s. A voltage source f (t) with an internal resistance Rg = Z0 is connected to the z = 0 end of the TL. and the z = I end is terminated by a load resistance RL 2 3Z0. a) (3 pts) What is the injection coefficient 73? %°’\ TS ’ 2%., 7. b) (3 pts) What is the reflection coefficient FL at the load end of the TL? 93%o—%o ’ | TL: ’ ail-9+ &; 7' c) (3 pts) What is the reflection coefficient F3 at the source end of the TL? (is = %a ’ 2:9 2;, 4" %o d) (6 pts) Construct a “bounce” diagram describing the voltage V(z,t) variation on the line for O<z<land0<t<6psforf(t)=6(t). =0 £;fl :2 S mew/Ade +0164 ‘ e) (6 pts) Write the expression for voltage V(%, t) for 0 < t < 6 ys as weighted sums of appropriately delayed impulses 6(t). I o \/(‘»c)=1:s6(Jch-)+ f‘g £,2e i} ZVr '55 L t’ZV‘, ’0‘.- +T5FL = l. ,. L , AIL 0W W f) (4 pts) Repeat (e) for the current I(%,t) for 0 < t < 6 us. 4:. g; 5 is . 1(a) flay—280?.) + (gowns) = 7.5805”) jojDSH'?) [k] /,, V;O @ Dow £44005 - 4. Consider a, lossless T.L which ‘ short cir uited at both ends. If the length of the TL. is l = 20 in, and v : %0 m/s for the line, ' a) (13 pts) What are the resonant frequencies of the line — frequencies at which source-free oscil~ lations (standing waves) of voltage and current are sustained — expressed in MHz units? T4,. mm mm We wwwsmlu m wen/ks wowv: wmwg IL: nA/z. “*7 M‘ W ’1 L V\ 5 $710,: 640 n e 5n MH? e; s i?- := '25Y5'm‘13h :— 2' log “ AM 40 b) (6 pts) Sketch the shapes of voltage magnitude as a. function of d (distance from the load end) corresponding to the three lowest resonance frequencies. Be sure to label each plot clearly. hfi‘ so = F, a) a 1 MW lv 1 PM”? [Vail ,fi-‘a—v [Q 0 c) (6 pts) Repeat (b) for current magnitude If as a. function of d. [EGO l ...
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This note was uploaded on 04/20/2010 for the course ECE ECE 329 taught by Professor Goddart during the Spring '10 term at University of Illinois at Urbana–Champaign.

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329fall2009_he3sol - ECE 329 Introduction to...

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