test 2 solutions

test 2 solutions - Carnegie Mellon University Department of...

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Unformatted text preview: Carnegie Mellon University Department of Electrical and Computer Engineering 18-100: Introduction to Electrical and Computer Engineering Fall 2009 Exam 2: October 29, 2009 Closed Book Write your answers in the space provided. Do your work as neatly as possible. Cross out any work that is not pertinent to your final solution. The grader reserves the right to mark solutions as incorrect if she cannot follow your train of thought in the problem, or read your handwriting. BE CLEAR AND CONCISE IN YOUR ANSWERS. Show all work! Answers that have incorrect units (or no units at all) will have points taken off. We recommend that you do the problems that you are comfortable with first and then attack the ones that may take you more time last. Problem 1 (30 points) Problem 2 (25 points) Problem 3 (25 points) Problem 4 (20 points) Total = ("r H”/ Name QLLU \ 3,0[08 Section (A: Monday eve., B: Tuesday eve“I C: Wednesday eve., D: Thursday eve., E: Friday aft.) Problem 1: (30 points total) Miscellaneous For each of the circuits below, calculate the value requested. For all parts, assume VD,0N = 0.6 V, VBE,0N = 0.6V, VCE,SAT = 0.2V, and [3 = 99. a) (10 points) Let VLEDDN = 1.4 V. Vcc=l 0V -' Vin Let Vin = 10V. What is ILED? (Hint: doing a Thevenin equivalent can make this part easier.) 1119mm C Wu M W” ‘ Len.- . . - , “cur— m w U06“ U19? 1‘” :- 81/ L .A win ir-Qlln'L-l-P‘Il“ 2L fl. ’ flTp: Mu—[I’him : [Olin— ftéo 1 1': *(B+‘..)1a=l°'°ifi- U_}\\; [mm / 3 FEM: 30911.4 4, L“ with. W Jazz“ i” Q _ __ .._ fl?"— F, f" : L __L 4’ a “A Lil “ "Lng 3054‘ J ‘3' Jags-5" Li L [LED = 3 b) (10 points) Let R1, R2, and R3 all = lkfl, and C = lpF for this circuit. Vo(t) If Vi(t) = 100030 000t) V, what is Vo(t)? (Note: functions of time don’t have j’s in them! Hint: break this problem into two pieces.) \legij : a gavhfb ; -VAH :2 —]'0 Us (1098+) V W [D 05({oeo-E-iwj V A Vii) \ ‘ —3 l 3 *-—' :: —-—‘—*—"" Q C. 2 in —-— r . ox was 3 5 Raf-'10 [A n _ T vs 4..., \,.:\,L Liz-"MMP-q {TX 2 “1 0X) \fi. 3:) ' '0 ( Ac +rr 53: VD(§I‘L fi (’03 (-01%: __.. FIT _, my“ ’ l“ t +373) “T “ _. [DOB 71" “‘5 “r (f a 09‘ - ' a'i" #5:: -|-' : 4-15» fl “’5 W H ‘1 I 1'!— .b 0“ [D oil-6f “1.”. "_' 1L”- ,— fi 050 ‘ Li) H V0(t) = ‘" lA-J 4 c) (10 points) For the Circuit shown below, assume we have a sinusoidal input voltage of V50) = 205in(211:*1000*t) and that the zener voltage for the diodes is Vz = 5v. On the axes below, sketch Vo(t) for two periods of the input sinusoid, beginning at t = US. Label your axes and your sketch well. SKQ 6'). Problem 2: (25 points total) Ola-amps For the op amp circuit below, you can assume the op amps are ideal and that the rules for circuits with negative feedback hold. The op amps are operating in their linear range. All voltages reference ground. a) (7 points) Find an expression for Vx as a function of.Vs. b) (8 points) Find an expression for Vx as a function of 15. c) (10 points) Find an expression for Vy as a function of Vx. UHF : V51V__ SO we 7.6T [J BUF- {fok £1.th OF firm? A Momffi‘JFmTinJi/z DtvFAm/D (firm/“JET~ N. C,unfl-’E'H# M“! 15$“ ‘71)? H] FIN}, 5,}, - v 'Vk :5 _ c3 .-; La. a _ {RI-Hi4. . -5 :1 J3 KT)”: 1 _ it; Vs R3 r‘l RS _ __ _ ._ fl__w- " Mi” if 2V, —* “(fth rim 451wa £31 {L1 5 J .___,5: :ILQ'f-Hf V av(l+ ' , Y (M 7m fl]. 1 Vx(Vs)= H’ "" VS . [3va LEN? {’1' - , ‘ P5 WWW!) vX<Is)= — (“M13 773?. I5 ‘ “U + L this c;er FMch £2: _. “43' also WW"): M l + ’“1 l 7‘? VX HALO WEED ‘ 7 Problem 3 (25 points total) Transistor circuit problem. For the transistor, assume that VBE,ON = 0.6v, Vce,sar = 0.2v, [3 = .99. All capacitors are “very large”, so they’re open circuits at DC and short circuits at AC. Let Vs(t) = 3.6v + Vs,ac Vs(t) (a) (10 points) Draw the large signal (DC) model for the circuit. What is the value of Rb that we would need if we desire the DC operating current, [[30, to be = 20uA? What is the value of V0,dc under these conditions? (M w: Lat? 0?ch (durum-Ci PT DC- Var—M 3V ‘2. Aoqfit Ru [DD-Hth 3v ; 304px- {LL Jr loo W's/L . Mg" - —s' . 3V *— 3”" “MVP 21v. 1v : 3005/3 {lb ___‘_\.’———— (L mas-Yr: a {arr—H: g0 lg fL' Vb)“ : UCL "" —(.qp§L 7' *fifl.9~ylgi'3y/§A V :(S‘V—ovqfidw Bgoc ‘1 IS’V -' SF.qu 1. filoufi Rb = (’0 K/k. Vo,dc= q '0 A Vw. W M; W” {wotecvoéfl‘fi 1* (LU. 9 (b) (15 points) Draw the small-signal (AC) model for the circuit. Calculate r“ for this part of the circuit. Find the AC gain, Av = Vo,ach,ac for this circuit. (Suggestion: Solve for the gain symbolically as a function of the components and parameters in the small signal circuit first, then plug in values at the end.) (Ms mt: W" chiCrJlr mitt SIMS? CI/Lmfl Fm {pg 5‘”.ka S’LMJPK meta \ ’10 ‘11 Problem 4 (20 points total) Signal Processing. Assume we have a signal m(t) containing some voice or music. The spectrum (frequency content) of m(t), the fimction M(f), looks like a triangle with maximum value A at DC and maximum frequency fm as we represented it in class: a) (5 points). Recall the modulation system below that we discussed for AM transmission: m(t) x(t) (modulatcdi’transmitted signal) c(t) = cos(e)ct) lfthe frequency of c(t) is (so = 27t* l 00 kHz, sketch X(f) for the MG) we have above if the frequency fm = lOkHz. Use the axes below (you must label them to get full credit). XU) Al. -' /\ i / "WWI JIM“ +614“ '. Him-us f flaw“; ID-‘v't'shc b) (5 points). Suppose we use the modulation system below that we discussed for commercial AM transmission: m(t) Mg—p x(t) (modulatedftransmitted signal) 1 c(t) = cos(mct) For the same m(t) and c(t) from part a), sketch X(f). Use the axes below (you must label them to get full credit). (The triangle is the flow diagram symbol for a simple amplifying/attenuating function.) X09 12 c) (5 points) Sketch the diagram for a demodulating system for a receiver that would work for both schemes a) and b) above such that we could hear the original m(t) content. To WWW-3U )er mm owme Staging wwLO WWL MOB-V56? TIJF DC 6665's? Fm b) who MT fit "th16er‘ {:3 Xth Mic] astute) if? Tufts weld? A (mods aneurysm J we maven C‘iMT GENO 9953 {AT-rm \th EHO ' Tu A Pita-Er» LemFrxtO PT gem with fiv’ cloklpci d) (5 points) Suggest an alternative demodulation system for the scheme in part b) that would allow us to (inexpensively) recover something close to m(t). Fat lo) v)? u») VSE W‘ S'TPPLE' (LCL‘T'EPEEN [Ari-O be)?” gifitw Swmti f\ XLE) W“ EL, CU“ ‘T'a $1.1"qu Pépu-S bf- an: (new WWW CENT 1p NELFISMVI- ...
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test 2 solutions - Carnegie Mellon University Department of...

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