311_exam1sol_sp10

311_exam1sol_sp10 - ECE 311 - Spring Quarter 2010 Exam #1...

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Unformatted text preview: ECE 311 - Spring Quarter 2010 Exam #1 April 21st, 2010 Write your name below and on each sheet of the exam if you tear out pages. Sign the honor pledge “No aid given, received, or observed” if it applies. There are 3 problems on this exam. Exam is open book and notes. Please box or underline your final answers, and remember to include units. Be sure to show all work clearly if you wish to obtain any partial credit.Try to keep your work within the provided space. Use the back of a previous sheet if necessary. A selected table of formulas is included below for your reference. Name: p; “The Pledge”: General Equations: y = oc+j[3 = A/(R'+jcoL')(G'+jcoC') Z0 = ./(R'+ij')/(G'+ij') L'C' = us G'/C' = 6/8 B = 21V?» up = % adB/m = 8.68590: V(z) = Vgern Vac” 7(2) = (Vge‘lz— Vbeyz)/Zo Lossless lines: [3 = (DA/[1:9 Z0 = W up = l/JiE Distortionless line: R'/L' = G'/C' 20 = W [3 = to L'C' OL = R'm Terminated lossless lines: F = (ZL—ZO)/(ZL+ZO) = V6/ V3 Z(—l) = ZO{[ZL +jZotan(Bl)]/[ZO +jZLtan(Bl)]} VSWR = (1 +|r|)/(1 —|r|) PM = [|V3|2(1—|r|2)]/(2zo) R 1 1 21m 2 Coax: v=_s(_+_ v: EL = 7178 R 2n a b) G ln(b/a) 27:1“(b/ “)0 ln(b/a) Parallelplate: 5% .411] .=}i_d =flV R = n /6 R W G d L W d 5 He 6 Problem 1 (5 parts, 4 points each): circle the best answer (1) Which of the following is FALSE about distortionless lines? (a) the characteristic impedance is purely real / '(bj'fiie line circuitpgrameters .R’. .=_ (c) the phase velocity is not a function of frequency (d) the complex propagation constant can have both real and imaginary parts (e) none of the above (2) The phasor current on a 75 Ohm transmission line is known to be 7(2) = 6e_j52 + 3ej52 mA. The VSWR on the line is (a) 1/3 (b) 1/2 (c) 1 (e) infinity 1w (3) A lossy transmission line OVEN“ 3 (a) always has a purely real input impedance (b) always has a purely real characteristic impedance (c) always has a purely imaginary input impedance (d) always__ a purely imaginary characteristic impedance (,4 (e) none of the abodve’) ,___......- —" (4) It is known that the attenuation constant on a line is 0.3 Np/m, the phase constant is 6 rads/m, and F = —0.5 . Which of the following time domain voltages is consistent with these properties? (a) v(z,” = 260.32 —0.32 (b) v(z, t) = 2e62cos(mt—0.3z)—e‘6zcos(mt+ 0.32) Volts (c) v(z, q) ? 2e_0_'3zc_os(0_)_t—_6z)_—e0'3 I (d) v(z, t) = 2e_6z cos (cot — 0.32) — e (e) none of the above cos(c0t — 6z) — e cos(c0t + 62) Volts zcosh('c-0t Volts ~- . . firth 6Zcos(cot + 0.32) Volts (5) A coaxial line is made with perfectly conducting plates (i.e. 0' c = 00) and has a medium with 8 = 480, u = uo , 0' = 0 between the conductors. Which of the following combinations of the inner radius a and outer radius b would result in a line with a characteristic impedance of r C 1mm,28mm (b)1mm,2. m i‘: L’/, : % (c)2cm,10.6cm b 5 gm L(3/A)fl\n (d) 2 cm, 93 cm (e) 0.8 mm, 2.8mm % 30 51h [aw—4 00 Lib/A): 3,7} -9 Live; 20.212 Problem 2 (4 parts: 44 points) A lossless transmission line with characteristic impedance 50 Ohms is operated in the circuit below as shown. The line is 20 cm long, and contains a medium with a = 1680 and u = uo. The 3V voltage source in the circuit shown is operating at a frequency of 800 MHZ. (a) Find the phase constant, the phase velocity, and the wavelength on this transmission line. (11 points) (b) Find the reflection coefficient (amplitude and phase) on the transmission line. (11 points) 2 ~33 , V: L “ L§h¥§stl_ ‘Cfiw< u \- C~ $L+¥° “+3‘W+ (o \ HKflkf 2 hMfi+3mmd : 0.32% L 0.849 ax) 50.9? (c) Find the impedance Zin. (11 points) l $9.: 7 ?: MWA< "CM §Q1 '7'.“ :: (96L‘0Lf owe-Wm k 4%. (d) Find the phat current that flows out of the voltage source W). (11 points) M M 1 V A. , W) V‘ ‘ \ MM ms) Problem 3 (4 parts, 36 points) 3 A transmission line has R' = Ohms/m, G' = 0, Mhos/m, L' = 0.5 uH/m, and C' = 226 pF/m, and is operated at [00 mph? &&.a§ (a) Circle true or false for each of the following (4 points each): This is a lossless line True This is a distortionless line True This line has dispersion False (b) A parallel plate line is created with these circuit parameters. Assuming the line is air-filled and the distance between the plates is 1 cm, find the plate width aad—eead-uetivrty-ofihepl-ete—metals. fwlfieh—hmwfithat are required. (12 points) ‘u \\ {\«m, -~ g: A Q, (c) Find the attenuation constant in dB/m for this line (6 points). ‘6: 61"?) \‘L')( (Lt-30C) a 64939; Aq (d) What impedance (give a numerical value) should terminate this line to create a “matched” load? (6 points) QC; 920 ‘D ’\ “WWW low, ...
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This note was uploaded on 11/11/2011 for the course ECE 311 taught by Professor Johnson,j during the Fall '08 term at Ohio State.

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311_exam1sol_sp10 - ECE 311 - Spring Quarter 2010 Exam #1...

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